Pith. sign in

REVIEW 1 major objections 6 minor 2 cited by

Multi-objective Deep Learning: Taxonomy and Survey of the State of the Art

T0 review · 1 major / 6 minor · reviewed 2026-08-12 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read This survey argues that every multi-objective deep learning method can be classified by when the decision maker chooses a trade-off—before, after, or during optimization—and by whether it uses scalarization, multiple-gradient descent…

desk verdict A useful map of multi-objective deep learning with a real but fixable seam in the taxonomy around adaptive weighting. read the letter →

arxiv 2412.01566 v2 pith:ULF3D2QZ submitted 2024-12-02 cs.LG math.OC

Sebastian Peitz , Sedjro Salomon Hotegni This is my paper · ORCID
classification cs.LGmath.OC
keywords multi-objectiveoptimizationdeeplearningtaxonomyParetofrontmulti-taskreinforcementscalarizationmultiple-gradientdescentalgorithm
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper is a survey whose main contribution is a taxonomy of multi-objective deep learning methods. It organizes the field by two questions: when the decision maker chooses a trade-off, and which optimization strategy is used. The authors argue that nearly all current work falls into decide-then-optimize or optimize-then-decide, with only scalarization, multiple-gradient descent, evolutionary algorithms, and continuation as the relevant method families. They also claim that interactive multi-objective deep learning, where a human steers training by preferences, has not yet been explored. A sympathetic reader should care because this map makes a rapidly growing and fragmented literature navigable, and it identifies a concrete open research gap.

What carries the argument

The load-bearing object is the taxonomy itself, presented in Figure 6 as a tree whose top decisions are decision timing and algorithm family, with dashed ellipses for hybrid extensions. It is backed by the Karush-Kuhn-Tucker condition $\sum_{k=1}^K \alpha_k^* \nabla L_k(\theta^*) = 0$, which defines Pareto-critical points and is the shared basis for MGDA and continuation methods. The taxonomy does the work of the paper: it partitions recent methods from supervised, unsupervised, generative, and reinforcement learning, reveals that MGDA is the practical workhorse for deep learning because it reuses standard gradient machinery, and makes the absence of interactive methods visible as an empty branch.

What would settle it

Find one published deep learning training method where a human decision maker changes preferences during optimization and the optimizer responds by moving along the Pareto front; that would fill the empty interactive branch and contradict the survey's main gap claim. Alternatively, find a method class that fits none of the two decision-timing branches and none of the four algorithm families, which would break the taxonomy's coverage.

Watch

Extended reading notes

Core claim

The central claim is taxonomic: the state of the art in multi-objective deep learning can be organized by a two-level classification. The top level asks whether the decision maker chooses a trade-off before optimization, after optimization, or interactively during optimization. The second level asks which algorithmic family is used: scalarization, multiple-gradient descent algorithms (MGDAs), multi-objective evolutionary algorithms (MOEAs), or continuation methods. Under this taxonomy, the paper reports that the deep learning community has mostly chosen the decide-then-optimize branch, with MGDA as the dominant gradient-based tool, while optimize-then-decide methods split between MOEAs and weight-varying scalarization. The authors further claim that the interactive branch is empty: methods that alternate between optimization and a decision maker's preferences exist in classical multi-objective optimization but have not been transferred to deep learning training. They also observe that over-parameterization can collapse the Pareto front for some multi-task problems, so conflicts between objectives may vanish on very large networks.

Load-bearing premise

The taxonomy's completeness is the load-bearing premise: if a major method class is missing, or if the surveyed papers are significantly misclassified, the survey's map and its claimed open gap for interactive methods collapse.

Editorial extensions

If this is right

  • A researcher encountering a new multi-objective deep learning method can classify it by two questions, and the classification immediately indicates which optimization machinery is relevant.
  • Gradient-based approaches, especially MGDA, are the practical choice for deep multi-objective training, while evolutionary algorithms remain mainly useful for architecture search and hybrid settings rather than direct network training.
  • The interactive branch is a concrete research gap: no published method currently lets a decision maker steer deep learning training by expressing preferences among objectives during optimization.
  • Because over-parameterized networks can resolve objective conflicts, multi-task deep learning on very large shared networks may not require full Pareto-front machinery.
  • Reinforcement learning is a special case of the taxonomy: single-policy algorithms correspond to decide-then-optimize, and multiple-policy algorithms correspond to optimize-then-decide, with the population being value functions rather than policies.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • An immediate testable next step would be to couple a preference-elicitation loop with continuation methods or MGDAs, giving a decision maker control over the output of deep multi-objective training while keeping gradient efficiency.
  • The over-parameterization observation implies that benchmark selection matters: on sufficiently large shared-parameter networks, multi-task objectives may not conflict, so studies of multi-objective deep learning should report network scale and verify that the Pareto front does not collapse.
  • The taxonomy's decision-timing axis could be extended to large language model alignment, where multiple reward models or judges are already combined by weighted sums; interactive preference steering during fine-tuning would fill the empty branch in a commercially relevant setting.
  • A deep learning benchmark with a known non-convex Pareto front would be valuable because the paper notes that no such benchmark currently exists, and it would separate scalarization methods that fail on non-convex frontiers from MGDA and other approaches that handle them.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

1 major / 6 minor

Summary. This manuscript presents a survey of multi-objective deep learning (MODL). Its central contribution is a taxonomy in Section III-A (Figure 6) that classifies methods by decision timing (decide-then-optimize, optimize-then-decide, interactive) and by algorithmic family (scalarization, MGDA, MOEA, continuation). The survey then reviews supervised, unsupervised/self-supervised, generative, and reinforcement learning settings, as well as neural architecture search and applications, and closes with a section on using deep learning for multi-objective optimization. The mathematical preliminaries (KKT conditions, Pareto critical sets, common descent directions, scalarization, continuation) are stated correctly, and the individual method descriptions are consistent with the cited literature in the spot-checks performed.

Significance. If the taxonomy is accepted as complete, the paper provides a useful organizing framework for a rapidly growing field, with broad coverage and technically sound preliminaries. The explicit algorithms for MGDA, MOEA, and continuation make the review self-contained, and the treatment of reinforcement learning as a special case is a reasonable structural choice. The survey's value hinges on the exhaustiveness of its taxonomy, which is stated as its main contribution; therefore, the omission of a method class that the survey itself treats as distinct weakens the central claim. This is fixable through a targeted revision rather than a fundamental rework.

major comments (1)
  1. [IV-B2 and Figure 6] The taxonomy in Figure 6 has no category that accommodates the 'adaptive weighting' class defined in Section IV-B2, creating an internal inconsistency in the survey's organizing contribution. In Section IV-B2 the authors write that adaptive weighting is 'unlike scalarization' and describe methods (e.g., [121], [149]) that dynamically adjust objective weights during training, do not compute an entire Pareto front, and are not interactive. These methods fit none of the three top-level branches or four algorithm families shown in Figure 6 without contradicting the text: they are not fixed-weight scalarization, not MGDA, not MOEA, not continuation, and not optimize-then-decide. The inconsistency is compounded by Section IV-A2, where FAMO [104] is described as a weighted sum with a dynamic weighting strategy, i.e., adaptive weighting is treated as a form of scalarization there. The authors should either subsume adaptive weighting under scalarization (and revise the 'Unlike scalarization' sentence and the placement of [104]) or add adaptive weighting explicitly to Figure 6 and discuss it in Section III-A; without this fix, the taxonomy cannot claim to organize the state of the art.
minor comments (6)
  1. [Algorithm 2] In the line 'the pupulation's fitness' and in the Algorithm 2 comment 'pupulation', 'pupulation' should be 'population'.
  2. [IV-A2] The word 'scalarizaiton' in the sentence 'A so-called conic scalarizaiton techinque' should be 'scalarization technique'.
  3. [IV-A3] The phrase 'realistic deep leraning applications' contains a typo; 'leraning' should be 'learning'.
  4. [IV-E] In the introductory sentence, 'multi-objetive deep learning' should be 'multi-objective deep learning'.
  5. [Remark 3] The phrase 'see also the survey [11] for for an extensive introduction' contains a duplicated 'for' and should be corrected.
  6. [IV-E2] In 'multi-task learning was used for for phoneme detection', the word 'for' is duplicated.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the taxonomy is a classification of the literature, not a derivation whose conclusions reduce to its inputs.

full rationale

The paper is a survey whose central contribution, the taxonomy in Section III-A and Figure 6, is a classification scheme built on the classical decision-timing trichotomy in multi-objective optimization (decide-then-optimize, optimize-then-decide, interactive) and on the algorithm families introduced in Section II-B3 (scalarization, MGDA, MOEA, continuation). No parameter is fitted, no quantity is predicted from data, and no theorem is derived whose conclusion is equivalent by construction to an input. The survey's claims about the state of the art rest on citations to external MOO and deep-learning literature, not on a self-citation chain. The authors' own prior works (e.g., references [3], [8], [18], [57], [74], [75], [136], [167], [168]) are cited for context or specific technical contributions, but none of these citations is invoked as a uniqueness theorem or as the sole justification for the taxonomy's structure. The reader's concern that the 'adaptive weighting' category in Section IV-B2 is not cleanly accommodated by Figure 6 is an internal coverage or consistency risk of the survey's completeness claim, not a circularity: it concerns whether the taxonomy exhaustively classifies the surveyed literature, not whether a result reduces to its own assumptions. Similarly, the paper's acknowledgements that interactive methods are unexplored and that benchmark problems are lacking are honest limitations rather than circular moves. Overall, the derivation chain, such as it is for a survey, is self-contained and the taxonomy has independent organizing content, so the circularity score is 0.

Assumptions & free parameters 0 free parameters · 2 assumptions · 0 invented entities

The survey makes no quantitative predictions and fits no parameters. Its only load-bearing structure is the taxonomy itself, which rests on the assumption that the chosen categories cover the literature.

assumptions (2)
  • domain assumption The taxonomy's two top-level branches (decision before or after optimization) and four algorithm families (scalarization, MGDA, MOEA, continuation) cover all relevant multi-objective deep learning methods.
    Underlies the survey's completeness claim; if a method class is missing, the survey's gap analysis is incomplete. Introduced in Section III-A and Figure 6.
  • standard math Standard Karush-Kuhn-Tucker conditions and the Pareto critical set definition apply to deep neural network losses, ignoring non-smoothness except where noted in Remark 2.
    Used in Section II-B2; standard, but deep learning losses are often non-smooth, and the survey only briefly addresses this.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Multi-objective Deep Learning: Taxonomy and Survey of the State of the Art." pith.science (2026). https://pith.science/paper/ULF3D2QZ

@misc{pith2026241201566,
  author       = {Pith},
  title        = {Pith review of: Multi-objective Deep Learning: Taxonomy and Survey of the State of the Art},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/ULF3D2QZ}},
  note         = {Machine review of arXiv:2412.01566}
}
read the original abstract

Simultaneously considering multiple objectives in machine learning has been a popular approach for several decades, with various benefits for multi-task learning, the consideration of secondary goals such as sparsity, or multicriteria hyperparameter tuning. However - as multi-objective optimization is significantly more costly than single-objective optimization - the recent focus on deep learning architectures poses considerable additional challenges due to the very large number of parameters, strong nonlinearities and stochasticity. This survey covers recent advancements in the area of multi-objective deep learning. We introduce a taxonomy of existing methods - based on the type of training algorithm as well as the decision maker's needs - before listing recent advancements, and also successful applications. All three main learning paradigms supervised learning, unsupervised learning and reinforcement learning are covered, and we also address the recently very popular area of generative modeling.

Figures

Figures reproduced from arXiv: 2412.01566 by the authors.

Figure 1
Figure 1. Left: Example of a convex Pareto front, where each point has a () [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. ℓ1 norm and ReLU activation function for θ ∈ R. 3) Overview of methods: There exists a large number of conceptually very different methods to find (approximate) solutions of (MOP). The first key question is—and this will come up again in our taxonomy—whether we put the decision￾making1 before (II-B3a) or after (II-B3b) optimization, or even consider an interactive approach (II-B3c). a) Computing individual Pareto op… view at source ↗
Figure 4
Figure 4. MOEA example, where a population of individuals is improved [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
Figures from the paper (4 more)
Figure 5
Figure 5. Figure 5: Continuation algorithms use predictor steps [PITH_FULL_IMAGE:figures/full_fig_p006_5.png]
Figure 6
Figure 6. Figure 6: Taxonomy of methods. The squares denote design decisions, the ellipses denote classes of algorithms. Dashed ellipses refer to extensions building [PITH_FULL_IMAGE:figures/full_fig_p008_6.png]
Figure 7
Figure 7. Figure 7: Pareto multi-task learning, where a population of points is optimized [PITH_FULL_IMAGE:figures/full_fig_p008_7.png]
Figure 8
Figure 8. Figure 8: Modification of the right branch of Figure [PITH_FULL_IMAGE:figures/full_fig_p011_8.png]

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Gradient-Based Multi-Objective Deep Learning: Algorithms, Theories, Applications, and Beyond

    cs.LG 2025-01 conditional novelty 4.0 of 10

    A comprehensive survey categorizes gradient-based multi-objective deep learning by output type, with theory, applications, datasets, libraries, and open challenges.

  2. Surrogate-assisted multi-objective design of complex multibody systems

    math.OC 2024-12 conditional novelty 4.0 of 10

    Iterative surrogate-assisted multi-objective optimization with NSGA-II and neural network surrogates is tested on a 24-parameter car suspension design problem, reporting faster Pareto front approximation.

Reference graph

Works this paper leans on

211 extracted references · 52 canonical work pages · cited by 2 Pith papers

  1. [121]

    Multi-objective optimization for self-adjusting weighted gradient in machine learning tasks,

    C. S. Miranda and F. J. V on Zuben, “Multi-objective optimization for self-adjusting weighted gradient in machine learning tasks,” arXiv preprint arXiv:1506.01113, 2015

    arXiv 2015

  2. [149]

    Weighted Ensemble Self-Supervised Learning

    Y . Ruan, S. Singh, W. Morningstar, A. A. Alemi, S. Ioffe, I. Fischer, and J. V . Dillon, “Weighted ensemble self-supervised learning,” arXiv preprint arXiv:2211.09981, 2022

    work page Pith review arXiv 2022

  3. [104]

    FAMO: Fast adaptive multitask optimization,

    B. Liu, Y . Feng, P. Stone, and Q. Liu, “FAMO: Fast adaptive multitask optimization,” Advances in Neural Information Processing Systems , vol. 36, 2024

    2024

  4. [1]

    Dynamic weights in multi-objective deep reinforcement learning,

    A. Abels, D. Roijers, T. Lenaerts, A. Now ´e, and D. Steckelmacher, “Dynamic weights in multi-objective deep reinforcement learning,” in Proceedings of the 36th International Conference on Machine Learn- ing, ser. Proceedings of Machine Learning Research, K. Chaudhuri and R. Salakhutdinov, Eds., vol. 97. PMLR, 09–15 Jun 2019, pp. 11–20

    2019

  5. [2]

    Multi-objective reinforcement learning with non-linear scalarization,

    M. Agarwal, V . Aggarwal, and T. Lan, “Multi-objective reinforcement learning with non-linear scalarization,” in Proceedings of the 21st Inter- national Conference on Autonomous Agents and Multiagent Systems , 2022, pp. 9–17

    2022

  6. [3]

    Common pitfalls to avoid while using multiobjective optimization in machine learning

    J. Akhter, P. D. F ¨ahrmann, K. Sonntag, and S. Peitz, “Common pitfalls to avoid while using multiobjective optimization in machine learning,” arXiv:2405.01480, 2024

    work page Pith review arXiv 2024

  7. [4]

    Multi-objective unsupervised feature selection and cluster based on symbiotic organism search,

    A. F. J. AL-Gburi, M. Z. A. Nazri, M. R. B. Yaakub, and Z. A. A. Alyasseri, “Multi-objective unsupervised feature selection and cluster based on symbiotic organism search,” Algorithms, vol. 17, no. 8, p. 355, 2024

    2024

  8. [5]

    Multi-objective training of generative adversarial net- works with multiple discriminators,

    I. Albuquerque, J. Monteiro, T. Doan, B. Considine, T. Falk, and I. Mitliagkas, “Multi-objective training of generative adversarial net- works with multiple discriminators,” in Proceedings of the 36th In- ternational Conference on Machine Learning , ser. Proceedings of Machine Learning Research, K. Chaudhuri and R. Salakhutdinov, Eds., vol. 97. PMLR, 2019...

    2019

Show all 211 references
  1. [6]

    S.-A. N. Alexandropoulos, C. K. Aridas, S. B. Kotsiantis, and M. N. Vrahatis, Multi-Objective Evolutionary Optimization Algorithms for Machine Learning: A Recent Survey . Cham: Springer International Publishing, 2019, pp. 35–55

    2019

  2. [7]

    A new semi-supervised clustering technique using multi-objective optimization,

    A. K. Alok, S. Saha, and A. Ekbal, “A new semi-supervised clustering technique using multi-objective optimization,” Applied Intelligence , vol. 43, pp. 633–661, 2015

    2015

  3. [8]

    A multiobjective continuation method to compute the regularization path of deep neural networks,

    A. C. Amakor, S. Peitz, and K. Sonntag, “A multiobjective continuation method to compute the regularization path of deep neural networks,” arXiv:2308.12044, 2023

    2023 arXiv

  4. [9]

    Hypervolume-based multiobjective optimization: Theoretical foundations and practical im- plications,

    A. Auger, J. Bader, D. Brockhoff, and E. Zitzler, “Hypervolume-based multiobjective optimization: Theoretical foundations and practical im- plications,” Theoretical Computer Science, vol. 425, pp. 75–103, 2012, theoretical Foundations of Evolutionary Computation

    2012

  5. [10]

    SVM classification for imbalanced data sets using a multiobjective optimization framework,

    A. As ¸kan and S. Sayın, “SVM classification for imbalanced data sets using a multiobjective optimization framework,” Annals of Operations Research, vol. 216, no. 1, p. 191–203, Jan. 2013

    2013

  6. [11]

    Hype: An algorithm for fast hypervolume- based many-objective optimization,

    J. Bader and E. Zitzler, “Hype: An algorithm for fast hypervolume- based many-objective optimization,” Evolutionary Computation , vol. 19, no. 1, pp. 45–76, 2011

    2011

  7. [12]

    Evolutionary multi-objective optimization of large language model prompts for balancing sentiments,

    J. Baumann and O. Kramer, “Evolutionary multi-objective optimization of large language model prompts for balancing sentiments,” in Inter- national Conference on the Applications of Evolutionary Computation (Part of EvoStar). Springer, 2024, pp. 212–224

    2024

  8. [13]

    The explicit linear quadratic regulator for constrained systems,

    A. Bemporad, M. Morari, V . Dua, and E. N. Pistikopoulos, “The explicit linear quadratic regulator for constrained systems,”Automatica, vol. 38, no. 1, pp. 3–20, 2002

    2002

  9. [14]

    Autoen- coders and their applications in machine learning: a survey,

    K. Berahmand, F. Daneshfar, E. S. Salehi, Y . Li, and Y . Xu, “Autoen- coders and their applications in machine learning: a survey,” Artificial Intelligence Review, vol. 57, no. 2, p. 28, 2024

    2024

  10. [15]

    Derivative-free multiobjective trust region descent method using radial basis function surrogate models,

    M. Berkemeier and S. Peitz, “Derivative-free multiobjective trust region descent method using radial basis function surrogate models,” Mathematical and Computational Applications , vol. 26, no. 2, 2021

    2021

  11. [16]

    Bertsekas, Reinforcement learning and optimal control

    D. Bertsekas, Reinforcement learning and optimal control . Athena Scientific, 2019, vol. 1

    2019

  12. [17]

    DeepSI: Interactive deep learning for semantic interaction,

    Y . Bian and C. North, “DeepSI: Interactive deep learning for semantic interaction,” in Proceedings of the 26th International Conference on Intelligent User Interfaces , ser. IUI ’21. New York, NY , USA: Association for Computing Machinery, 2021, p. 197–207

    2021

  13. [18]

    On the Treatment of Optimization Problems with L1 Penalty Terms via Multiobjective Continuation,

    K. Bieker, B. Gebken, and S. Peitz, “On the Treatment of Optimization Problems with L1 Penalty Terms via Multiobjective Continuation,” IEEE Transactions on Pattern Analysis and Machine Intelligence , vol. 44, no. 11, pp. 7797–7808, 2022

    2022

  14. [19]

    C. M. Bishop, Pattern Recognition and Machine Learning, 1st ed., ser. Information Science and Statistics. Springer, 2006

    2006

  15. [20]

    C. M. Bishop and H. Bishop, Deep Learning: Foundations and Concepts. Springer International Publishing, 2024

    2024

  16. [21]

    On gradients and hybrid evolutionary algorithms for real-valued multiobjective optimization,

    P. A. N. Bosman, “On gradients and hybrid evolutionary algorithms for real-valued multiobjective optimization,” IEEE Transactions on Evolutionary Computation, vol. 16, no. 1, pp. 51–69, 2012

    2012

  17. [22]

    Enhancing multi-objective optimisation through machine learning-supported multiphysics simulation,

    D. Botache, J. Decke, W. Ripken, A. Dornipati, F. G ¨otz-Hahn, M. Ayeb, and B. Sick, “Enhancing multi-objective optimisation through machine learning-supported multiphysics simulation,” in Machine Learning and Knowledge Discovery in Databases. Applied Data Science Track , A. B...

    2024

  18. [23]

    A survey on active learning and human-in-the-loop deep learning for medical image analysis,

    S. Budd, E. C. Robinson, and B. Kainz, “A survey on active learning and human-in-the-loop deep learning for medical image analysis,” Medical Image Analysis , vol. 71, p. 102062, 2021

    2021

  19. [24]

    MoMAC: Multi-objective optimization to combine multiple association rules into an interpretable classification,

    D. Bui-Thi, P. Meysman, and K. Laukens, “MoMAC: Multi-objective optimization to combine multiple association rules into an interpretable classification,” Applied Intelligence , vol. 52, no. 3, pp. 3090–3102, 2022

    2022

  20. [25]

    A Bregman learning framework for sparse neural networks,

    L. Bungert, T. Roith, D. Tenbrinck, and M. Burger, “A Bregman learning framework for sparse neural networks,” Journal of Machine Learning Research, vol. 23, no. 192, pp. 1–43, 2022

    2022

  21. [26]

    Ad-dmkde: Anomaly detection through density matrices and fourier features,

    O. A. Bustos-Brinez, J. A. Gallego-Mejia, and F. A. Gonz ´alez, “Ad-dmkde: Anomaly detection through density matrices and fourier features,” in International Conference on Information Technology & Systems. Springer, 2023, pp. 327–338. 14

    2023

  22. [27]

    Deep clustering for unsupervised learning of visual features,

    M. Caron, P. Bojanowski, A. Joulin, and M. Douze, “Deep clustering for unsupervised learning of visual features,” in Proceedings of the European conference on computer vision (ECCV) , 2018, pp. 132–149

    2018

  23. [28]

    EMORL: Effective multi-objective reinforcement learning method for hyperparameter optimization,

    S. Chen, J. Wu, and X. Liu, “EMORL: Effective multi-objective reinforcement learning method for hyperparameter optimization,” En- gineering Applications of Artificial Intelligence , vol. 104, p. 104315, 2021

    2021

  24. [29]

    Semi-supervised and unsupervised deep visual learning: A survey,

    Y . Chen, M. Mancini, X. Zhu, and Z. Akata, “Semi-supervised and unsupervised deep visual learning: A survey,” IEEE transactions on pattern analysis and machine intelligence , vol. 46, no. 3, pp. 1327– 1347, 2022

    2022

  25. [30]

    A tutorial on kernel density estimation and recent ad- vances,

    Y .-C. Chen, “A tutorial on kernel density estimation and recent ad- vances,” Biostatistics & Epidemiology, vol. 1, no. 1, pp. 161–187, 2017

    2017

  26. [31]

    Pareto self- supervised training for few-shot learning,

    Z. Chen, J. Ge, H. Zhan, S. Huang, and D. Wang, “Pareto self- supervised training for few-shot learning,” in Proceedings of the IEEE/CVF conference on computer vision and pattern recognition , 2021, pp. 13 663–13 672

    2021

  27. [32]

    Handling computationally expensive multiobjective optimization problems with evolutionary algorithms-a survey,

    T. Chugh, K. Sindhya, J. Hakanen, and K. Miettinen, “Handling computationally expensive multiobjective optimization problems with evolutionary algorithms-a survey,” Reports of the Department of Math- ematical Information Technology, Series B, Scientific Computing no. B, vol. 4...

    2015

  28. [33]

    F. H. Clarke, Optimization and nonsmooth analysis . SIAM, 1990

    1990

  29. [34]

    C. A. Coello Coello, G. B. Lamont, and D. A. Van Veldhuizen, Evolutionary Algorithms for Solving Multi-Objective Problems, 2nd ed. Springer, 2007

    2007

  30. [35]

    A fast and elitist multiobjective genetic algorithm: NSGA-II,

    K. Deb, A. Pratap, S. Agarwal, and T. Meyarivan, “A fast and elitist multiobjective genetic algorithm: NSGA-II,” IEEE Transactions on Evolutionary Computation, vol. 6, no. 2, p. 182–197, 2002

    2002

  31. [36]

    Surrogate modeling approaches for multiobjective optimization: Methods, taxonomy, and results,

    K. Deb, P. C. Roy, and R. Hussein, “Surrogate modeling approaches for multiobjective optimization: Methods, taxonomy, and results,” Mathe- matical and Computational Applications , vol. 26, no. 1, 2021

    2021

  32. [37]

    Magnetic control of tokamak plasmas through deep reinforcement learning,

    J. Degrave, F. Felici, J. Buchli, M. Neunert, B. Tracey, F. Carpanese, T. Ewalds, R. Hafner, A. Abdolmaleki, D. de Las Casas et al. , “Magnetic control of tokamak plasmas through deep reinforcement learning,” Nature, vol. 602, no. 7897, pp. 414–419, 2022

    2022

  33. [38]

    Covering pareto sets by multilevel subdivision techniques,

    M. Dellnitz, O. Sch ¨utze, and T. Hestermeyer, “Covering pareto sets by multilevel subdivision techniques,” Journal of Optimization Theory and Applications, vol. 124, no. 1, p. 113–136, 2005

    2005

  34. [39]

    Static video summarization with multi-objective constrained optimization,

    M. Dhanushree, R. Priya, P. Aruna, and R. Bhavani, “Static video summarization with multi-objective constrained optimization,” Journal of Ambient Intelligence and Humanized Computing , vol. 15, no. 4, pp. 2621–2639, 2024

    2024

  35. [40]

    Survey on unsupervised learning methods for optical flow estimation,

    T. Dobri ˇcki, X. Zhuang, K. J. Won, and B.-W. Hong, “Survey on unsupervised learning methods for optical flow estimation,” in 2022 13th International Conference on Information and Communication Technology Convergence (ICTC), 2022

    2022

  36. [41]

    Generative multi-adversarial networks,

    I. Durugkar, I. Gemp, and S. Mahadevan, “Generative multi-adversarial networks,” in International Conference on Learning Representations , 2017

    2017

  37. [42]

    Multiple-gradient descent algorithm (MGDA) for mul- tiobjective optimization,

    J.-A. D ´esid´eri, “Multiple-gradient descent algorithm (MGDA) for mul- tiobjective optimization,”Comptes Rendus. Math´ematique, vol. 350, no. 5–6, p. 313–318, Mar. 2012

    2012

  38. [43]

    Ehrgott, Multicriteria optimization, 2nd ed

    M. Ehrgott, Multicriteria optimization, 2nd ed. Springer, 2005

    2005

  39. [44]

    An adaptive scalarization method in multiobjective optimization,

    G. Eichfelder, “An adaptive scalarization method in multiobjective optimization,” SIAM Journal on Optimization, vol. 19, no. 4, pp. 1694– 1718, 2009

    2009

  40. [45]

    Efficient multi-objective neural architecture search via Lamarckian evolution,

    T. Elsken, J. H. Metzen, and F. Hutter, “Efficient multi-objective neural architecture search via Lamarckian evolution,” in International Conference on Learning Representations , 2019

    2019

  41. [46]

    Neural architecture search: A survey,

    ——, “Neural architecture search: A survey,” Journal of Machine Learning Research, vol. 20, no. 55, pp. 1–21, 2019

    2019

  42. [47]

    Pareto navigator for interactive nonlinear multiobjective optimization,

    P. Eskelinen, K. Miettinen, K. Klamroth, and J. Hakanen, “Pareto navigator for interactive nonlinear multiobjective optimization,” OR Spectrum, vol. 32, no. 1, pp. 211–227, 2010

    2010

  43. [48]

    Multi-objective reinforcement learning based on decomposition: A taxonomy and framework,

    F. Felten, E.-G. Talbi, and G. Danoy, “Multi-objective reinforcement learning based on decomposition: A taxonomy and framework,” Jour- nal of Artificial Intelligence Research , vol. 79, pp. 679–723, 2024

    2024

  44. [49]

    Multi-objective adversarial gesture generation,

    Y . Ferstl, M. Neff, and R. McDonnell, “Multi-objective adversarial gesture generation,” in Proceedings of the 12th ACM SIGGRAPH Conference on Motion, Interaction and Games , 2019

    2019

  45. [50]

    Newton’s method for multiobjective optimization,

    J. Fliege, L. M. Gra ˜na Drummond, and B. F. Svaiter, “Newton’s method for multiobjective optimization,” SIAM Journal on Optimiza- tion, vol. 20, no. 2, pp. 602–626, 2009

    2009

  46. [51]

    Steepest descent methods for multicriteria optimization,

    J. Fliege and B. F. Svaiter, “Steepest descent methods for multicriteria optimization,” Mathematical Methods of Operations Research , vol. 51, no. 3, pp. 479–494, 2000

    2000

  47. [52]

    A method for constrained multiobjective optimization based on sqp techniques,

    J. Fliege and A. I. F. Vaz, “A method for constrained multiobjective optimization based on sqp techniques,” SIAM Journal on Optimization, vol. 26, no. 4, pp. 2091–2119, 2016

    2016

  48. [53]

    An overview of evolutionary algorithms in multiobjective optimization,

    C. M. Fonseca and P. J. Fleming, “An overview of evolutionary algorithms in multiobjective optimization,” Evolutionary Computation, vol. 3, no. 1, pp. 1–16, 1995

    1995

  49. [54]

    DessiLBI: Exploring structural sparsity of deep networks via differential inclusion paths,

    Y . Fu, C. Liu, D. Li, X. Sun, J. Zeng, and Y . Yao, “DessiLBI: Exploring structural sparsity of deep networks via differential inclusion paths,” in Proceedings of the 37th International Conference on Machine Learning, vol. 119. PMLR, 2020, pp. 3315–3326

    2020

  50. [55]

    Exploring structural sparsity of deep networks via inverse scale spaces,

    Y . Fu, C. Liu, D. Li, Z. Zhong, X. Sun, J. Zeng, and Y . Yao, “Exploring structural sparsity of deep networks via inverse scale spaces,” IEEE Transactions on Pattern Analysis and Machine Intelligence , vol. 45, no. 2, pp. 1749–1765, 2023

    2023

  51. [56]

    Mpgan: Multi pareto generative adversarial network for the denoising and quantitative analysis of low-dose pet images of human brain,

    Y . Fu, S. Dong, Y . Huang, M. Niu, C. Ni, L. Yu, K. Shi, Z. Yao, and C. Zhuo, “Mpgan: Multi pareto generative adversarial network for the denoising and quantitative analysis of low-dose pet images of human brain,” Medical Image Analysis , vol. 98, p. 103306, 2024

    2024

  52. [57]

    An Efficient Descent Method for Locally Lip- schitz Multiobjective Optimization Problems,

    B. Gebken and S. Peitz, “An Efficient Descent Method for Locally Lip- schitz Multiobjective Optimization Problems,” Journal of Optimization Theory and Applications , vol. 188, pp. 696–723, 2021

    2021

  53. [58]

    A Descent Method for Equality and Inequality Constrained Multiobjective Optimization Problems,

    B. Gebken, S. Peitz, and M. Dellnitz, “A Descent Method for Equality and Inequality Constrained Multiobjective Optimization Problems,” in Numerical and Evolutionary Optimization – NEO 2017 , L. Trujillo, O. Sch ¨utze, Y . Maldonado, and P. Valle, Eds. Springer, Cham, 2019, pp. 29–61

    2017

  54. [59]

    On the hierarchical structure of Pareto critical sets,

    ——, “On the hierarchical structure of Pareto critical sets,” Journal of Global Optimization, vol. 73, no. 4, pp. 891–913, 2019

    2019

  55. [60]

    Unsupervised band selection based on evolutionary multiobjective optimization for hyperspectral images,

    M. Gong, M. Zhang, and Y . Yuan, “Unsupervised band selection based on evolutionary multiobjective optimization for hyperspectral images,” IEEE Transactions on Geoscience and Remote Sensing , vol. 54, no. 1, pp. 544–557, 2015

    2015

  56. [61]

    Improving constrained clustering via decomposition-based multiobjective optimization with memetic elitism,

    G. Gonz ´alez-Almagro, A. Rosales-P ´erez, J. Luengo, J.-R. Cano, and S. Garc´ıa, “Improving constrained clustering via decomposition-based multiobjective optimization with memetic elitism,” in Proceedings of the 2020 Genetic and Evolutionary Computation Conference, 2020, pp. 333–341

    2020

  57. [62]

    Goodfellow, Y

    I. Goodfellow, Y . Bengio, and A. Courville, Deep Learning . MIT Press, 2016

    2016

  58. [63]

    Generative adversarial nets,

    I. Goodfellow, J. Pouget-Abadie, M. Mirza, B. Xu, D. Warde-Farley, S. Ozair, A. Courville, and Y . Bengio, “Generative adversarial nets,” in Advances in Neural Information Processing Systems , Z. Ghahramani, M. Welling, C. Cortes, N. Lawrence, and K. Weinberger, Eds., vol. 27....

    2014

  59. [64]

    A survey on self-supervised learning: Algorithms, applications, and future trends,

    J. Gui, T. Chen, J. Zhang, Q. Cao, Z. Sun, H. Luo, and D. Tao, “A survey on self-supervised learning: Algorithms, applications, and future trends,” arXiv preprint arXiv:2301.05712 , 2023

    2023 arXiv

  60. [65]

    Constructing multiple tasks for augmentation: Improving neural image classification with k-means features,

    T. Gui, L. Qing, Q. Zhang, J. Ye, H. Yan, Z. Fei, and X. Huang, “Constructing multiple tasks for augmentation: Improving neural image classification with k-means features,” arXiv:1911.07518, 2019

    1911 arXiv

  61. [66]

    Soft actor-critic: Off- policy maximum entropy deep reinforcement learning with a stochastic actor,

    T. Haarnoja, A. Zhou, P. Abbeel, and S. Levine, “Soft actor-critic: Off- policy maximum entropy deep reinforcement learning with a stochastic actor,” in International conference on machine learning. PMLR, 2018, pp. 1861–1870

    2018

  62. [67]

    Kill two birds with one stone: A multi-view multi-adversarial learning approach for joint air quality and weather prediction,

    J. Han, H. Liu, H. Zhu, and H. Xiong, “Kill two birds with one stone: A multi-view multi-adversarial learning approach for joint air quality and weather prediction,” IEEE Transactions on Knowledge and Data Engineering, vol. 35, no. 11, pp. 11 515–11 528, 2023

    2023

  63. [68]

    Feature subset selection in unsupervised learning via multiobjective optimization,

    J. Handl and J. Knowles, “Feature subset selection in unsupervised learning via multiobjective optimization,” International Journal of Computational Intelligence Research, vol. 2, no. 3, pp. 217–238, 2006

    2006

  64. [69]

    Hastie, R

    T. Hastie, R. Tibshirani, and J. Friedman, The Elements of Statistical Learning. Springer New York, 2009

    2009

  65. [70]

    A practical guide to multi- objective reinforcement learning and planning,

    C. F. Hayes, R. R ˘adulescu, E. Bargiacchi, J. K ¨allstr¨om, M. Macfarlane, M. Reymond, T. Verstraeten, L. M. Zintgraf, R. Dazeley, F. Heintz, E. Howley, A. A. Irissappane, P. Mannion, A. Now ´e, G. Ramos, M. Restelli, P. Vamplew, and D. M. Roijers, “A practical guide to multi...

    2022

  66. [71]

    Evolutionary multiobjective optimization driven by generative adversarial networks (gans),

    C. He, S. Huang, R. Cheng, K. C. Tan, and Y . Jin, “Evolutionary multiobjective optimization driven by generative adversarial networks (gans),” arXiv:1910.04966, 2019

    1910 arXiv

  67. [72]

    Masked autoencoders are scalable vision learners,

    K. He, X. Chen, S. Xie, Y . Li, P. Doll ´ar, and R. Girshick, “Masked autoencoders are scalable vision learners,” in Proceedings of the IEEE/CVF conference on computer vision and pattern recognition , 2022, pp. 16 000–16 009. 15

    2022

  68. [73]

    Hillermeier, Nonlinear Multiobjective Optimization: A Generalized Homotopy Approach

    C. Hillermeier, Nonlinear Multiobjective Optimization: A Generalized Homotopy Approach. Birkh ¨auser, 2001

    2001

  69. [74]

    Multi-objective optimiza- tion for sparse deep multi-task learning,

    S. S. Hotegni, M. Berkemeier, and S. Peitz, “Multi-objective optimiza- tion for sparse deep multi-task learning,” in 2024 International Joint Conference on Neural Networks (IJCNN) , 2024, pp. 1–9

    2024

  70. [75]

    MOREL: Enhancing adversarial robustness through multi-objective representation learning,

    S. S. Hotegni and S. Peitz, “MOREL: Enhancing adversarial robustness through multi-objective representation learning,” arXiv:2410.01697, 2024

    2024 arXiv

  71. [76]

    A generative Kriging surrogate model for constrained and unconstrained multi-objective optimization,

    R. Hussein and K. Deb, “A generative Kriging surrogate model for constrained and unconstrained multi-objective optimization,” in Proceedings of the Genetic and Evolutionary Computation Conference 2016, ser. GECCO ’16. New York, NY , USA: Association for Computing Machinery, 20...

    2016

  72. [77]

    Multi-objective GFlowNets,

    M. Jain, S. C. Raparthy, A. Hern ´andez-Garc´ıa, J. Rector-Brooks, Y . Bengio, S. Miret, and E. Bengio, “Multi-objective GFlowNets,” in Proceedings of the 40th International Conference on Machine Learning, ser. Proceedings of Machine Learning Research, A. Krause, E. Brunskill,...

    2023

  73. [78]

    Visual rep- resentation learning with stochastic frame prediction,

    H. Jang, D. Kim, J. Kim, J. Shin, P. Abbeel, and Y . Seo, “Visual rep- resentation learning with stochastic frame prediction,” arXiv preprint arXiv:2406.07398, 2024

    2024 arXiv

  74. [79]

    Feature dimensionality reduction: a review,

    W. Jia, M. Sun, J. Lian, and S. Hou, “Feature dimensionality reduction: a review,”Complex & Intelligent Systems, vol. 8, no. 3, pp. 2663–2693, 2022

    2022

  75. [80]

    Jin, Ed., Multi-Objective Machine Learning

    Y . Jin, Ed., Multi-Objective Machine Learning . Springer Berlin Heidelberg, 2006

    2006

  76. [81]

    Pareto-based multiobjective machine learning: An overview and case studies,

    Y . Jin and B. Sendhoff, “Pareto-based multiobjective machine learning: An overview and case studies,” IEEE Transactions on Systems, Man, and Cybernetics, Part C (Applications and Reviews) , vol. 38, no. 3, pp. 397–415, 2008

    2008

  77. [82]

    Evolutionary multi-objective opti- mization of spiking neural networks,

    Y . Jin, R. Wen, and B. Sendhoff, “Evolutionary multi-objective opti- mization of spiking neural networks,” in Artificial Neural Networks – ICANN 2007, J. M. de S ´a, L. A. Alexandre, W. Duch, and D. Mandic, Eds. Berlin, Heidelberg: Springer Berlin Heidelberg, 2007, pp. 370– 379

    2007

  78. [83]

    Self-supervised spatiotem- poral feature learning via video rotation prediction,

    L. Jing, X. Yang, J. Liu, and Y . Tian, “Self-supervised spatiotem- poral feature learning via video rotation prediction,” arXiv preprint arXiv:1811.11387, 2018

    2018 arXiv

  79. [84]

    Multi-objective hyperparameter optimization in machine learning—an overview,

    F. Karl, T. Pielok, J. Moosbauer, F. Pfisterer, S. Coors, M. Binder, L. Schneider, J. Thomas, J. Richter, M. Lang, E. C. Garrido-Merch ´an, J. Branke, and B. Bischl, “Multi-objective hyperparameter optimization in machine learning—an overview,”ACM Transactions on Evolutionary ...

    2023

  80. [85]

    Physics-informed machine learning,

    G. E. Karniadakis, I. G. Kevrekidis, L. Lu, P. Perdikaris, S. Wang, and L. Yang, “Physics-informed machine learning,” Nature Reviews Physics, vol. 3, no. 6, pp. 422–440, 2021

    2021

  81. [86]

    A conic scalarization method in multi-objective opti- mization,

    R. Kasimbeyli, “A conic scalarization method in multi-objective opti- mization,” Journal of Global Optimization , vol. 56, no. 2, p. 279–297, Sep. 2011

    2011

  82. [87]

    A survey of the self supervised learning mechanisms for vision transformers,

    A. Khan, A. Sohail, M. Fiaz, M. Hassan, T. H. Afridi, S. U. Marwat, F. Munir, S. Ali, H. Naseem, M. Z. Zaheer et al. , “A survey of the self supervised learning mechanisms for vision transformers,” arXiv preprint arXiv:2408.17059, 2024

    2024 arXiv

  83. [88]

    Scale-invariant gradient aggregation for constrained multi-objective reinforcement learning,

    D. Kim, M. Hong, J. Park, and S. Oh, “Scale-invariant gradient aggregation for constrained multi-objective reinforcement learning,” arXiv:2403.00282, 2024

    2024 arXiv

  84. [89]

    MDARTS: Multi-objective differentiable neural architecture search,

    S. Kim, H. Kwon, E. Kwon, Y . Choi, T.-H. Oh, and S. Kang, “MDARTS: Multi-objective differentiable neural architecture search,” in 2021 Design, Automation & Test in Europe Conference & Exhibition (DATE). IEEE, 2021, pp. 1344–1349

    2021

  85. [90]

    Adam: A method for stochastic optimization,

    D. P. Kingma and J. Ba, “Adam: A method for stochastic optimization,” arXiv:1412.6980, 2014

    2014 arXiv

  86. [91]

    Auto-encoding variational Bayes,

    D. P. Kingma and M. Welling, “Auto-encoding variational Bayes,” arXiv:1312.6114, 2013

    2013 arXiv

  87. [92]

    An introduction to variational autoencoders,

    D. P. Kingma, M. Welling et al. , “An introduction to variational autoencoders,” Foundations and Trends® in Machine Learning, vol. 12, no. 4, pp. 307–392, 2019

    2019

  88. [93]

    Reinforcement learning in robotics: A survey,

    J. Kober, J. A. Bagnell, and J. Peters, “Reinforcement learning in robotics: A survey,” The International Journal of Robotics Research , vol. 32, no. 11, pp. 1238–1274, 2013

    2013

  89. [94]

    Intensity-modulated radiotherapy - a large scale multi- criteria programming problem,

    K.-H. K ¨ufer, A. Scherrer, M. Monz, F. Alonso, H. Trinkaus, T. Bortfeld, and C. Thieke, “Intensity-modulated radiotherapy - a large scale multi- criteria programming problem,” OR Spectrum , vol. 25, no. 2, p. 223–249, May 2003

    2003

  90. [95]

    Contrastive self-supervised learning: review, progress, challenges and future research directions,

    P. Kumar, P. Rawat, and S. Chauhan, “Contrastive self-supervised learning: review, progress, challenges and future research directions,” International Journal of Multimedia Information Retrieval , vol. 11, no. 4, pp. 461–488, 2022

    2022

  91. [96]

    Deep learning,

    Y . LeCun, Y . Bengio, and G. Hinton, “Deep learning,” Nature, vol. 521, no. 7553, pp. 436–444, 2015

    2015

  92. [97]

    Lassonet: A neural network with feature sparsity,

    I. Lemhadri, F. Ruan, L. Abraham, and R. Tibshirani, “Lassonet: A neural network with feature sparsity,” Journal of Machine Learning Research, vol. 22, no. 127, pp. 1–29, 2021

    2021

  93. [98]

    It’s morphing time: Unleashing the potential of multiple llms via multi-objective optimization,

    B. Li, Z. Di, Y . Yang, H. Qian, P. Yang, H. Hao, K. Tang, and A. Zhou, “It’s morphing time: Unleashing the potential of multiple llms via multi-objective optimization,” arXiv:2407.00487, 2024

    2024 arXiv

  94. [99]

    Deep reinforcement learning for mul- tiobjective optimization,

    K. Li, T. Zhang, and R. Wang, “Deep reinforcement learning for mul- tiobjective optimization,” IEEE Transactions on Cybernetics , vol. 51, no. 6, pp. 3103–3114, 2021

    2021

  95. [100]

    Multi-augmentation contrastive learning as multi- objective optimization for graph neural networks,

    X. Li and Y . Chen, “Multi-augmentation contrastive learning as multi- objective optimization for graph neural networks,” in Pacific-Asia Conference on Knowledge Discovery and Data Mining . Springer, 2023, pp. 495–507

    2023

  96. [101]

    Neural manifold clustering and embedding,

    Z. Li, Y . Chen, Y . LeCun, and F. T. Sommer, “Neural manifold clustering and embedding,” arXiv preprint arXiv:2201.10000 , 2022

    2022 arXiv

  97. [102]

    Continuous control with deep reinforce- ment learning,

    T. P. Lillicrap, J. J. Hunt, A. Pritzel, N. Heess, T. Erez, Y . Tassa, D. Silver, and D. Wierstra, “Continuous control with deep reinforce- ment learning,” arXiv:1509.02971, 2015

    2015 arXiv

  98. [103]

    Pareto multi- task learning,

    X. Lin, H.-L. Zhen, Z. Li, Q.-F. Zhang, and S. Kwong, “Pareto multi- task learning,” in Advances in Neural Information Processing Systems , H. Wallach, H. Larochelle, A. Beygelzimer, F. d'Alch ´e-Buc, E. Fox, and R. Garnett, Eds., vol. 32. Curran Associates, Inc., 2019

    2019

  99. [105]

    Conflict-averse gradient descent for multi-task learning,

    B. Liu, X. Liu, X. Jin, P. Stone, and Q. Liu, “Conflict-averse gradient descent for multi-task learning,” Advances in Neural Information Processing Systems, vol. 34, pp. 18 878–18 890, 2021

    2021

  100. [106]

    Multiobjective reinforcement learning: A comprehensive overview,

    C. Liu, X. Xu, and D. Hu, “Multiobjective reinforcement learning: A comprehensive overview,” IEEE Transactions on Systems, Man, and Cybernetics: Systems, vol. 45, no. 3, pp. 385–398, 2015

    2015

  101. [107]

    Large language model for multi-objective evolutionary optimization,

    F. Liu, X. Lin, Z. Wang, S. Yao, X. Tong, M. Yuan, and Q. Zhang, “Large language model for multi-objective evolutionary optimization,” arXiv:2310.12541, 2023

    2023 arXiv

  102. [108]

    Structure learning for deep neural networks based on multiobjective optimization,

    J. Liu, M. Gong, Q. Miao, X. Wang, and H. Li, “Structure learning for deep neural networks based on multiobjective optimization,” IEEE transactions on neural networks and learning systems , vol. 29, no. 6, pp. 2450–2463, 2017

    2017

  103. [109]

    Stein variational gradient descent: A general pur- pose bayesian inference algorithm,

    Q. Liu and D. Wang, “Stein variational gradient descent: A general pur- pose bayesian inference algorithm,” in Advances in Neural Information Processing Systems, D. Lee, M. Sugiyama, U. Luxburg, I. Guyon, and R. Garnett, Eds., vol. 29. Curran Associates, Inc., 2016

    2016

  104. [110]

    The stochastic multi-gradient algorithm for multi-objective optimization and its application to supervised ma- chine learning,

    S. Liu and L. N. Vicente, “The stochastic multi-gradient algorithm for multi-objective optimization and its application to supervised ma- chine learning,” Annals of Operations Research , vol. 339, no. 3, p. 1119–1148, Mar. 2021

    2021

  105. [111]

    Self-supervised learning: Generative or contrastive,

    X. Liu, F. Zhang, Z. Hou, L. Mian, Z. Wang, J. Zhang, and J. Tang, “Self-supervised learning: Generative or contrastive,” IEEE transac- tions on knowledge and data engineering , vol. 35, no. 1, pp. 857–876, 2021

    2021

  106. [112]

    Profiling Pareto front with multi- objective stein variational gradient descent,

    X. Liu, X. Tong, and Q. Liu, “Profiling Pareto front with multi- objective stein variational gradient descent,” Advances in Neural In- formation Processing Systems , vol. 34, pp. 14 721–14 733, 2021

    2021

  107. [113]

    Multi-objective genetic algorithm for missing data imputation,

    F. Lobato, C. Sales, I. Araujo, V . Tadaiesky, L. Dias, L. Ramos, and A. Santana, “Multi-objective genetic algorithm for missing data imputation,” Pattern Recognition Letters, vol. 68, pp. 126–131, 2015

    2015

  108. [114]

    Multi-objective reinforcement learning: Convexity, stationarity and pareto optimality,

    H. Lu, D. Herman, and Y . Yu, “Multi-objective reinforcement learning: Convexity, stationarity and pareto optimality,” in The Eleventh Inter- national Conference on Learning Representations , 2023

    2023

  109. [115]

    Self-supervised multi-object tracking with path consistency,

    Z. Lu, B. Shuai, Y . Chen, Z. Xu, and D. Modolo, “Self-supervised multi-object tracking with path consistency,” in CVPR 2024, 2024

    2024

  110. [116]

    Efficient continuous pareto exploration in multi-task learning,

    P. Ma, T. Du, and W. Matusik, “Efficient continuous pareto exploration in multi-task learning,” in Proceedings of the 37th International Con- ference on Machine Learning , ser. Proceedings of Machine Learning Research, H. D. III and A. Singh, Eds., vol. 119. PMLR, 13–18 Jul 20...

    2020

  111. [117]

    An introduction to autoencoders,

    U. Michelucci, “An introduction to autoencoders,” arXiv preprint arXiv:2201.03898, 2022

    2022 arXiv

  112. [118]

    Information preserving multi-objective feature selection for unsupervised learning,

    I. Mierswa and M. Wurst, “Information preserving multi-objective feature selection for unsupervised learning,” in Proceedings of the 8th annual conference on Genetic and evolutionary computation, 2006, pp. 1545–1552. 16

    2006

  113. [119]

    Interactive bundle-based method for nondifferentiable multiobjeective optimization: NIMBUS,

    K. Miettinen and M. M ¨akel¨a, “Interactive bundle-based method for nondifferentiable multiobjeective optimization: NIMBUS,” Optimiza- tion, vol. 34, no. 3, pp. 231–246, 1995

    1995

  114. [120]

    Miettinen, Nonlinear Multiobjective Optimization

    K. Miettinen, Nonlinear Multiobjective Optimization . Springer US, 1998

    1998

  115. [122]

    A unified multi-view clustering algorithm using multi-objective optimization coupled with generative model,

    S. Mitra, M. Hasanuzzaman, and S. Saha, “A unified multi-view clustering algorithm using multi-objective optimization coupled with generative model,” ACM Transactions on Knowledge Discovery from Data (TKDD), vol. 14, no. 1, pp. 1–31, 2020

    2020

  116. [123]

    Momentum-based gradient methods in multi-objective recommendation,

    B. Mitrevski, M. Filipovic, D. Antognini, E. L. Glaude, B. Faltings, and C. Musat, “Momentum-based gradient methods in multi-objective recommendation,” arXiv:2009.04695, 2020

    2009 arXiv

  117. [124]

    Human-level control through deep reinforcement learning,

    V . Mnih, K. Kavukcuoglu, D. Silver, A. A. Rusu, J. Veness, M. G. Bellemare, A. Graves, M. Riedmiller, A. K. Fidjeland, G. Ostrovski, S. Petersen, C. Beattie, A. Sadik, I. Antonoglou, H. King, D. Kumaran, D. Wierstra, S. Legg, and D. Hassabis, “Human-level control through deep...

    2015

  118. [125]

    A survey on multi-objective hyperparameter optimization algorithms for machine learning,

    A. Morales-Hern ´andez, I. Van Nieuwenhuyse, and S. Rojas Gonzalez, “A survey on multi-objective hyperparameter optimization algorithms for machine learning,” Artificial Intelligence Review , vol. 56, no. 8, p. 8043–8093, Dec. 2022

    2022

  119. [126]

    Human-in-the-loop machine learn- ing: a state of the art,

    E. Mosqueira-Rey, E. Hernandez-Pereira, D. Alonso-Rios, J. Bobes- Bascaran, and A. Fernandez-Leal, “Human-in-the-loop machine learn- ing: a state of the art,” Artificial Intelligence Review, vol. 56, no. 4, p. 3005–3054, 2022

    2022

  120. [127]

    Multi- objective deep reinforcement learning,

    H. Mossalam, Y . M. Assael, D. M. Roijers, and S. Whiteson, “Multi- objective deep reinforcement learning,” arXiv:1610.02707, 2016

    2016 arXiv

  121. [128]

    Anomaly detection with density estimation,

    B. Nachman and D. Shih, “Anomaly detection with density estimation,” Physical Review D , vol. 101, no. 7, p. 075042, 2020

    2020

  122. [129]

    Multi-task learning as a bargaining game,

    A. Navon, A. Shamsian, I. Achituve, H. Maron, K. Kawaguchi, G. Chechik, and E. Fetaya, “Multi-task learning as a bargaining game,” arXiv:2202.01017, 2022

    2022 arXiv

  123. [130]

    The role of over-parametrization in generalization of neural networks,

    B. Neyshabur, Z. Li, S. Bhojanapalli, Y . LeCun, and N. Srebro, “The role of over-parametrization in generalization of neural networks,” in International Conference on Learning Representations , 2019

    2019

  124. [131]

    A multi-objective deep reinforcement learning frame- work,

    T. T. Nguyen, N. D. Nguyen, P. Vamplew, S. Nahavandi, R. Dazeley, and C. P. Lim, “A multi-objective deep reinforcement learning frame- work,” Engineering Applications of Artificial Intelligence , vol. 96, p. 103915, 2020

    2020

  125. [132]

    Multi- objective ADAM optimizer (MAdam),

    F. Nikbakhtsarvestani, M. Ebrahimi, and S. Rahnamayan, “Multi- objective ADAM optimizer (MAdam),” in 2023 IEEE International Conference on Systems, Man, and Cybernetics (SMC), 2023, pp. 3860– 3867

    2023

  126. [133]

    Multi-objective optimization for video streaming,

    T. Ozc ¸elebi, “Multi-objective optimization for video streaming,” Ph.D. dissertation, PhD Thesis, Graduate School of Sciences and Engineering, Koc University, 2006

    2006

  127. [134]

    Scalarizing vector optimization prob- lems,

    A. Pascoletti and P. Serafini, “Scalarizing vector optimization prob- lems,” Journal of Optimization Theory and Applications, vol. 42, no. 4, pp. 499–524, 1984

    1984

  128. [135]

    Multi-adversarial domain adap- tation,

    Z. Pei, Z. Cao, M. Long, and J. Wang, “Multi-adversarial domain adap- tation,” Proceedings of the AAAI Conference on Artificial Intelligence , vol. 32, no. 1, 2018

    2018

  129. [136]

    A Survey of Recent Trends in Multiobjective Optimal Control – Surrogate Models, Feedback Control and Objective Reduction,

    S. Peitz and M. Dellnitz, “A Survey of Recent Trends in Multiobjective Optimal Control – Surrogate Models, Feedback Control and Objective Reduction,” Mathematical and Computational Applications , vol. 23, no. 2, 2018

    2018

  130. [137]

    Gradient-based multiobjective optimization with uncertainties,

    ——, “Gradient-based multiobjective optimization with uncertainties,” in NEO 2016, Y . Maldonado, L. Trujillo, O. Sch¨utze, A. Riccardi, and M. Vasile, Eds. Springer, 2018, vol. 731, pp. 159–182

    2016

  131. [138]

    Distributed Control of Partial Differential Equations Using Convolutional Reinforcement Learning,

    S. Peitz, J. Stenner, V . Chidananda, O. Wallscheid, S. L. Brunton, and K. Taira, “Distributed Control of Partial Differential Equations Using Convolutional Reinforcement Learning,” Physica D: Nonlinear Phenomena, vol. 461, p. 134096, 2024

    2024

  132. [139]

    Gaussian process optimization for adaptable multi-objective text generation using linearly-weighted language models,

    M. M. A. Pour, A. Pesaranghader, E. Cohen, and S. Sanner, “Gaussian process optimization for adaptable multi-objective text generation using linearly-weighted language models,” in Findings of the Association for Computational Linguistics: NAACL 2024 , 2024, pp. 1529–1536

    2024

  133. [140]

    Quasi-newton’s method for multiobjective optimization,

    Z. Povalej, “Quasi-newton’s method for multiobjective optimization,” Journal of Computational and Applied Mathematics, vol. 255, pp. 765– 777, 2014

    2014

  134. [141]

    A comprehensive review of machine learning in multi-objective optimization,

    Q. Qu, Z. Ma, A. Clausen, and B. N. Jorgensen, “A comprehensive review of machine learning in multi-objective optimization,” in 2021 IEEE 4th International Conference on Big Data and Artificial Intelli- gence (BDAI). IEEE, Jul. 2021, p. 7–14

    2021

  135. [142]

    Exploring multiobjective training in multiclass classification,

    M. M. Raimundo, T. F. Drumond, A. C. R. Marques, C. Lyra, A. Rocha, and F. J. V on Zuben, “Exploring multiobjective training in multiclass classification,” Neurocomputing, vol. 435, pp. 307–320, 2021

    2021

  136. [143]

    Gaussian mixture models

    D. A. Reynolds et al. , “Gaussian mixture models.” Encyclopedia of biometrics, vol. 741, no. 659-663, 2009

    2009

  137. [144]

    Data vs. physics: The apparent Pareto front of physics-informed neural networks,

    F. M. Rohrhofer, S. Posch, C. G ¨oßnitzer, and B. C. Geiger, “Data vs. physics: The apparent Pareto front of physics-informed neural networks,” IEEE Access, vol. 11, pp. 86 252–86 261, 2023

    2023

  138. [145]

    A survey of multi-objective sequential decision-making,

    D. M. Roijers, P. Vamplew, S. Whiteson, and R. Dazeley, “A survey of multi-objective sequential decision-making,” Journal of Artificial Intelligence Research, vol. 48, p. 67–113, Oct. 2013

    2013

  139. [146]

    Why multi-objective reinforcement learning?

    D. M. Roijers, S. Whiteson, P. Vamplew, and R. Dazeley, “Why multi-objective reinforcement learning?” in European Workshop on Reinforcement Learning, 2015, pp. 1–2

    2015

  140. [147]

    Computing convex coverage sets for faster multi-objective coordination,

    D. M. Roijers, S. Whiteson, and F. A. Oliehoek, “Computing convex coverage sets for faster multi-objective coordination,” Journal of Arti- ficial Intelligence Research , vol. 52, p. 399–443, Mar. 2015

    2015

  141. [148]

    High-resolution image synthesis with latent diffusion models,

    R. Rombach, A. Blattmann, D. Lorenz, P. Esser, and B. Ommer, “High-resolution image synthesis with latent diffusion models,” in Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, 2022, pp. 10 684–10 695

    2022

  142. [150]

    Scalable pareto front approximation for deep multi-objective learning,

    M. Ruchte and J. Grabocka, “Scalable pareto front approximation for deep multi-objective learning,” in 2021 IEEE International Conference on Data Mining (ICDM) , 2021, pp. 1306–1311

    2021

  143. [151]

    An introduction to deep generative model- ing,

    L. Ruthotto and E. Haber, “An introduction to deep generative model- ing,” GAMM-Mitteilungen, vol. 44, no. 2, May 2021

    2021

  144. [152]

    Multi-dimensional optimization for text summarization via reinforcement learning,

    S. Ryu, H. Do, Y . Kim, G. Lee, and J. Ok, “Multi-dimensional optimization for text summarization via reinforcement learning,” in Proceedings of the 62nd Annual Meeting of the Association for Com- putational Linguistics (Volume 1: Long Papers), L.-W. Ku, A. Martins, and V . Sr...

    2024

  145. [153]

    M2ASR: Multilingual multi-task automatic speech recognition via multi-objective optimization,

    A. F. M. Saif, L. Chen, X. Cui, S. Lu, B. Kingsbury, and T. Chen, “M2ASR: Multilingual multi-task automatic speech recognition via multi-objective optimization,” in Interspeech 2024 , 2024, pp. 1240– 1244

    2024

  146. [154]

    Think globally, fit locally: unsupervised learning of low dimensional manifolds,

    L. K. Saul and S. T. Roweis, “Think globally, fit locally: unsupervised learning of low dimensional manifolds,” Journal of Machine Learning Research, vol. 4, no. null, p. 119–155, 2003

    2003

  147. [155]

    Stochastic method for the solution of unconstrained vector optimization problems,

    S. Sch ¨affler, R. Schultz, and K. Weinzierl, “Stochastic method for the solution of unconstrained vector optimization problems,” Journal of Optimization Theory and Applications , vol. 114, no. 1, p. 209–222, 2002

    2002

  148. [156]

    A survey on semi-, self- and unsupervised learning for image classification,

    L. Schmarje, M. Santarossa, S.-M. Schr ¨oder, and R. Koch, “A survey on semi-, self- and unsupervised learning for image classification,” IEEE Access, 2021

    2021

  149. [157]

    Proximal policy optimization algorithms,

    J. Schulman, F. Wolski, P. Dhariwal, A. Radford, and O. Klimov, “Proximal policy optimization algorithms,” arXiv:1707.06347, 2017

    2017 arXiv

  150. [158]

    Pareto Explorer: a global/local exploration tool for many-objective optimiza- tion problems,

    O. Sch ¨utze, O. Cuate, A. Mart ´ın, S. Peitz, and M. Dellnitz, “Pareto Explorer: a global/local exploration tool for many-objective optimiza- tion problems,” Engineering Optimization, vol. 52, no. 5, pp. 832–855, 2020

    2020

  151. [159]

    Sch ¨utze, S

    O. Sch ¨utze, S. Mostaghim, M. Dellnitz, and J. Teich, Covering Pareto Sets by Multilevel Evolutionary Subdivision Techniques . Springer Berlin Heidelberg, 2003, p. 118–132

    2003

  152. [160]

    Multi-task learning in deep neural net- works for improved phoneme recognition,

    M. L. Seltzer and J. Droppo, “Multi-task learning in deep neural net- works for improved phoneme recognition,” in 2013 IEEE International Conference on Acoustics, Speech and Signal Processing , 2013, pp. 6965–6969

    2013

  153. [161]

    Multi-task learning as multi-objective opti- mization,

    O. Sener and V . Koltun, “Multi-task learning as multi-objective opti- mization,” Advances in neural information processing systems , vol. 31, 2018

    2018

  154. [162]

    Multi-criteria feature selection on cost-sensitive data with missing values,

    W. Shu and H. Shen, “Multi-criteria feature selection on cost-sensitive data with missing values,” Pattern Recognition, vol. 51, pp. 268–280, 2016

    2016

  155. [163]

    A general reinforcement learning algorithm that masters chess, shogi, and go through self-play,

    D. Silver, T. Hubert, J. Schrittwieser, I. Antonoglou, M. Lai, A. Guez, M. Lanctot, L. Sifre, D. Kumaran, T. Graepel, T. Lillicrap, K. Si- monyan, and D. Hassabis, “A general reinforcement learning algorithm that masters chess, shogi, and go through self-play,” Science, vol. 3...

    2018

  156. [164]

    A survey on supervised and unsuper- vised learning techniques,

    K. Sindhu Meena and S. Suriya, “A survey on supervised and unsuper- vised learning techniques,” in Proceedings of international conference on artificial intelligence, smart grid and smart city applications: AISGSC 2019. Springer, 2020, pp. 627–644

    2019

  157. [165]

    Deep unsupervised learning using nonequilibrium thermodynamics,

    J. Sohl-Dickstein, E. Weiss, N. Maheswaranathan, and S. Ganguli, “Deep unsupervised learning using nonequilibrium thermodynamics,” in Proceedings of the 32nd International Conference on Machine Learning, ser. Proceedings of Machine Learning Research, F. Bach and D. Blei, Eds.,...

    2015

  158. [166]

    Metric-based regularization and temporal ensemble for multi-task learning using heterogeneous unsupervised tasks,

    B. C. Song, D. H. Kim, and S. hyun Lee, “Metric-based regularization and temporal ensemble for multi-task learning using heterogeneous unsupervised tasks,” in 2019 IEEE/CVF International Conference on Computer Vision Workshop (ICCVW) . IEEE, 2019, pp. 2903–2912

    2019

  159. [167]

    Fast convergence of inertial multiobjective gradient-like systems with asymptotic vanishing damping,

    K. Sonntag and S. Peitz, “Fast convergence of inertial multiobjective gradient-like systems with asymptotic vanishing damping,” SIAM Jour- nal on Optimization , vol. 34, pp. 2259–2286, 2024

    2024

  160. [168]

    Fast Multiobjective Gradient Methods with Nesterov Accelera- tion via Inertial Gradient-like Systems,

    ——, “Fast Multiobjective Gradient Methods with Nesterov Accelera- tion via Inertial Gradient-like Systems,”Journal of Optimization Theory and Applications, vol. 201, pp. 539–582, 2024

    2024

  161. [169]

    Hypervolume maximization via set based newton’s method,

    V . A. Sosa Hern ´andez, O. Sch ¨utze, and M. Emmerich, “Hypervolume maximization via set based newton’s method,” in EVOLVE - A Bridge between Probability, Set Oriented Numerics, and Evolutionary Com- putation V , A.-A. Tantar, E. Tantar, J.-Q. Sun, W. Zhang, Q. Ding, O. Sch ¨...

    2014

  162. [170]

    Multi-objective differentiable neural architecture search,

    R. S. Sukthanker, A. Zela, B. Staffler, S. Dooley, J. Grabocka, and F. Hutter, “Multi-objective differentiable neural architecture search,” arXiv:2402.18213, 2024

    2024 arXiv

  163. [171]

    Building an effective intrusion detection system using unsupervised feature selection in multi-objective optimization framework,

    C. Suman, S. Tripathy, and S. Saha, “Building an effective intrusion detection system using unsupervised feature selection in multi-objective optimization framework,” arXiv:1905.06562, 2019

    1905 arXiv

  164. [172]

    Multiple-target deep learning for lstm-rnn based speech enhancement,

    L. Sun, J. Du, L.-R. Dai, and C.-H. Lee, “Multiple-target deep learning for lstm-rnn based speech enhancement,” in 2017 Hands-free Speech Communications and Microphone Arrays (HSCMA) , 2017, pp. 136– 140

    2017

  165. [173]

    R. S. Sutton and A. G. Barto, Reinforcement learning: An introduction. MIT press, 2018

    2018

  166. [174]

    Suttorp and C

    T. Suttorp and C. Igel, Multi-Objective Optimization of Support Vector Machines. Berlin, Heidelberg: Springer Berlin Heidelberg, 2006, pp. 199–220

    2006

  167. [175]

    Multiobjective optimiza- tion for politically fair districting: A scalable multilevel approach,

    R. Swamy, D. M. King, and S. H. Jacobson, “Multiobjective optimiza- tion for politically fair districting: A scalable multilevel approach,” Operations Research, vol. 71, no. 2, pp. 536–562, 2023

    2023

  168. [176]

    A survey on handling computationally expensive multiobjective optimization problems using surrogates: non-nature inspired methods,

    M. Tabatabaei, J. Hakanen, M. Hartikainen, K. Miettinen, and K. Sind- hya, “A survey on handling computationally expensive multiobjective optimization problems using surrogates: non-nature inspired methods,” Structural and Multidisciplinary Optimization , vol. 52, no. 1, p. 1–...

    2015

  169. [177]

    Modular multi-objective deep reinforcement learning with decision values,

    T. Tajmajer, “Modular multi-objective deep reinforcement learning with decision values,” in 2018 Federated Conference on Computer Science and Information Systems (FedCSIS) , 2018, pp. 85–93

    2018

  170. [178]

    Proximal gradient methods for multiobjective optimization and their applications,

    H. Tanabe, E. H. Fukuda, and N. Yamashita, “Proximal gradient methods for multiobjective optimization and their applications,” Com- putational Optimization and Applications , vol. 72, no. 2, p. 339–361, 2018

    2018

  171. [179]

    An accelerated proximal gradient method for multiobjective optimization,

    ——, “An accelerated proximal gradient method for multiobjective optimization,” Computational Optimization and Applications , vol. 86, no. 2, p. 421–455, 2023

    2023

  172. [180]

    A preference- based evolutionary algorithm for multi-objective optimization,

    L. Thiele, K. Miettinen, P. J. Korhonen, and J. Molina, “A preference- based evolutionary algorithm for multi-objective optimization,” Evolu- tionary Computation, vol. 17, no. 3, pp. 411–436, 2009

    2009

  173. [181]

    Evo- lutionary large-scale multi-objective optimization: A survey,

    Y . Tian, L. Si, X. Zhang, R. Cheng, C. He, K. C. Tan, and Y . Jin, “Evo- lutionary large-scale multi-objective optimization: A survey,” ACM Comput. Surv., vol. 54, no. 8, Oct. 2021

    2021

  174. [182]

    Triantaphyllou, Multi-Criteria Decision Making Methods

    E. Triantaphyllou, Multi-Criteria Decision Making Methods . Boston, MA: Springer US, 2000, pp. 5–21

    2000

  175. [183]

    Em- pirical evaluation methods for multiobjective reinforcement learning algorithms,

    P. Vamplew, R. Dazeley, A. Berry, R. Issabekov, and E. Dekker, “Em- pirical evaluation methods for multiobjective reinforcement learning algorithms,” Machine Learning, vol. 84, no. 1-2, pp. 51–80, Jul. 2011

    2011

  176. [184]

    Scalar reward is not enough: a response to silver, singh, precup and sutton (2021),

    P. Vamplew, B. J. Smith, J. K ¨allstr¨om, G. Ramos, R. R ˘adulescu, D. M. Roijers, C. F. Hayes, F. Heintz, P. Mannion, P. J. K. Libin, R. Dazeley, and C. Foale, “Scalar reward is not enough: a response to silver, singh, precup and sutton (2021),” Autonomous Agents and Multi-Ag...

    2021

  177. [185]

    Numerical differentia- tion of noisy data: A unifying multi-objective optimization framework,

    F. Van Breugel, J. N. Kutz, and B. W. Brunton, “Numerical differentia- tion of noisy data: A unifying multi-objective optimization framework,” IEEE Access, vol. 8, pp. 196 865–196 877, 2020

    2020

  178. [186]

    Deep reinforcement learning with double q-learning,

    H. Van Hasselt, A. Guez, and D. Silver, “Deep reinforcement learning with double q-learning,” Proceedings of the AAAI Conference on Artificial Intelligence, vol. 30, no. 1, Mar. 2016

    2016

  179. [187]

    Multi-objective reinforcement learning using sets of Pareto dominating policies,

    K. Van Moffaert and A. Now ´e, “Multi-objective reinforcement learning using sets of Pareto dominating policies,” The Journal of Machine Learning Research, vol. 15, no. 1, pp. 3483–3512, 2014

    2014

  180. [188]

    Attention is all you need,

    A. Vaswani, N. Shazeer, N. Parmar, J. Uszkoreit, L. Jones, A. N. Gomez, L. u. Kaiser, and I. Polosukhin, “Attention is all you need,” in Advances in Neural Information Processing Systems , I. Guyon, U. V . Luxburg, S. Bengio, H. Wallach, R. Fergus, S. Vishwanathan, and R. Garn...

    2017

  181. [189]

    Recent advances in applying deep reinforcement learning for flow control: Perspectives and future directions,

    C. Vignon, J. Rabault, and R. Vinuesa, “Recent advances in applying deep reinforcement learning for flow control: Perspectives and future directions,” Physics of fluids , vol. 35, no. 3, 2023

    2023

  182. [190]

    Unsupervised active learning with loss prediction,

    C. Wan, F. Jin, Z. Qiao, W. Zhang, and Y . Yuan, “Unsupervised active learning with loss prediction,” Neural Computing and Applications, pp. 1–9, 2023

    2023

  183. [191]

    Multi-objective deep data generation with correlated prop- erty control,

    S. Wang, X. Guo, X. Lin, B. Pan, Y . Du, Y . Wang, Y . Ye, A. Petersen, A. Leitgeb, S. Alkhalifa, K. Minbiole, W. M. Wuest, A. Shehu, and L. Zhao, “Multi-objective deep data generation with correlated prop- erty control,” in Advances in Neural Information Processing Systems , ...

    2022

  184. [192]

    Multi-objective workflow scheduling with deep-q-network- based multi-agent reinforcement learning,

    Y . Wang, H. Liu, W. Zheng, Y . Xia, Y . Li, P. Chen, K. Guo, and H. Xie, “Multi-objective workflow scheduling with deep-q-network- based multi-agent reinforcement learning,” IEEE Access , vol. 7, pp. 39 974–39 982, 2019

    2019

  185. [193]

    Nonparametric density estimation for high-dimensional data—algorithms and applications,

    Z. Wang and D. W. Scott, “Nonparametric density estimation for high-dimensional data—algorithms and applications,” Wiley Interdis- ciplinary Reviews: Computational Statistics , vol. 11, no. 4, p. e1461, 2019

    2019

  186. [194]

    A survey of unsupervised deep domain adaptation,

    G. Wilson and D. J. Cook, “A survey of unsupervised deep domain adaptation,” ACM Transactions on Intelligent Systems and Technology (TIST), vol. 11, no. 5, pp. 1–46, 2020

    2020

  187. [195]

    Multi- objective policy gradients with topological constraints,

    K. H. Wray, S. Tiomkin, M. J. Kochenderfer, and P. Abbeel, “Multi- objective policy gradients with topological constraints,” in 2022 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS). IEEE, 2022, pp. 9034–9039

    2022

  188. [196]

    A survey of human-in-the-loop for machine learning,

    X. Wu, L. Xiao, Y . Sun, J. Zhang, T. Ma, and L. He, “A survey of human-in-the-loop for machine learning,” Future Generation Computer Systems, vol. 135, pp. 364–381, 2022

    2022

  189. [197]

    Molecule optimization via multi-objective evolutionary in implicit chemical space,

    X. Xia, Y . Su, C. Zheng, and X. Zeng, “Molecule optimization via multi-objective evolutionary in implicit chemical space,” arXiv preprint arXiv:2212.08826, 2022

    2022 arXiv

  190. [198]

    Short video creation mode based on interactive multi-objective optimization algorithm,

    H. Xu, “Short video creation mode based on interactive multi-objective optimization algorithm,” in International Conference on Frontier Com- puting. Springer, 2023, pp. 9–14

    2023

  191. [199]

    The perfect blend: Redefining RLHF with mixture of judges,

    T. Xu, E. Helenowski, K. A. Sankararaman, D. Jin, K. Peng, E. Han, S. Nie, C. Zhu, H. Zhang, W. Zhou et al. , “The perfect blend: Redefining RLHF with mixture of judges,” arXiv:2409.20370, 2024

    2024 arXiv

  192. [200]

    Multi-objective learning and mask-based post-processing for deep neural network based speech enhancement,

    Y . Xu, J. Du, Z. Huang, L.-R. Dai, and C.-H. Lee, “Multi-objective learning and mask-based post-processing for deep neural network based speech enhancement,” arxiv:1703.07172, 2017

    2017 arXiv

  193. [201]

    A pair- wise comparison relation-assisted multi-objective evolutionary neu- ral architecture search method with multi-population mechanism,

    Y . Xue, C. Zhu, M. Zhou, M. Wahib, and M. Gabbouj, “A pair- wise comparison relation-assisted multi-objective evolutionary neu- ral architecture search method with multi-population mechanism,” arXiv:2407.15600, 2024

    2024

  194. [202]

    Deep spectral clustering using dual autoencoder network,

    X. Yang, C. Deng, F. Zheng, J. Yan, and W. Liu, “Deep spectral clustering using dual autoencoder network,” in Proceedings of the IEEE/CVF conference on computer vision and pattern recognition , 2019, pp. 4066–4075

    2019

  195. [203]

    Gradient shaping for multi-constraint safe reinforcement learning,

    Y . Yao, Z. Liu, Z. Cen, P. Huang, T. Zhang, W. Yu, and D. Zhao, “Gradient shaping for multi-constraint safe reinforcement learning,” in 6th Annual Learning for Dynamics & Control Conference . PMLR, 2024, pp. 25–39

    2024

  196. [204]

    Proud: Pareto-guided diffusion model for multi-objective generation,

    Y . Yao, Y . Pan, J. Li, I. Tsang, and X. Yao, “Proud: Pareto-guided diffusion model for multi-objective generation,”Machine Learning, vol. 113, no. 9, p. 6511–6538, 2024

    2024

  197. [205]

    Gra- dient surgery for multi-task learning,

    T. Yu, S. Kumar, A. Gupta, S. Levine, K. Hausman, and C. Finn, “Gra- dient surgery for multi-task learning,” Advances in Neural Information Processing Systems, vol. 33, pp. 5824–5836, 2020

    2020

  198. [206]

    A convolutional neural network-based surrogate model for multi-objective optimization evolu- 18 tionary algorithm based on decomposition,

    T. Zhang, F. Li, X. Zhao, W. Qi, and T. Liu, “A convolutional neural network-based surrogate model for multi-objective optimization evolu- 18 tionary algorithm based on decomposition,” Swarm and Evolutionary Computation, vol. 72, p. 101081, Jul. 2022

    2022

  199. [207]

    Hypervolume maximization: a geometric view of Pareto set learning,

    X. Zhang, X. Lin, B. Xue, Y . Chen, and Q. Zhang, “Hypervolume maximization: a geometric view of Pareto set learning,” in Proceedings of the 37th International Conference on Neural Information Processing Systems. Red Hook, NY , USA: Curran Associates Inc., 2023

    2023

  200. [208]

    PMGDA: A preference-based multiple gradient descent algorithm,

    X. Zhang, X. Lin, and Q. Zhang, “PMGDA: A preference-based multiple gradient descent algorithm,” arXiv:2402.09492, 2024

    2024 arXiv

  201. [209]

    Multiobjective evolutionary algorithms: A survey of the state of the art,

    A. Zhou, B.-Y . Qu, H. Li, S.-Z. Zhao, P. N. Suganthan, and Q. Zhang, “Multiobjective evolutionary algorithms: A survey of the state of the art,” Swarm and Evolutionary Computation , vol. 1, no. 1, pp. 32–49, 2011

    2011

  202. [210]

    Anchor-changing regularized natural policy gradient for multi-objective reinforcement learning,

    R. Zhou, T. Liu, D. Kalathil, P. Kumar, and C. Tian, “Anchor-changing regularized natural policy gradient for multi-objective reinforcement learning,” Advances in Neural Information Processing Systems, vol. 35, pp. 13 584–13 596, 2022

    2022

  203. [211]

    A reinforcement learn- ing approach for dynamic multi-objective optimization,

    F. Zou, G. G. Yen, L. Tang, and C. Wang, “A reinforcement learn- ing approach for dynamic multi-objective optimization,” Information Sciences, vol. 546, pp. 815–834, 2021

    2021

Pith tools

Reviewed August 12, 2026 · model on record in the stance chip above.