Pith. sign in

REVIEW 2 major objections 4 minor 44 references

STIMULUS: Achieving Fast Convergence and Low Sample Complexity in Stochastic Multi-Objective Learning

T0 review · 2 major / 4 minor · reviewed 2026-08-15 · deepseek-v4-flash

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

Pith's one-line read STIMULUS is a stochastic multi-objective optimization algorithm that claims deterministic-level convergence and near-linear sample complexity through recursive variance-reduced multi-gradient estimation.

desk verdict The non-convex half of STIMULUS is a solid SPIDER-for-MOO result; the strongly convex half is vacuous because Assumption 4 collapses the problem to single-objective. read the letter →

arxiv 2506.19883 v1 pith:PHSW3IPI submitted 2025-06-24 cs.LG cs.AI

Zhuqing Liu , Chaosheng Dong , Michinari Momma , Simone Shao , Shaoyuan Xu , Yan Gao , Haibo Yang , Jia Liu This is my paper · ORCID
classification cs.LGcs.AI MSC 90C2990C1590C2690C25
keywords multi-objectiveoptimizationParetostationaritystochasticmulti-gradientdescentvariancereductionsamplecomplexitylinearconvergenceadaptivebatchingmomentum
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

STIMULUS is a stochastic algorithm for multi-objective optimization that claims the convergence rate of deterministic multi-gradient descent while keeping per-iteration cost low. For non-convex objectives it achieves $O(1/T)$ Pareto-stationarity convergence, and for $\mu$-strongly convex objectives it achieves linear $O(\exp(-\mu T))$ convergence; the corresponding sample complexities are $O(n+\sqrt{n}/\epsilon)$ and $O(n+\sqrt{n}\ln(\mu/\epsilon))$. A recursive estimator of the multi-gradient, refreshed by the full gradient every $\lceil\sqrt{n}\rceil$ steps, suppresses the noise that makes plain stochastic multi-gradient descent stall at $O(1/\sqrt{T})$. The paper further adds momentum (STIMULUS-M) and adaptive-batching (STIMULUS+ and STIMULUS-M+) variants that retain these rates and avoid exact full-gradient evaluations.

What carries the argument

The object that carries the argument is the recursive multi-gradient estimator $u_t^s = u_{t-1}^s + \frac{1}{|A|}\sum_{j\in A}(\nabla f_{sj}(x_t) - \nabla f_{sj}(x_{t-1}))$, reinitialized to the full multi-gradient every $q$ iterations. This estimator keeps the mean-square error $\mathbb{E}\|\nabla f_s(x_t)-u_t^s\|^2$ bounded by $L^2/|A|$ times the sum of squared step lengths over the current window, so the error does not accumulate across the whole trajectory. The descent direction $d_t=\sum_s \lambda_t^s u_t^s$ is chosen by minimizing $\|\sum_s \lambda_s u_t^s\|^2$ over the simplex, and the key descent lemma $f_s(x_{t+1}) \le f_s(x_t) + \frac{\eta}{2}\|\nabla f_s(x_t)-u_t^s\|^2 - \frac{\eta}{4}\|d_t\|^2$ converts estimator error into a telescoping bound. In the strongly convex analysis, the contraction factor $1-3\mu\eta/4$ comes from combining this descent inequality with Assumption 4 and averaging outputs with weights $w_t=(1-3\mu\eta/4)^{1-t}$.

What would settle it

On the two-objective strongly convex pair $f_1(x)=(x+1)^2$, $f_2(x)=(x-1)^2$ with $x^*=0$, Assumption 4 fails even though both objectives are $\mu$-strongly convex; simulating STIMULUS and checking whether $\mathbb{E}\|x_t-x^*\|^2$ still decays at the claimed $3\eta\mu/4$ rate would show whether the linear rate is a property of strong convexity or only of the extra quadratic-growth condition.

Watch

Extended reading notes

Core claim

On its own terms, the paper's central discovery is that a path-integrated recursive estimator can carry variance reduction into multi-objective optimization without biasing the search across the Pareto front. Using this estimator in a multi-gradient descent loop yields a Pareto-stationarity gap $\frac{1}{T}\sum_{t=0}^{T-1}\min_{\lambda\in C}\mathbb{E}\|\lambda^\top\nabla F(x_t)\|^2 = O(1/T)$ for non-convex finite-sum problems, and $\mathbb{E}\|x_t-x^*\|^2 = O(\mu \exp(-3\eta\mu T/4))$ in the strongly convex case. With $q=|A|=\lceil\sqrt{n}\rceil$ the method needs $O(n+\sqrt{n}\epsilon^{-1})$ incremental first-order oracle calls for $\epsilon$-stationarity and $O(n+\sqrt{n}\ln(\mu/\epsilon))$ for $\epsilon$-optimality. STIMULUS+ replaces the periodic exact gradient with an adaptively sized stochastic batch, so the algorithm applies even when exact gradients are unavailable, with the same order bounds.

Load-bearing premise

For the strongly convex results, the load-bearing assumption is that every objective grows at least quadratically from one fixed Pareto-optimal point $x^*$, an assumption stronger than strong convexity that can fail when objectives have different minimizers.

Editorial extensions

If this is right

  • Stochastic multi-objective training can match the $O(1/T)$ rate of deterministic MGD, so a full-gradient refresh every $\sqrt{n}$ steps is enough to remove the stochastic bottleneck.
  • The sample complexities $O(n+\sqrt{n}/\epsilon)$ and $O(n+\sqrt{n}\ln(\mu/\epsilon))$ improve on the $O(\epsilon^{-2})$ and $O(\epsilon^{-1})$ costs of prior stochastic MOO methods, helping in large-$n$ regimes.
  • The strongly convex result gives a stochastic MOO algorithm with logarithmic sample dependence on $1/\epsilon$, so high-precision Pareto solutions become plausible with finite-sum or online objectives.
  • The adaptive-batching variants mean the algorithm no longer requires exact full gradients, making it applicable to expectation-form and streaming objectives while retaining the same order of sample complexity.
  • Momentum and adaptive batching are compatible in one family, giving practitioners a tuning knob between convergence speed and per-iteration cost.

Reading between the lines

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

  • If the bounds are tight, the $\sqrt{n}$ term in the sample complexity suggests that data parallelism or approximate gradient oracles could be pushed further; one could derive lower bounds to see whether $O(n+\sqrt{n}/\epsilon)$ is optimal for stochastic MOO.
  • The strong-convexity analysis depends on Assumption 4 relative to one fixed Pareto point; for objectives with distinct minimizers this may not hold, so practitioners should check quadratic growth before expecting linear convergence.
  • The recursive estimator could be combined with other multi-gradient aggregation schemes, such as min-norm solvers with different regularizers, and with adaptive step sizes, potentially improving constant factors.
  • A natural testable extension is to use the adaptive-batching size rule as a heuristic in single-objective multi-task training, where the batch size grows in response to large recent gradient norms.
Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 4 minor

Summary. The paper proposes STIMULUS, a stochastic multi-gradient algorithm for multi-objective optimization that uses a SPIDER-style recursive variance-reduced gradient estimator, together with momentum (STIMULUS-M) and adaptive-batching (STIMULUS+/STIMULUS-M+) variants. It claims an O(1/T) Pareto-stationarity convergence rate and O(n + sqrt(n)/epsilon) sample complexity for non-convex MOO, and linear convergence O(exp(-mu T)) with O(n + sqrt(n) log(mu/epsilon)) sample complexity for strongly convex MOO. The non-convex analysis follows the standard SPIDER proof template, with the improved sample complexity coming from setting the inner loop length and batch size to sqrt(n). The strongly convex analysis is based on a quadratic-growth assumption (Assumption 4) and a weighted-averaging output rule.

Significance. If the technical issues were repaired, the paper would be a useful contribution: applying variance reduction to the multi-gradient direction is natural, and the claimed O(n + sqrt(n)/epsilon) sample complexity for non-convex MOO is the expected near-optimal finite-sum complexity. The momentum and adaptive-batching extensions are practically motivated, and the non-convex part of the analysis is structurally sound and closely follows Fang et al. (2018). However, the strongly convex results as stated are not a genuine MOO contribution, because Assumption 4 forces all objectives to share a common minimizer and hence removes the Pareto trade-off. The paper contains no code or machine-checked proofs, so its value rests on the correctness and precision of the written proofs.

major comments (2)
  1. [Section 4.1, Assumption 4 and Theorems 2, 4, 6] Assumption 4 is not a benign addition to strong convexity; it makes the strongly convex results vacuous for MOO. If ∇f_j(x*) ≠ 0 for some j, then by L-smoothness, for small δ > 0 the point x* − δ∇f_j(x*) satisfies f_j(x* − δ∇f_j(x*)) ≤ f_j(x*) − δ‖∇f_j(x*)‖² + (L/2)δ²‖∇f_j(x*)‖² < f_j(x*) when δ < 2/L, while Assumption 4 requires f_j(x) − f_j(x*) ≥ (c_j/2)‖x − x*‖² ≥ 0 for all x. Hence Assumption 4 forces ∇f_j(x*) = 0 for every j, so every strongly convex objective has its unique minimizer at the same point x*. In that regime the multi-objective problem has a common minimizer, there is no Pareto trade-off, and the linear rates in Theorems 2, 4, and 6 do not cover genuine strongly convex MOO. The proof of Theorem 2 also never uses the constants c_j or their minimum, and the final rate O(μ exp(−μT)) is independent of any quadratic-growth constant; under a non-vacuous relaxation such as a Pareto-PL condition, that constant would necessarily enter the rate. The authors should either replace Assumption 4 with a meaningful condition and re-derive the strongly convex rates with the correct dependence on the quadratic-growth constants, or remove the strongly convex optimality claims and restrict the paper's claims to the non-convex setting.
  2. [Section 4.1, Theorem 1 proof and Definition 3] The stationarity measure bounded in the proof of Theorem 1 is not the measure stated in Definition 3. The proof controls (1/T) Σ_t E‖Σ_s λ_t^s ∇f_s(x_t)‖², where λ_t is the data-dependent minimizer of ‖Σ_s λ u_t^s‖². However, Definition 3 concerns min_{λ∈C} E‖λ^T∇F(x_t)‖², in which the minimization is over a fixed weight vector before the expectation is taken. Since λ_t is random and is chosen using the stochastic estimators u_t rather than the true gradients, the inequality min_{λ∈C} E‖λ^T∇F(x_t)‖² ≤ E‖Σ_s λ_t^s ∇f_s(x_t)‖² is not justified and can fail: a pointwise-adaptive weight can make the expected squared norm smaller than every fixed-weight expectation. If the intended metric is instead E[min_{λ∈C}‖λ^T∇F(x_t)‖²], then Definition 3 and the theorem statements should be changed accordingly, and the output rule and sample-complexity statement should be aligned with that corrected metric.
minor comments (4)
  1. [Throughout, figures and tables] Figure 1 and Table 3 use the name "STIMULATE" instead of "STIMULUS", and Table 3 also uses "SGMD" instead of "SMGD"; these should be corrected.
  2. [Section 3.3, Eq. (6)] The definition of the adaptive batch size uses γ_t with subscripts and summations that are hard to parse, and the text switches between n_k and n_t; please clarify the indexing and restate γ_{t+1} unambiguously.
  3. [Section 4.1, Assumption 4] Assumption 4 is stated for "any x in R^n" although the ambient dimension is d, and x* is not explicitly defined as common to all objectives; please state the assumption in R^d and clarify the status of x*.
  4. [Section 5] The experimental comparison reports training loss only and does not include variances or multiple seeds; adding error bars or a brief statement about variability would strengthen the empirical claims.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity; the strong-convexity claim has a vacuity/soundness issue in Assumption 4, but it is not a self-referential derivation.

full rationale

I walked the derivation chain for Theorems 1-6 and the sample-complexity corollaries. The non-convex results (Theorems 1, 3, 5 and Corollaries 1, 3, 5) are SPIDER/SARAH-style variance-reduction proofs built on external lemmas from Fang et al. (2018) and Karimireddy et al. (2020); the O(1/T) rate follows by telescoping the descent inequality, and the sample complexities are direct IFO counts with q=|A|=sqrt(n). No fitted parameter is relabeled as a prediction. The strongly convex results (Theorems 2, 4, 6) rest on Assumption 4, a quadratic-growth condition around the Pareto-optimal point x*; under Assumptions 1 and 3 this condition forces every objective's minimizer to coincide at x*, so the theorem covers only the common-minimizer (single-objective-equivalent) case, and the proof's final step never uses the constants c_j. This is a vacuity/correctness limitation, not a circularity: Assumption 4 does not define the algorithm's output, and the derivation still attempts a descent-telescoping argument. All load-bearing citations are to external work, not to the authors' own prior results, so no circular step is present.

Assumptions & free parameters 5 free parameters · 7 assumptions · 0 invented entities

The central claims rest on standard smoothness and variance assumptions, plus the nonstandard Assumption 4 for strong convexity. The algorithm introduces no new physical or mathematical entities; gamma_t is a running statistic, not an invented object. The free parameters are algorithm hyperparameters and experiment-specific settings, not fitted constants that secretly determine the result.

free parameters (5)
  • inner loop length q = ceil(sqrt(n)) (theory); not reported for experiments
    The sample complexity O(n + sqrt(n)/epsilon) is derived with q = ceil(sqrt(n)); in experiments q is not specified, so the link between theory and practice is incomplete.
  • mini-batch size |A| = 96 in MultiMNIST experiments
    Set to 96 in MultiMNIST, 32 in CelebA, and 8 in river flow experiments, while theory requires ceil(sqrt(n)). The experimental batch sizes do not match the theoretical condition q=|A|=ceil(sqrt(n)).
  • learning rate eta = 0.3, 0.0005, 0.001, 0.005
    Chosen per experiment; theory requires eta <= 1/(2L) for non-convex and eta <= min{1/2, 1/(2mu), 1/(8L), mu/(64L^2)} for strongly convex. The experiments do not verify L or mu.
  • momentum coefficient alpha = 0.5, 0.01, 0.1, 0.3
    Tuned per experiment; the theory only requires alpha in (0,1) for the convergence of STIMULUS-M.
  • adaptive-batching constants c_gamma, c_epsilon = c = 32 in experiments
    Theory requires c_gamma >= 8 and c_epsilon >= eta for non-convex, and c_gamma >= 8mu/eta plus c_epsilon >= mu/2 for strongly convex. The experiments use fixed batch size 96, so these constants are not actually exercised.
assumptions (7)
  • domain assumption Assumption 1: L-smoothness of each f_s
    Standard for first-order optimization; used in Lemma 1 and Lemma 2.
  • domain assumption Assumption 2: bounded variance of stochastic gradients
    Used for STIMULUS+ and STIMULUS-M+; the adaptive batch size formula requires knowledge of sigma^2.
  • domain assumption Assumption 3: mu-strong convexity of each f_s
    Used in Theorems 2, 4, and 6 for the strongly convex setting.
  • ad hoc to paper Assumption 4: quadratic growth f_j(x)-f_j(x*) >= (c_j/2)||x-x*||^2
    Not implied by strong convexity when objectives have distinct minimizers; this condition is close to the linear convergence conclusion and is the main additional burden for the strongly convex results.
  • standard math Lemma 1 from Fang et al. 2018 (SPIDER estimator bound)
    Used without proof as the core estimate for the recursive gradient estimator in Lemma 1.
  • standard math Lemma 2.1 from Desideri 2012 (min-norm property of common descent direction)
    Justifies that <d_t, u_t^s> >= ||d_t||^2 for the min-norm convex-combination direction.
  • standard math Lemma 1 from Karimireddy et al. 2020 (SCAFFOLD analysis lemma)
    Used to convert the one-step contraction into an exponential convergence bound in the strongly convex proofs.

how reviews work

0 comments
Cite this review

Pith. "Pith review of STIMULUS: Achieving Fast Convergence and Low Sample Complexity in Stochastic Multi-Objective Learning." pith.science (2026). https://pith.science/paper/PHSW3IPI

@misc{pith2026250619883,
  author       = {Pith},
  title        = {Pith review of: STIMULUS: Achieving Fast Convergence and Low Sample Complexity in Stochastic Multi-Objective Learning},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/PHSW3IPI}},
  note         = {Machine review of arXiv:2506.19883}
}
abstract

Recently, multi-objective optimization (MOO) has gained attention for its broad applications in ML, operations research, and engineering. However, MOO algorithm design remains in its infancy and many existing MOO methods suffer from unsatisfactory convergence rate and sample complexity performance. To address this challenge, in this paper, we propose an algorithm called STIMULUS( stochastic path-integrated multi-gradient recursive e\ulstimator), a new and robust approach for solving MOO problems. Different from the traditional methods, STIMULUS introduces a simple yet powerful recursive framework for updating stochastic gradient estimates to improve convergence performance with low sample complexity. In addition, we introduce an enhanced version of STIMULUS, termed STIMULUS-M, which incorporates a momentum term to further expedite convergence. We establish $O(1/T)$ convergence rates of the proposed methods for non-convex settings and $O (\exp{-\mu T})$ for strongly convex settings, where $T$ is the total number of iteration rounds. Additionally, we achieve the state-of-the-art $O \left(n+\sqrt{n}\epsilon^{-1}\right)$ sample complexities for non-convex settings and $O\left(n+ \sqrt{n} \ln ({\mu/\epsilon})\right)$ for strongly convex settings, where $\epsilon>0$ is a desired stationarity error. Moreover, to alleviate the periodic full gradient evaluation requirement in STIMULUS and STIMULUS-M, we further propose enhanced versions with adaptive batching called STIMULUS+/ STIMULUS-M+ and provide their theoretical analysis.

Figures

Figures reproduced from arXiv: 2506.19883 by the authors.

Figure 1
Figure 1. Training loss convergence comparisons between different MOO algorithms. [PITH_FULL_IMAGE:figures/full_fig_p008_1.png] view at source ↗
Figure 2
Figure 2. Training loss conver￾gence comparison (40-task). We use a ResNet-18 He et al. [2016] model without the final layer for each attribute, and we attach a lin￾ear layer to each attribute for clas￾sification. In this experiment, we set η = 0.0005, α = 0.01, the full batch size for MGD is 1024, and the batch size for SMGD, CR-MOGM and MOCO and the inner loop batch size |Ns| for STIMULUS, STIMULUS-M, STIMULUS+ , STIMULUS-M… view at source ↗
Figure 3
Figure 3. Convergence comparison on strongly-convex optimization problem. [PITH_FULL_IMAGE:figures/full_fig_p037_3.png] view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: Training loss conver￾gence comparison (8-objective). We further test our algorithms on an 8-task problem with the river flow dataset [Nie et al., 2017], which is for flow prediction at eight locations in the Mississippi river network. In this experiment, we set η = 0.0…

Review history (2 revisions) →

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

44 extracted references · 28 canonical work pages

  1. [1]

    Uncertainty-aware search framework for multi-objective bayesian optimization

    Syrine Belakaria, Aryan Deshwal, Nitthilan Kannappan Jayakodi, and Janardhan Rao Doppa. Uncertainty-aware search framework for multi-objective bayesian optimization. In Proceedings of the AAAI Conference on Artificial Intelligence, volume 34, pages 10044--10052, 2020

    work page 2020

  2. [2]

    Convex optimization

    Stephen P Boyd and Lieven Vandenberghe. Convex optimization. Cambridge university press, 2004

    2004

  3. [3]

    An analysis of the softmax cross entropy loss for learning-to-rank with binary relevance

    Sebastian Bruch, Xuanhui Wang, Michael Bendersky, and Marc Najork. An analysis of the softmax cross entropy loss for learning-to-rank with binary relevance. In Proceedings of the 2019 ACM SIGIR international conference on theory of information retrieval, pages 75--78, 2019

    2019

  4. [4]

    Co-attentive multi-task learning for explainable recommendation

    Zhongxia Chen, Xiting Wang, Xing Xie, Tong Wu, Guoqing Bu, Yining Wang, and Enhong Chen. Co-attentive multi-task learning for explainable recommendation. In IJCAI, pages 2137--2143, 2019

    work page 2019

  5. [5]

    A fast and elitist multiobjective genetic algorithm: Nsga-ii

    Kalyanmoy Deb, Amrit Pratap, Sameer Agarwal, and TAMT Meyarivan. A fast and elitist multiobjective genetic algorithm: Nsga-ii. IEEE transactions on evolutionary computation, 6 0 (2): 0 182--197, 2002

    2002

  6. [6]

    Multiple-gradient descent algorithm (mgda) for multiobjective optimization

    Jean-Antoine D \'e sid \'e ri. Multiple-gradient descent algorithm (mgda) for multiobjective optimization. Comptes Rendus Mathematique, 350 0 (5-6): 0 313--318, 2012

    2012

  7. [7]

    Multicriteria optimization, volume 491

    Matthias Ehrgott. Multicriteria optimization, volume 491. Springer Science & Business Media, 2005

    work page 2005

  8. [8]

    Spider: Near-optimal non-convex optimization via stochastic path-integrated differential estimator

    Cong Fang, Chris Junchi Li, Zhouchen Lin, and Tong Zhang. Spider: Near-optimal non-convex optimization via stochastic path-integrated differential estimator. In S. Bengio, H. Wallach, H. Larochelle, K. Grauman, N. Cesa-Bianchi, and R. Garnett, editors, Advances in Neural Information Processing Systems, volume 31. Curran Associates, Inc., 2018

    work page 2018

Show all 44 references
  1. [9]

    Mitigating gradient bias in multi-objective learning: A provably convergent stochastic approach

    Heshan Fernando, Han Shen, Miao Liu, Subhajit Chaudhury, Keerthiram Murugesan, and Tianyi Chen. Mitigating gradient bias in multi-objective learning: A provably convergent stochastic approach. arXiv preprint arXiv:2210.12624, 2022

    arXiv

  2. [10]

    Variance reduction can improve trade-off in multi-objective learning

    Heshan Fernando, Lisha Chen, Songtao Lu, Pin-Yu Chen, Miao Liu, Subhajit Chaudhury, Keerthiram Murugesan, Gaowen Liu, Meng Wang, and Tianyi Chen. Variance reduction can improve trade-off in multi-objective learning. In ICASSP 2024 - 2024 IEEE International Conference on Acoust...

    2024

  3. [11]

    Steepest descent methods for multicriteria optimization

    J \"o rg Fliege and Benar Fux Svaiter. Steepest descent methods for multicriteria optimization. Mathematical methods of operations research, 51 0 (3): 0 479--494, 2000

    2000

  4. [12]

    Complexity of gradient descent for multiobjective optimization

    J \"o rg Fliege, A Ismael F Vaz, and Lu \' s Nunes Vicente. Complexity of gradient descent for multiobjective optimization. Optimization Methods and Software, 34 0 (5): 0 949--959, 2019

    2019

  5. [13]

    Stochastic first-and zeroth-order methods for nonconvex stochastic programming

    Saeed Ghadimi and Guanghui Lan. Stochastic first-and zeroth-order methods for nonconvex stochastic programming. SIAM Journal on Optimization, 23 0 (4): 0 2341--2368, 2013

    2013

  6. [14]

    Deep residual learning for image recognition

    Kaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian Sun. Deep residual learning for image recognition. cvpr. 2016. arXiv preprint arXiv:1512.03385, 2016

    2016 arXiv

  7. [15]

    Fine-grained fashion representation learning by online deep clustering

    Yang Jiao, Ning Xie, Yan Gao, Chien-Chih Wang, and Yi Sun. Fine-grained fashion representation learning by online deep clustering. In European Conference on Computer Vision, pages 19--35. Springer, 2022

    2022

  8. [16]

    Learning attribute and class-specific representation duet for fine-grained fashion analysis

    Yang Jiao, Yan Gao, Jingjing Meng, Jin Shang, and Yi Sun. Learning attribute and class-specific representation duet for fine-grained fashion analysis. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 11050--11059, 2023

    2023

  9. [17]

    A deep survival analysis method based on ranking

    Bingzhong Jing, Tao Zhang, Zixian Wang, Ying Jin, Kuiyuan Liu, Wenze Qiu, Liangru Ke, Ying Sun, Caisheng He, Dan Hou, et al. A deep survival analysis method based on ranking. Artificial intelligence in medicine, 98: 0 1--9, 2019

    2019

  10. [18]

    SCAFFOLD : Stochastic controlled averaging for federated learning

    Sai Praneeth Karimireddy, Satyen Kale, Mehryar Mohri, Sashank Reddi, Sebastian Stich, and Ananda Theertha Suresh. SCAFFOLD : Stochastic controlled averaging for federated learning. In Hal Daumé III and Aarti Singh, editors, Proceedings of the 37th International Conference on M...

    2020

  11. [19]

    Deep attentive ranking networks for learning to order sentences

    Pawan Kumar, Dhanajit Brahma, Harish Karnick, and Piyush Rai. Deep attentive ranking networks for learning to order sentences. In Proceedings of the AAAI Conference on Artificial Intelligence, volume 34, pages 8115--8122, 2020

    2020

  12. [20]

    Bayesian optimization algorithms for multi-objective optimization

    Marco Laumanns and Jiri Ocenasek. Bayesian optimization algorithms for multi-objective optimization. In International Conference on Parallel Problem Solving from Nature, pages 298--307. Springer, 2002

    2002

  13. [21]

    Mnist handwritten digit database

    Yann LeCun, Corinna Cortes, and CJ Burges. Mnist handwritten digit database. Available: http://yann. lecun. com/exdb/mnist, 1998

    1998

  14. [22]

    Pareto multi-task learning

    Xi Lin, Hui-Ling Zhen, Zhenhua Li, Qing-Fu Zhang, and Sam Kwong. Pareto multi-task learning. Advances in neural information processing systems, 32, 2019

    2019

  15. [23]

    The stochastic multi-gradient algorithm for multi-objective optimization and its application to supervised machine learning

    Suyun Liu and Luis Nunes Vicente. The stochastic multi-gradient algorithm for multi-objective optimization and its application to supervised machine learning. Annals of Operations Research, pages 1--30, 2021

    2021

  16. [24]

    Deep learning face attributes in the wild

    Ziwei Liu, Ping Luo, Xiaogang Wang, and Xiaoou Tang. Deep learning face attributes in the wild. In Proceedings of the IEEE international conference on computer vision, pages 3730--3738, 2015

    2015

  17. [25]

    Deep match to rank model for personalized click-through rate prediction

    Ze Lyu, Yu Dong, Chengfu Huo, and Weijun Ren. Deep match to rank model for personalized click-through rate prediction. In Proceedings of the AAAI Conference on Artificial Intelligence, volume 34, pages 156--163, 2020

    2020

  18. [26]

    Multi-label learning to rank through multi-objective optimization

    Debabrata Mahapatra, Chaosheng Dong, Yetian Chen, and Michinari Momma. Multi-label learning to rank through multi-objective optimization. In Proceedings of the 29th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, 2023 a

    2023

  19. [27]

    Querywise fair learning to rank through multi-objective optimization

    Debabrata Mahapatra, Chaosheng Dong, and Michinari Momma. Querywise fair learning to rank through multi-objective optimization. In Proceedings of the 29th ACM SIGKDD Conference on Knowledge Discovery and Data Mining, 2023 b

    2023

  20. [28]

    A stochastic multiple gradient descent algorithm

    Quentin Mercier, Fabrice Poirion, and Jean-Antoine D \'e sid \'e ri. A stochastic multiple gradient descent algorithm. European Journal of Operational Research, 271 0 (3): 0 808--817, 2018

    2018

  21. [29]

    Nonlinear multiobjective optimization, volume 12

    Kaisa Miettinen. Nonlinear multiobjective optimization, volume 12. Springer Science & Business Media, 2012

    2012

  22. [30]

    Algorithms for multicriterion optimization

    Hiroaki Mukai. Algorithms for multicriterion optimization. IEEE transactions on automatic control, 25 0 (2): 0 177--186, 1980

    1980

  23. [31]

    Image retrieval with attribute-associated auxiliary references

    Lin Nie, Keze Wang, Wenxiong Kang, and Yuefang Gao. Image retrieval with attribute-associated auxiliary references. In 2017 International Conference on Digital Image Computing: Techniques and Applications (DICTA), pages 1--6. IEEE, 2017

    2017

  24. [32]

    Policy gradient approaches for multi-objective sequential decision making

    Simone Parisi, Matteo Pirotta, Nicola Smacchia, Luca Bascetta, and Marcello Restelli. Policy gradient approaches for multi-objective sequential decision making. In 2014 International Joint Conference on Neural Networks (IJCNN), pages 2323--2330. IEEE, 2014

    2014

  25. [33]

    Multi-task video captioning with video and entailment generation

    Ramakanth Pasunuru and Mohit Bansal. Multi-task video captioning with video and entailment generation. In Proceedings of the 55th Annual Meeting of the Association for Computational Linguistics, 2017

    2017

  26. [34]

    Learning with average precision: Training image retrieval with a listwise loss

    Jerome Revaud, Jon Almazan, Rafael S Rezende, and Cesar Roberto de Souza. Learning with average precision: Training image retrieval with a listwise loss. In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 5107--5116, 2019

    2019

  27. [35]

    Dynamic routing between capsules

    Sara Sabour, Nicholas Frosst, and Geoffrey E Hinton. Dynamic routing between capsules. Advances in neural information processing systems, 30, 2017

    2017

  28. [36]

    Multi-task learning as multi-objective optimization

    Ozan Sener and Vladlen Koltun. Multi-task learning as multi-objective optimization. Advances in neural information processing systems, 31, 2018

    2018

  29. [37]

    Pairwise learning for neural link prediction

    Zhitao Wang, Yong Zhou, Litao Hong, Yuanhang Zou, Hanjing Su, and Shouzhi Chen. Pairwise learning for neural link prediction. arXiv preprint arXiv:2112.02936, 2021

    2021 arXiv

  30. [38]

    Deep multi-interest network for click-through rate prediction

    Zhibo Xiao, Luwei Yang, Wen Jiang, Yi Wei, Yi Hu, and Hao Wang. Deep multi-interest network for click-through rate prediction. In Proceedings of the 29th ACM International Conference on Information & Knowledge Management, pages 2265--2268, 2020

    2020

  31. [39]

    Empirically testing deep and shallow ranking models for click-through rate (ctr) prediction

    Yi-Che Yang, Ping-Ching Lai, and Hung-Hsuan Chen. Empirically testing deep and shallow ranking models for click-through rate (ctr) prediction. In 2020 International Conference on Technologies and Applications of Artificial Intelligence (TAAI), pages 147--152. IEEE, 2020

    2020

  32. [40]

    Pareto policy pool for model-based offline reinforcement learning

    Yijun Yang, Jing Jiang, Tianyi Zhou, Jie Ma, and Yuhui Shi. Pareto policy pool for model-based offline reinforcement learning. In International Conference on Learning Representations, 2022

    2022

  33. [41]

    Wassrank: Listwise document ranking using optimal transport theory

    Hai-Tao Yu, Adam Jatowt, Hideo Joho, Joemon M Jose, Xiao Yang, and Long Chen. Wassrank: Listwise document ranking using optimal transport theory. In Proceedings of the twelfth ACM international conference on web search and data mining, pages 24--32, 2019

    2019

  34. [42]

    Moea/d: A multiobjective evolutionary algorithm based on decomposition

    Qingfu Zhang and Hui Li. Moea/d: A multiobjective evolutionary algorithm based on decomposition. IEEE Transactions on evolutionary computation, 11 0 (6): 0 712--731, 2007

    2007

  35. [43]

    On the convergence of stochastic multi-objective gradient manipulation and beyond

    Shiji Zhou, Wenpeng Zhang, Jiyan Jiang, Wenliang Zhong, Jinjie GU, and Wenwu Zhu. On the convergence of stochastic multi-objective gradient manipulation and beyond. In Alice H. Oh, Alekh Agarwal, Danielle Belgrave, and Kyunghyun Cho, editors, Advances in Neural Information Pro...

    2022

  36. [44]

    Multi-task learning on heterogeneous graph neural network for substitute recommendation

    Tianchen Zhou, Michinari Momma, Chaosheng Dong, Fan Yang, Chenghuan Guo, Jin Shang, and Jia Kevin Liu. Multi-task learning on heterogeneous graph neural network for substitute recommendation. In 19th International Workshop on Mining and Learning with Graphs, 2023

    2023

Pith tools

Reviewed August 15, 2026 · model on record in the stance chip above.