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Memory-Computation Tradeoffs in Semi Amortized Parametric Optimization

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Pith's one-line read Semi-amortized optimization's memory needs scale with parameter dimension, not solver dimension

desk verdict A real first pass at a memory-computation theory for amortized optimization, but the lower-bound theorems overclaim: they need geometry conditions that never make it into the statements. read the letter →

arxiv 2607.20769 v1 pith:Z66SPM76 submitted 2026-07-22 cs.LG

Shijie Pan , Agustin Castellano , Zeyu Shen , Enrique Mallada This is my paper · ORCID
classification cs.LG MSC 90C2590C60
keywords amortizedoptimizationmemorycomplexityparametricconvexprojectedgradientdescentwarm-startcoveringnumberstrongconvexitybeta-growthcondition
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

Offline memory can substitute for online computation when solving a family of parameterized convex optimization problems, but the exchange rate is set by two structural quantities: how fast the online optimizer converges and how sensitively the optimal solution moves with the problem parameter. This paper proves that the minimum memory M(K,ε) needed to guarantee ε-accuracy after K steps of projected gradient descent scales as (ρ^K/ε)^{dΘ} for strongly convex smooth problems — up to a factor of two in the ε exponent — where dΘ is the dimension of the parameter space, not the dimension of the decision variable. For objectives satisfying a β-growth condition with β>2, the memory requirement is close to (ε^{-(β-2)/β} − K)^{dΘ/(β-2)} and exhibits a phase transition: once K reaches roughly ε^{-(β-2)/β}, additional memory provides no benefit. The paper also shows that accelerating a fast linearly-convergent solver with memory is exponentially costly in K, while accelerating a slow sublinear solver is only polynomially costly. These bounds, verified on parameterized ridge regression, give the first matching memory–computation–accuracy characterization for semi-amortized parametric convex optimization.

What carries the argument

The central object is the (K,ε)-Θ-net: a finite set of stored parameters whose nearest-neighbour predictor returns a warm start close enough that K steps of projected gradient descent reach ε accuracy. Memory complexity M(K,ε) is the minimum cardinality of such a net. The proof machinery reduces the problem to covering Θ at radius R ≈ E^{-1}(K,ε)/(2LΘ), where E(K,gap) is PGD's convergence-rate bound and the optimality gap is Lipschitz in the parameter with constant 2LΘ (Lemma 3). The lower bounds are produced by explicit hard function families — a quadratic with minimizer x⋆(θ)=(LΘ/μRX)(θ,0) for strong convexity, and f(x;θ)=Φ∥x−(θ,0)/(RX+RΘ)∥^β₂ for β-growth — whose PGD dynamics are exactly

What would settle it

Construct a strongly convex parametric family with fixed parameter dimension dΘ and two different decision dimensions dX; if the measured minimal memory M(K,ε) moves with dX, Theorem 1's dΘ-only scaling fails. Alternatively, on a β-growth family with known Φ,Lf,2, fix ε and increase K while adding memory; if required memory keeps shrinking when K is pushed past the predicted threshold ε^{-(β-2)/β}, the phase-transition claim is contradicted.

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Extended reading notes

Core claim

The paper establishes that the memory complexity M(K,ε) — the fewest stored optimal solutions needed so that K steps of projected gradient descent reach ε accuracy for every parameter — is governed by a covering of the parameter space whose radius is set by the optimizer's convergence rate and the parameter-Lipschitz constant of the objective. Theorem 1 gives Ω((RΘLΘ ρ^K/√ε)^{dΘ}) ≤ M(K,ε) ≤ O((RΘLΘ ρ^K/ε)^{dΘ}) under μ-strong convexity and smoothness, where ρ=1−μ/Lf,2 is PGD's contraction rate; thus memory depends on the parameter dimension dΘ rather than the decision dimension dX, and warm-start memory is useful only while K < log(1/ε)/log(1/ρ). Theorem 2 extends near-matching bounds to co

Load-bearing premise

The load-bearing premise is that the lower-bound hard instances are representative of all allowed geometries; the β-growth lower bound is proven only for instances satisfying RX>RΘ and RX+RΘ≥2.314, yet Theorem 2 states it without those conditions, so for other geometries the claimed memory requirement may be an overestimate.

Editorial extensions

If this is right

  • Memory scales with the parameter dimension dΘ, not the decision dimension dX, so amortization is viable precisely when the parameter space is low-dimensional relative to the decision space.
  • Under strong convexity, extra memory yields essentially nothing once K ≥ log(1/ε)/log(1/ρ); past that threshold PGD alone already reaches ε-accuracy and M(K,ε)=Θ(1).
  • Accelerating fast solvers is exponentially expensive: to improve PGD's linear rate by a factor α, memory must grow like (1/α)^{KdΘ}.
  • For β-growth problems with β>2, memory is a cheap substitute: the memory cost of α-acceleration grows only polynomially in K.
  • A phase transition separates the regimes: beyond K≈ε^{-(β-2)/β}, memory stops helping; the transition appears in both upper and lower bounds, marking it intrinsic to the problem class.

Reading between the lines

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

  • Editorial inference: the dΘ-dependence means any reduction in effective parameter dimension — a manifold, sparsity, or symmetry — should multiplicatively shrink memory; this is a roadmap, not a result, in the paper.
  • Editorial inference: the β-growth phase transition should be visible in a single experiment: fix ε and plot required memory vs K; the curve should flatten at K≈(16βLf,2/((β−2)Φ^{2/β}))ε^{-(β-2)/β}. The paper's Figure 2 already shows this flattening for β=4,6.
  • Editorial concern about the lower bound: the hard instance requires RX>RΘ and RX+RΘ≥2.314, conditions absent from Theorem 2's statement; whether the Ω bound survives without them is open.
  • Editorial extension: the meta-framework's two-input structure suggests the same memory–computation tradeoff can be derived for accelerated methods, projection-free schemes, or nonconvex problems once their convergence rates are known.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 3 minor

Summary. The paper studies a semi-amortized parametric optimization protocol: an offline phase stores M optimal solutions at selected parameters; online, a nearest-neighbor warm start is refined by K projected gradient descent steps. It defines M(K,ε), the minimal memory needed to guarantee ε-accuracy over the whole parameter space, and derives upper and lower bounds for μ-strongly convex objectives (Theorem 1) and for convex objectives satisfying a β-growth condition with β>2 (Theorem 2, restated as Theorem 4). It also provides corollaries on the memory cost of acceleration, a meta-framework reducing the analysis to an optimizer convergence rate and a solution-map sensitivity, and experiments on parameterized Tikhonov regression.

Significance. If the results held in the stated generality, they would provide a useful complexity-theoretic characterization of memory–computation tradeoffs in amortized optimization: memory scales with the parameter dimension dΘ rather than the decision dimension dX, linearly convergent optimizers are exponentially expensive to accelerate, and β-growth problems exhibit a phase transition in the online budget K. The paper's strengths include explicit constants, detailed proofs in the appendices, no fitted parameters in the bounds, a clear reduction framework, and experiments whose structural constants are computed in closed form. The main caveat is that both lower-bound proofs rely on geometric restrictions on X and Θ that are not present in the theorem statements, so the matching/near-matching lower bounds are not yet established for the full claimed class.

major comments (2)
  1. [Theorem 4 / Appendix F, Eq. (22)] The lower bound in Theorem 4 is proved by reusing the hard family (13) from Appendix E, which is introduced 'with RX > RΘ (strict) and RX + RΘ ≥ 2.314' (Appendix E, below Eq. (13)). Neither condition appears in Theorem 4's hypotheses. These conditions are needed for the proof: the unconstrained minimizer x⋆(θ)=θ/(RX+RΘ) must lie in X, the warm start and all PGD iterates must remain in B2(0,RΘ) where the sublinear analysis is valid, and the initial distance must satisfy ∥x0−x⋆∥≤0.865RΘ for the Bernoulli/linearization step leading to Eq. (20). If RX≤RΘ or RX+RΘ<2.314, the projection onto X can become active and the telescoping argument in Appendix E is no longer valid. Thus the Ω lower bound in Eq. (22), and with it the claimed phase transition in K, is not established for all geometries satisfying Assumptions 1–4 and 6. The same issue affects the lower-bound statement of Theorem 2 in Sect
  2. [Theorem 1 / Appendix D] The lower-bound construction in Appendix D assumes RX ≥ sqrt(LΘRΘ/µ) to ensure that the unconstrained minimizer x⋆(θ)=LΘθ/(µRX) lies in B2(0,RX). This condition is not part of Theorem 1's statement or of Assumptions 1–5. If RX < sqrt(LΘRΘ/µ), the analytic minimizer is outside X, the projection onto X is active, and the derivation of the exact warm-start gap and the tight rate ρ² collapses. Hence the bound Ω((RΘLΘρ^K/√ε)^{dΘ}) is not proved for the full parameter regime claimed. The theorem should either include this condition explicitly or be extended with a different hard instance for small X.
minor comments (3)
  1. [Abstract and Section 4.1] The abstract says 'matching upper and lower bounds' for the strongly convex case, but Theorem 1 has an ε versus √ε gap in the exponent; the body correctly calls these 'almost matching.' Please reword the abstract to avoid overstating the result.
  2. [Theorem 2 statement, Section 4.2] The notation '−O(K)' and '−Ω(K)' inside the bounds is non-quantitative; the explicit constants C1 and C2 appear only in Theorem 4 in Appendix F. Please use the explicit constants in the main statement.
  3. [Section 4.3 and Contributions] Mα(K) is defined as the 'minimum memory required' for a prescribed acceleration, but Corollaries 1 and 2 only provide suff suff suff suff suff suff suff suff suff suff suff suff suff suff suff suff suff suff suff suff suff suff suff suff suff suff suff suff suff suff suff suff suff suff suff suff suff suff suff suff suff suff suff suff suff suff suff suff suff suff suff suff suff suff suff suff suff suff suff suff suff suff suff suff suff suff suff suff suff suff suff suff suff suff suff suff suff suff suff suff suff suff suff suff suff suff suff suff suff suff suff suff suff suff suff suff suff suff suff suff suff suff suff suff suff suff suff suff suff suff suff suff suff suff suff suff suff suff suff suff suff suff suff suff suff suff suff suff suff suff suff suff suff suff suff suff suff suff suff suff suff suff suff suff suff suff suff suff suff suff suff suff suff suff suff suff su

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the memory bounds are cover/pack consequences of stated assumptions and external convergence theorems, not restatements of the conclusion.

full rationale

The derivation is self-contained as a reduction. M(K,ε) is defined (Defs. 1–2) as the minimum cardinality of a (K,ε)-Θ-net, and the upper bounds chain Lemma 3 (proved in Appendix C) with standard PGD/KL convergence rates ([9],[12],[17]; Lemma 5 is proved in Appendix F) and covering of Θ; the lower bounds use explicit hard families with closed-form minimizers and PGD dynamics (quadratic family in Appendix D; β-growth family (13)/(30) in Appendices E/F) followed by packing. No fitted parameter is renamed as a prediction, and the experiments compare measured K of warm-started PGD with the bounds rather than fitting the bounds. The only self-citation, [13], motivates a geometric ball-containment definition in Appendix A; the main lower-bound proofs take Θ to be a ball and do not rely on it, so it is not load-bearing. The flagged assumption gap in the β-growth lower bound—Appendix E constructs the hard instance only for RX>RΘ and RX+RΘ≥2.314, conditions not stated in Theorem 4—is a correctness/completeness gap, not circularity: the lower bound is derived from an explicit instance class and does not presuppose the theorem's conclusion.

Assumptions & free parameters 0 free parameters · 11 assumptions · 0 invented entities

The central claims rest on standard convex-optimization assumptions and cited convergence-rate theorems; no new entities are postulated and no constants are fitted. The only non-standard moves are the hard-instance constructions in the lower-bound proofs, which are proof devices, not extra assumptions.

assumptions (11)
  • domain assumption Assumption 1: f(·;θ) convex in x
    Restricts problem class; used for convergence rates.
  • domain assumption Assumption 2: X, Θ compact convex with radii RX, RΘ; dX ≫ dΘ
    Compactness enables covering; dimension controls exponent.
  • domain assumption Assumption 3: f LΘ-Lipschitz in θ, Lf,1-Lipschitz and Lf,2-smooth in x
    Lipschitzness in θ bounds warm-start gap; smoothness used in PGD rates.
  • domain assumption Assumption 4: fixed feasible set X
    Allows PGD projection onto fixed set.
  • domain assumption Assumption 5: μ-strong convexity (Theorem 1)
    Gives linear convergence.
  • domain assumption Assumption 6: β-growth condition (Theorem 2)
    Gives sublinear convergence for β>2.
  • domain assumption Assumption 7: positive reach of Θ complement (random sampling, Appendix A)
    Needed for probabilistic covering guarantees.
  • standard math Linear convergence of PGD for smooth strongly convex functions (Section 9.3.1 of [12])
    Used as the convergence-rate input in Theorem 1 upper bound and lower bound hard instance.
  • standard math β-growth convergence bound of Lemma 5 from Frankel et al. [17, Theorem 4.iii]
    Provides the sublinear rate used in Theorem 2 upper bound; not derived in the paper.
  • standard math Covering/packing volume bounds (Lemmas 1–2) and γ-scaled ball containment (Definition 3)
    Used to convert covering radius to memory M.
  • standard math Norm equivalence in finite-dimensional spaces ([22, Theorem 2.1])
    Transfers covering/packing between ∥·∥ and ∥·∥2.

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Cite this review

Pith. "Pith review of Memory-Computation Tradeoffs in Semi Amortized Parametric Optimization." pith.science (2026). https://pith.science/paper/Z66SPM76

@misc{pith2026260720769,
  author       = {Pith},
  title        = {Pith review of: Memory-Computation Tradeoffs in Semi Amortized Parametric Optimization},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/Z66SPM76}},
  note         = {Machine review of arXiv:2607.20769}
}
abstract

Learning-enabled decision systems often use offline data or computation to reduce online compute cost. Despite the empirical success of such approaches, there is limited general understanding of how much offline information is needed to achieve a desired accuracy under a fixed online computation budget. We study this question through the lens of amortized parametric optimization: an offline phase stores a finite memory of solved problem instances, and an online phase produces a solution to a new instance by retrieving a warm start and applying $K$ steps of projected gradient descent. We analyze this setup for smooth convex parametric optimization over a compact domain, using a nonparametric predictor built from the stored offline solutions. For $\mu$-strongly convex objectives, we establish matching upper and lower bounds on the memory required to guarantee $\varepsilon$-accuracy under a fixed online iteration budget $K$. For convex objectives satisfying a $\beta$-growth condition ($\beta>2$), we obtain near-matching bounds and identify a phase transition in $K$ beyond which additional memory provides no benefit. We further provide a general proof framework that (i) explicitly quantifies the memory cost of acceleration---how much offline memory is required to achieve a prescribed speedup over the unaided online optimizer---and (ii) identifies two key quantities driving this cost: the convergence rate of the online optimizer and the Lipschitz sensitivity of the solution map to the problem parameter. Experiments on parameterized ridge regression confirm the predicted memory--computation--accuracy tradeoffs.

Figures

Figures reproduced from arXiv: 2607.20769 by the authors.

Figure 1
Figure 1. An overview of our framework [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. Average K to reach accuracy ε as a function of memory size M on the Tikhonov family (5); (a) is ridge regression. Shaded bands show ±1 standard deviation over N = 100 samples of θ. the predicted memory–computation tradeoff in both the strongly convex (Theorem 1) and β-growth (Theorem 2) regimes. Setup. We consider the parametric Tikhonov-regularized regression problem min x∈X 1 β ∥Ax − θ∥ β 2 + λ β ∥x∥ β 2 , (5) on … view at source ↗
Figure 3
Figure 3. The uniform grid cover ΘM,Uni is constructed over an irregular set Θ. Geometric regularity In order to use Algorithm 3 for random sampling over Θ, we need the following assumption to avoid ill-condition sets. Assumption 7 (Geometric regularity (Definition 2.2 in [2])). We assume that for Θ ⊂ R dΘ , its complement Θc has positive reach, i.e., reach(Θc ) ≥ r for some r > 0. Positive reach excludes pathological geometr… view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: The examples used to establish the Ω(·) lower bounds in Theorems 1, 2 are constructed based on this figure. Both X (orange) and Θ (blue) are taken to be balls centered at the origin, with dimensions dΘ < dX and radii RΘ ≤ RX , respectively. Under this construction, we …

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Works this paper leans on

48 extracted references · 4 linked inside Pith

  1. [13]

    Data-driven acceleration of MPC with guarantees.arXiv preprint arXiv:2511.13588, 2025

    Agustin Castellano, Shijie Pan, and Enrique Mallada. Data-driven acceleration of MPC with guarantees.arXiv preprint arXiv:2511.13588, 2025

    arXiv 2025

  2. [1]

    Zico Kolter

    Akshay Agrawal, Brandon Amos, Shane Barratt, Stephen Boyd, Steven Diamond, and J. Zico Kolter. Differentiable convex optimization layers. InAdvances in Neural Information Processing Systems, volume 32, 2019

    2019

  3. [2]

    Geometry of a set and its random covers.arXiv preprint arXiv:2112.14979, 2021

    Enrique Alvarado, Bala Krishnamoorthy, and Kevin R Vixie. Geometry of a set and its random covers.arXiv preprint arXiv:2112.14979, 2021

    arXiv 2021

  4. [3]

    Tutorial on amortized optimization.Foundations and Trends in Machine Learning, 16(5):592–732, 2023

    Brandon Amos. Tutorial on amortized optimization.Foundations and Trends in Machine Learning, 16(5):592–732, 2023

    2023

  5. [4]

    Zico Kolter

    Brandon Amos and J. Zico Kolter. OptNet: Differentiable optimization as a layer in neural networks. InProceedings of the 34th International Conference on Machine Learning, volume 70, pages 136–145. PMLR, 2017

    2017

  6. [5]

    Hoffman, David Pfau, Tom Schaul, Brendan Shillingford, and Nando de Freitas

    Marcin Andrychowicz, Misha Denil, Sergio Gomez, Matthew W. Hoffman, David Pfau, Tom Schaul, Brendan Shillingford, and Nando de Freitas. Learning to learn by gradient descent by gradient descent. InAdvances in Neural Information Processing Systems, volume 29, 2016

    2016

  7. [6]

    Semi-explicit linear MPC using a warm-started active-set QP algorithm with exact complexity guarantees

    Daniel Arnström and Daniel Axehill. Semi-explicit linear MPC using a warm-started active-set QP algorithm with exact complexity guarantees. In2021 60th IEEE Conference on Decision and Control (CDC), pages 2557–2562. IEEE, 2021

    2021

  8. [7]

    Data-driven algorithm design

    Maria-Florina Balcan. Data-driven algorithm design. In Tim Roughgarden, editor,Beyond the Worst-Case Analysis of Algorithms, pages 626–645. Cambridge University Press, 2021

    2021

Show all 48 references
  1. [8]

    Bauschke and Patrick L

    Heinz H. Bauschke and Patrick L. Combettes. Correction to: convex analysis and monotone operator theory in Hilbert spaces. InConvex Analysis and Monotone Operator Theory in Hilbert Spaces, pages C1–C4. Springer, 2020

    2020

  2. [9]

    Gradient-based algorithms with applications to signal-recovery problems

    Amir Beck and Marc Teboulle. Gradient-based algorithms with applications to signal-recovery problems. InConvex Optimization in Signal Processing and Communications, pages 42–88. Cambridge University Press, 2010

    2010

  3. [10]

    Online mixed-integer optimization in milliseconds

    Dimitris Bertsimas and Bartolomeo Stellato. Online mixed-integer optimization in milliseconds. INFORMS Journal on Computing, 34(4):2229–2248, 2022

    2022

  4. [11]

    Jérôme Bolte, Trong Phong Nguyen, Juan Peypouquet, and Bruce W. Suter. From error bounds to the complexity of first-order descent methods for convex functions.Mathematical Programming, 165(2):471–507, 2017

    2017

  5. [12]

    Cambridge University Press, 2004

    Stephen Boyd and Lieven Vandenberghe.Convex Optimization. Cambridge University Press, 2004

    2004

  6. [14]

    Learning to optimize: A primer and a benchmark.Journal of Machine Learning Research, 23(189):1–59, 2022

    Tianlong Chen, Xiaohan Chen, Wuyang Chen, Howard Heaton, Jialin Liu, Zhangyang Wang, and Wotao Yin. Learning to optimize: A primer and a benchmark.Journal of Machine Learning Research, 23(189):1–59, 2022

    2022

  7. [15]

    Model-agnostic meta-learning for fast adapta- tion of deep networks

    Chelsea Finn, Pieter Abbeel, and Sergey Levine. Model-agnostic meta-learning for fast adapta- tion of deep networks. InInternational Conference on Machine Learning, pages 1126–1135. PMLR, 2017

    2017

  8. [16]

    Probabilistic model-agnostic meta-learning

    Chelsea Finn, Kelvin Xu, and Sergey Levine. Probabilistic model-agnostic meta-learning. Advances in Neural Information Processing Systems, 31, 2018

    2018

  9. [17]

    Splitting methods with variable met- ric for Kurdyka–Łojasiewicz functions and general convergence rates.Journal of Optimization Theory and Applications, 165(3):874–900, 2015

    Pierre Frankel, Guillaume Garrigos, and Juan Peypouquet. Splitting methods with variable met- ric for Kurdyka–Łojasiewicz functions and general convergence rates.Journal of Optimization Theory and Applications, 165(3):874–900, 2015

    2015

  10. [18]

    Learning fast approximations of sparse coding

    Karol Gregor and Yann LeCun. Learning fast approximations of sparse coding. InProceedings of the 27th International Conference on Machine Learning, pages 399–406, 2010. 10

    2010

  11. [19]

    Data-driven algorithm design.Communications of the ACM, 63(6):87–94, 2020

    Rishi Gupta and Tim Roughgarden. Data-driven algorithm design.Communications of the ACM, 63(6):87–94, 2020

    2020

  12. [20]

    Learning an approximate model predictive controller with guarantees.IEEE Control Systems Letters, 2(3):543–548, 2018

    Michael Hertneck, Johannes Köhler, Sebastian Trimpe, and Frank Allgöwer. Learning an approximate model predictive controller with guarantees.IEEE Control Systems Letters, 2(3):543–548, 2018

    2018

  13. [21]

    Jerez, Paul J

    Juan L. Jerez, Paul J. Goulart, Stefan Richter, George A. Constantinides, Eric C. Kerrigan, and Manfred Morari. Embedded online optimization for model predictive control at megahertz rates. IEEE Transactions on Automatic Control, 59(12):3238–3251, 2014

    2014

  14. [22]

    World Scientific Publishing Company, 2016

    Xiao Qing Jin and Seak-Weng V ong.An Introduction to Applied Matrix Analysis, volume 20. World Scientific Publishing Company, 2016

    2016

  15. [23]

    Balcan, Ameet Talwalkar, and Sergei Vassilvitskii

    Mikhail Khodak, Maria-Florina F. Balcan, Ameet Talwalkar, and Sergei Vassilvitskii. Learning predictions for algorithms with predictions. InAdvances in Neural Information Processing Systems, volume 35, pages 3542–3555, 2022

    2022

  16. [24]

    Miller, David Sontag, and Alexander M

    Yoon Kim, Sam Wiseman, Andrew C. Miller, David Sontag, and Alexander M. Rush. Semi- amortized variational autoencoders. InProceedings of the 35th International Conference on Machine Learning, volume 80, pages 2678–2687. PMLR, 2018

    2018

  17. [25]

    Kingma and Max Welling

    Diederik P. Kingma and Max Welling. Auto-encoding variational Bayes. InInternational Conference on Learning Representations, 2014

    2014

  18. [26]

    Machine learning-based warm starting of active set methods in embedded model predictive control.Engineering Applications of Artificial Intelligence, 77:1–8, 2019

    Martin Klauˇco, Martin Kalúz, and Michal Kvasnica. Machine learning-based warm starting of active set methods in embedded model predictive control.Engineering Applications of Artificial Intelligence, 77:1–8, 2019

    2019

  19. [27]

    Guoyin Li and Ting Kei Pong. Calculus of the exponent of Kurdyka–Łojasiewicz inequality and its applications to linear convergence of first-order methods.Foundations of Computational Mathematics, 18(5):1199–1232, 2018

    2018

  20. [28]

    Competitive caching with machine learned advice

    Thodoris Lykouris and Sergei Vassilvitskii. Competitive caching with machine learned advice. InProceedings of the 35th International Conference on Machine Learning, volume 80, pages 3302–3311. PMLR, 2018

    2018

  21. [29]

    Warm start of mixed-integer programs for model predictive control of hybrid systems.IEEE Transactions on Automatic Control, 66(6):2433–2448, 2020

    Tobia Marcucci and Russ Tedrake. Warm start of mixed-integer programs for model predictive control of hybrid systems.IEEE Transactions on Automatic Control, 66(6):2433–2448, 2020

    2020

  22. [30]

    David Q. Mayne. Model predictive control: Recent developments and future promise.Automat- ica, 50(12):2967–2986, 2014

    2014

  23. [31]

    Algorithms with predictions

    Michael Mitzenmacher and Sergei Vassilvitskii. Algorithms with predictions. In Tim Rough- garden, editor,Beyond the Worst-Case Analysis of Algorithms, pages 646–662. Cambridge University Press, 2021

    2021

  24. [32]

    Clustered task-aware meta-learning by learning from learning paths.IEEE Transactions on Pattern Analysis and Machine Intelligence, 45(8):9426–9438, 2023

    Danni Peng and Sinno Jialin Pan. Clustered task-aware meta-learning by learning from learning paths.IEEE Transactions on Pattern Analysis and Machine Intelligence, 45(8):9426–9438, 2023

    2023

  25. [33]

    Improving online algorithms via ML predic- tions

    Manish Purohit, Zoya Svitkina, and Ravi Kumar. Improving online algorithms via ML predic- tions. InAdvances in Neural Information Processing Systems, volume 31, 2018

    2018

  26. [34]

    James Requeima, Jonathan Gordon, John Bronskill, Sebastian Nowozin, and Richard E. Turner. Fast and flexible multi-task classification using conditional neural adaptive processes.Advances in Neural Information Processing Systems, 32, 2019

    2019

  27. [35]

    Stochastic backpropagation and approximate inference in deep generative models

    Danilo Jimenez Rezende, Shakir Mohamed, and Daan Wierstra. Stochastic backpropagation and approximate inference in deep generative models. InProceedings of the 31st International Conference on Machine Learning, volume 32, pages 1278–1286. PMLR, 2014

    2014

  28. [36]

    End-to-end learning to warm-start for real-time quadratic optimization

    Rajiv Sambharya, Georgina Hall, Brandon Amos, and Bartolomeo Stellato. End-to-end learning to warm-start for real-time quadratic optimization. InLearning for Dynamics and Control Conference, pages 220–234. PMLR, 2023. 11

    2023

  29. [37]

    Learning to warm- start fixed-point optimization algorithms.Journal of Machine Learning Research, 25(166):1–46, 2024

    Rajiv Sambharya, Georgina Hall, Brandon Amos, and Bartolomeo Stellato. Learning to warm- start fixed-point optimization algorithms.Journal of Machine Learning Research, 25(166):1–46, 2024

    2024

  30. [38]

    Schmidtobreick, Daniel Arnström, Paul Häusner, and Jens Sjölund

    Ella J. Schmidtobreick, Daniel Arnström, Paul Häusner, and Jens Sjölund. Warm-starting active-set solvers using graph neural networks.arXiv preprint arXiv:2511.13174, 2025

    2025 arXiv

  31. [39]

    Use of machine learning models to warmstart column generation for unit commitment.INFORMS Journal on Computing, 36(4):1129–1146, 2024

    Nagisa Sugishita, Andreas Grothey, and Ken McKinnon. Use of machine learning models to warmstart column generation for unit commitment.INFORMS Journal on Computing, 36(4):1129–1146, 2024

    2024

  32. [40]

    Sutton and Andrew G

    Richard S. Sutton and Andrew G. Barto.Reinforcement Learning: An Introduction, volume 1. MIT Press, 2018

    2018

  33. [41]

    Zeilinger, Sebastian Trimpe, and Johannes Köh- ler

    Abdullah Tokmak, Christian Fiedler, Melanie N. Zeilinger, Sebastian Trimpe, and Johannes Köh- ler. Automatic nonlinear MPC approximation with closed-loop guarantees.IEEE Transactions on Automatic Control, 70:6388–6403, 2025

    2025

  34. [42]

    Neural fixed-point acceleration for convex optimiza- tion.arXiv preprint arXiv:2107.10254, 2021

    Shobha Venkataraman and Brandon Amos. Neural fixed-point acceleration for convex optimiza- tion.arXiv preprint arXiv:2107.10254, 2021

    2021 arXiv

  35. [43]

    Risto Vuorio, Shao-Hua Sun, Hexiang Hu, and Joseph J. Lim. Multimodal model-agnostic meta-learning via task-aware modulation.Advances in Neural Information Processing Systems, 32, 2019

    2019

  36. [44]

    Structured prediction for conditional meta-learning.Advances in Neural Information Processing Systems, 33:2587–2598, 2020

    Ruohan Wang, Yiannis Demiris, and Carlo Ciliberto. Structured prediction for conditional meta-learning.Advances in Neural Information Processing Systems, 33:2587–2598, 2020

    2020

  37. [45]

    Xavier, Feng Qiu, and Shabbir Ahmed

    Álinson S. Xavier, Feng Qiu, and Shabbir Ahmed. Learning to solve large-scale security- constrained unit commitment problems.INFORMS Journal on Computing, 33(2):739–756, 2021

    2021

  38. [46]

    Stochastic convex optimization: Faster local growth implies faster global convergence

    Yi Xu, Qihang Lin, and Tianbao Yang. Stochastic convex optimization: Faster local growth implies faster global convergence. InInternational Conference on Machine Learning, pages 3821–3830. PMLR, 2017

    2017

  39. [47]

    Safe and near-optimal policy learning for model predictive control using primal-dual neural networks

    Xiaojing Zhang, Monimoy Bujarbaruah, and Francesco Borrelli. Safe and near-optimal policy learning for model predictive control using primal-dual neural networks. In2019 American Control Conference (ACC), pages 354–359. IEEE, 2019

    2019

  40. [48]

    p(p−1)ε min{Lf,2, LΘ} − p−2 p (RX +R Θ) 2(p−2) p − 2 min{Lf,2, LΘ} Lf,2 p−2 p−1 K # dΘ p−2 +   (xii) ≥Ω  

    Dominic Zhao, Seijin Kobayashi, João Sacramento, and Johannes von Oswald. Meta-learning via hypernetworks. In4th Workshop on Meta-Learning at NeurIPS 2020 (MetaLearn 2020). NeurIPS, 2020. A Oracle assumption gap between uniform grid sampling and uniform random sampling All the...

    2020

Pith tools

Reviewed August 1, 2026 · model on record in the stance chip above.