math.OC · 2026-10-02 · No. 131

Optimization and Control, 2026-10-02.

5 new papers in math.OC. Titles, authors, abstracts. Links to arXiv. Want this in your inbox every morning? Subscribe →

01 — The papers

5 entries
  1. 01

    Optimal Stochastic Bilevel Optimization with First-Order Oracles

    Linxuan Pan, Junchi Yang

    math.OC · cs.LG

    We study nonconvex--strongly-convex bilevel optimization under a stochastic first-order oracle. We introduce MRT-FD, a single-loop first-order method that simultaneously tracks the upper-level variable, the lower-level solution, and the auxiliary response arising from implicit differentiation of the hyperobjective. MRT-FD performs one update of each variable per iteration and approximates the second-order derivative actions using order-$p$...

    arxiv.org/abs/2610.01843 · PDF

  2. 02

    Lower Bounds for Stochastic First-Order Algorithms with Variance Reduction in Nonconvex--Concave Minimax Optimization

    Jiayi Song, Zi Xu

    math.OC · cs.LG · stat.ML

    We establish complexity lower bounds for stochastic first-order algorithms in nonconvex--concave minimax optimization, allowing algorithms to use variance reduction. Our main contribution is a lower bound for a zero-respecting algorithm class that permits variance reduction, extending beyond the algorithmic restrictions imposed by some existing lower bounds. We consider objectives with an $L$-Lipschitz continuous joint gradient, a compact...

    arxiv.org/abs/2610.01662 · PDF

  3. 03

    Convergence Analysis of STORM Under Different Geometries

    Wei Jiang, Yibo Wang, Wenhao Yang, Rui Yan, Lijun Zhang, Zechao Li

    math.OC · cs.LG

    Stochastic recursive momentum (STORM) achieves fast convergence for nonconvex optimization via the variance reduction effect, but existing analyses rely on the strong average smoothness assumption. In this paper, we study the convergence of STORM for different objectives without average smoothness. We first revisit the results under average smoothness, obtaining the $O(T^{-1/3})$ bound for nonconvex objectives and the $O(σ^2/(μT))$ bound for...

    arxiv.org/abs/2610.01599 · PDF

  4. 04

    Optimal Momentum Methods for Stochastic Multilevel Compositional Optimization

    Wei Jiang, Rui Yan, Sifan Yang, Yuanyu Wan, Lijun Zhang, Zechao Li

    math.OC · cs.LG

    This paper investigates stochastic multi-level optimization where the objective is a nested composition of several smooth non-convex functions. We assume that only stochastic estimates of the gradient and function values for each level are accessible. Consequently, obtaining an accurate estimate of the overall gradient is challenging due to the nested structure. To address this, we employ a momentum-based estimator with mini-batches to track...

    arxiv.org/abs/2610.01572 · PDF

  5. 05

    Reinforcement Learning to Accelerate Primal-Dual Hybrid Gradient for Linear Programming

    Jinhwan Sul, Alex Oshin, Evangelos A. Theodorou

    math.OC · cs.AI · cs.LG

    Primal-dual hybrid gradient (PDHG) methods solve large-scale linear programs (LPs) using GPU-friendly matrix-vector products and projections, but their practical performance depends on coordinating algorithm parameters, acceleration, and restarts. We introduce GALLOP, which uses reinforcement learning to jointly learn continuous algorithm parameters and discrete restart decisions without differentiating through the solver. Its generalized...

    arxiv.org/abs/2610.01546 · PDF

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