Acceleration by stepsize hedging: Multi-step descent and the silver stepsize schedule

J Altschuler, P Parrilo - Journal of the ACM, 2023 - dl.acm.org
Can we accelerate the convergence of gradient descent without changing the algorithm—
just by judiciously choosing stepsizes? Surprisingly, we show that the answer is yes. Our …

Accelerated primal-dual gradient method for smooth and convex-concave saddle-point problems with bilinear coupling

D Kovalev, A Gasnikov… - Advances in Neural …, 2022 - proceedings.neurips.cc
In this paper we study the convex-concave saddle-point problem $\min_x\max_y f (x)+
y^\top\mathbf {A} xg (y) $, where $ f (x) $ and $ g (y) $ are smooth and convex functions. We …

Sharper rates for separable minimax and finite sum optimization via primal-dual extragradient methods

Y **, A Sidford, K Tian - Conference on Learning Theory, 2022 - proceedings.mlr.press
We design accelerated algorithms with improved rates for several fundamental classes of
optimization problems. Our algorithms all build upon techniques related to the analysis of …

Lifted primal-dual method for bilinearly coupled smooth minimax optimization

KK Thekumparampil, N He… - … Conference on Artificial …, 2022 - proceedings.mlr.press
We study the bilinearly coupled minimax problem: $\min_ {x}\max_ {y} f (x)+ y^\top A xh (y) $,
where $ f $ and $ h $ are both strongly convex smooth functions and admit first-order …

Smooth monotone stochastic variational inequalities and saddle point problems: A survey

A Beznosikov, B Polyak, E Gorbunov… - European Mathematical …, 2023 - ems.press
This paper is a survey of methods for solving smooth,(strongly) monotone stochastic
variational inequalities. To begin with, we present the deterministic foundation from which …

No-regret dynamics in the fenchel game: A unified framework for algorithmic convex optimization

JK Wang, J Abernethy, KY Levy - Mathematical Programming, 2024 - Springer
We develop an algorithmic framework for solving convex optimization problems using no-
regret game dynamics. By converting the problem of minimizing a convex function into an …

Semi-Streaming Bipartite Matching in Fewer Passes and Optimal Space∗

S Assadi, A Jambulapati, Y **, A Sidford, K Tian - Proceedings of the 2022 …, 2022 - SIAM
We provide Õ (∊–1)-pass semi-streaming algorithms for computing (1–∊)-approximate
maximum cardinality matchings in bipartite graphs. Our most efficient methods are …

Robust accelerated primal-dual methods for computing saddle points

X Zhang, NS Aybat, M Gürbüzbalaban - SIAM Journal on Optimization, 2024 - SIAM
We consider strongly-convex-strongly-concave saddle point problems assuming we have
access to unbiased stochastic estimates of the gradients. We propose a stochastic …

Inexact model: A framework for optimization and variational inequalities

F Stonyakin, A Tyurin, A Gasnikov… - Optimization Methods …, 2021 - Taylor & Francis
In this paper, we propose a general algorithmic framework for the first-order methods in
optimization in a broad sense, including minimization problems, saddle-point problems and …

Regularized box-simplex games and dynamic decremental bipartite matching

A Jambulapati, Y **, A Sidford, K Tian - arxiv preprint arxiv:2204.12721, 2022 - arxiv.org
Box-simplex games are a family of bilinear minimax objectives which encapsulate graph-
structured problems such as maximum flow [She17], optimal transport [JST19], and bipartite …