Near-Optimal Pure Single-Loop Extragradient Method for Strongly Convex--Strongly Concave Minimax Optimization
A pure single-loop damped extragradient method achieves last-iterate linear convergence for strongly convex–strongly concave minimax optimization with near-optimal gradient complexity.
The method uses fixed parameters, two full-gradient evaluations per iteration, and an auxiliary feedback recursion, requiring no inner solves, accuracy schedules, or staged restarts. Reducing the squared Euclidean distance to the saddle point to an ε fraction requires O(√(κxκy)·log(2κxκy/ε)) full-gradient queries, attaining the optimal condition-number order up to logarithmic factors. Numerical experiments demonstrate the method's effectiveness.
- Fixed-parameter single-loop extragradient with two full-gradient evaluations per iteration
- O(√(κxκy)log(2κxκy/ε)) gradient queries matches optimal order up to logs
- No inner solves, accuracy schedules, or staged restarts required
- Last-iterate linear convergence proven for smooth strongly convex–strongly concave problems
From the original article
1 min read at arxiv.orgWe study smooth strongly convex--strongly concave minimax optimization with general nonlinear coupling in the deterministic unconstrained setting. We propose a pure single-loop damped extragradient method with fixed parameters and two new full-gradient evaluations per iteration after one initialization query.
By Minhao Zhang · arxiv.org
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