Polyak-Type Extragradient Methods for Monotone Root-Finding Problems
Read the original on arXiv Machine Learning →The paper investigates Polyak-type step-size strategies for extragradient methods applied to deterministic and stochastic monotone root-finding problems. It shows that the projection-based correction in deterministic extragradient can be derived by minimizing an upper bound on the distance to a solution, mirroring classical Polyak step-size construction. The authors provide a unified deterministic analysis that does not require global Lipschitz continuity, achieving sublinear convergence under H"older or “(L0, L1)-Lipschitz” conditions and linear convergence with strong monotonicity, and extend the approach to stochastic settings with both direct and decreasing step-size variants.
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