Dual-Anchor Acceleration Is Near-Optimal for Stochastic Monotone Root-Finding

תקציר מקורי באנגליתarXiv:2609.36033v1 Announce Type: cross Abstract: Among distinct optimal acceleration mechanisms for deterministic monotone root-finding problems and fixed-point problems, dual-anchoring has recently been shown to admit a more robust direct stochastic extension than standard anchor acceleration. However, without additional strong monotonicity, the existing stochastic dual-anchoring guarantee has two limitations: first, it requires cocoercivity in expectation, and second, it attains only $O(\epsilon^{-3})$ oracle complexity, leaving a gap to the near-optimal $\tilde{O}(\epsilon^{-2})$ complexity achieved by other methods. In this work, we address both of these limitations by combining dual-anchoring with stochastic resolvent approximation and optimized variance control. For unbiased stochas