Approaching Quartic Convergence Rates for Quasi-Stochastic Approximation with Application to Gradient-Free OptimizationDownload PDF

Published: 31 Oct 2022, Last Modified: 14 Oct 2022NeurIPS 2022 AcceptReaders: Everyone
Keywords: Stochastic Approximation, Gradient-Free Optimization, Optimization
Abstract: Stochastic approximation is a foundation for many algorithms found in machine learning and optimization. It is in general slow to converge: the mean square error vanishes as $O(n^{-1})$. A deterministic counterpart known as quasi-stochastic approximation is a viable alternative in many applications, including gradient-free optimization and reinforcement learning. It was assumed in prior research that the optimal achievable convergence rate is $O(n^{-2})$. It is shown in this paper that through design it is possible to obtain far faster convergence, of order $O(n^{-4+\delta})$, with $\delta>0$ arbitrary. Two techniques are introduced for the first time to achieve this rate of convergence. The theory is also specialized within the context of gradient-free optimization, and tested on standard benchmarks. The main results are based on a combination of novel application of results from number theory and techniques adapted from stochastic approximation theory.
TL;DR: Convergence rate to the power of two with clever exploration
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