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Finite-Sample Analysis of Contractive Stochastic Approximation Using Smooth Convex Envelopes
Zaiwei Chen · Siva Theja Maguluri · Sanjay Shakkottai · Karthikeyan Shanmugam

Tue Dec 08 09:00 AM -- 11:00 AM (PST) @ Poster Session 1 #432

Stochastic Approximation (SA) is a popular approach for solving fixed-point equations where the information is corrupted by noise. In this paper, we consider an SA involving a contraction mapping with respect to an arbitrary norm, and show its finite-sample error bounds while using different stepsizes. The idea is to construct a smooth Lyapunov function using the generalized Moreau envelope, and show that the iterates of SA have negative drift with respect to that Lyapunov function. Our result is applicable in Reinforcement Learning (RL). In particular, we use it to establish the first-known convergence rate of the V-trace algorithm for off-policy TD-learning [18]. Importantly, our construction results in only a logarithmic dependence of the convergence bound on the size of the state-space.

Author Information

Zaiwei Chen (Georgia Institute of Technology)
Siva Theja Maguluri (Georgia Institute of Technology)
Sanjay Shakkottai (University of Texas at Austin)
Karthikeyan Shanmugam (IBM Research, NY)

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