Title: Stochastic Variance Reduction Methods for Policy Evaluation,
Abstract: Policy evaluation is a crucial step in many reinforcement-learning
procedures, which estimates a value function that predicts states' long-term
value under a given policy. In this paper, we focus on policy evaluation with
linear function approximation over a fixed dataset. We first transform the
empirical policy evaluation problem into a (quadratic) convex-concave saddle
point problem, and then present a primal-dual batch gradient method, as well as
two stochastic variance reduction methods for solving the problem. These
algorithms scale linearly in both sample size and feature dimension. Moreover,
they achieve linear convergence even when the saddle-point problem has only
strong concavity in the dual variables but no strong convexity in the primal
variables. Numerical experiments on benchmark problems demonstrate the
effectiveness of our methods.