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Policy Learning and Evaluation with Randomized Quasi-Monte Carlo

S├ębastien Arnold · Pierre L'Ecuyer · Liyu Chen · Yi-fan Chen · Fei Sha


Hard integrals arise frequently in reinforcement learning, for example when computing expectations in policy evaluation and policy iteration. They are often analytically intractable and typically estimated with Monte Carlo methods, whose sampling contributes to high variance in policy values and gradients. In this work, we propose to replace Monte Carlo samples with low-discrepancy point sets. We combine policy gradient methods with Randomized Quasi-Monte Carlo, yielding variance-reduced formulations of policy gradient and actor-critic algorithms. These formulations are effective for policy evaluation and policy improvement, as they outperform state-of-the-art algorithms on standardized continuous control benchmarks. Our empirical analyses validate the intuition that replacing Monte Carlo with Quasi-Monte Carlo yields significantly more accurate gradient estimates.

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