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Provably Convergent Two−Timescale Off−Policy Actor−Critic with Function Approximation

Shangtong Zhang‚ Bo Liu‚ Hengshuai Yao and Shimon Whiteson


We present GradientDICE for estimating the density ratio between the state distribution of the target policy and the sampling distribution in off-policy reinforcement learning. GradientDICE fixes several problems of GenDICE (Zhang et al., 2020a), the state-of-the-art for estimating such density ratios. Namely, the optimization problem in GenDICE is not a convex-concave saddle- point problem once nonlinearity in optimization variable parameterization is introduced to ensure positivity, so any primal-dual algorithm is not guaranteed to converge or find the desired solution. However, such nonlinearity is essential to ensure the consistency of GenDICE even with a tabular representation. This is a fundamental contradiction, resulting from GenDICE's original formulation of the optimization problem. In GradientDICE, we optimize a different objective from GenDICE by using the Perron-Frobenius theorem and eliminating GenDICE'€™s use of divergence, such that nonlinearity in parameterization is not necessary for GradientDICE, which is provably convergent under linear function approximation.

Book Title
ICML 2020: Proceedings of the Thirty−Seventh International Conference on Machine Learning