GradientDICE: Rethinking Generalized Offline Estimation of Stationary Values

Abstract

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., 2020), 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. Consequently, nonlinearity in parameterization is not necessary for GradientDICE, which is provably convergent under linear function approximation.

arXiv commentICML 2020

References in corpus (7)

• Addressing Function Approximation Error in Actor-Critic Methods
• DualDICE: Behavior-Agnostic Estimation of Discounted Stationary Distribution Corrections
• Finite-Sample Analysis of Proximal Gradient TD Algorithms
• Breaking the Curse of Horizon: Infinite-Horizon Off-Policy Estimation
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