Doubly Robust Off-Policy Value and Gradient Estimation for Deterministic Policies
This addresses a key challenge in offline reinforcement learning for applications like medicine, where experimentation is limited, by enabling evaluation and learning of deterministic policies from logged data.
The paper tackles the problem of estimating policy value and gradient for deterministic policies from off-policy data with continuous actions, where standard estimators fail due to non-existent density ratios. It proposes new doubly robust estimators using kernelization approaches and shows they achieve asymptotic mean-squared error rates independent of horizon length.
Offline reinforcement learning, wherein one uses off-policy data logged by a fixed behavior policy to evaluate and learn new policies, is crucial in applications where experimentation is limited such as medicine. We study the estimation of policy value and gradient of a deterministic policy from off-policy data when actions are continuous. Targeting deterministic policies, for which action is a deterministic function of state, is crucial since optimal policies are always deterministic (up to ties). In this setting, standard importance sampling and doubly robust estimators for policy value and gradient fail because the density ratio does not exist. To circumvent this issue, we propose several new doubly robust estimators based on different kernelization approaches. We analyze the asymptotic mean-squared error of each of these under mild rate conditions for nuisance estimators. Specifically, we demonstrate how to obtain a rate that is independent of the horizon length.