Temporal-Difference Value Estimation via Uncertainty-Guided Soft Updates

Temporal-Difference (TD) learning methods, such as Q-Learning, have proven effective at learning a policy to perform control tasks. One issue with methods like Q-Learning is that the value update introduces bias when predicting the TD target of a unfamiliar state. Estimation noise becomes a bias after the max operator in the policy improvement step, and carries over to value estimations of other states, causing Q-Learning to overestimate the Q value. Algorithms like Soft Q-Learning (SQL) introduce the notion of a soft-greedy policy, which reduces the estimation bias via soft updates in early stages of training. However, the inverse temperature $\beta$ that controls the softness of an update is usually set by a hand-designed heuristic, which can be inaccurate at capturing the uncertainty in the target estimate. Under the belief that $\beta$ is closely related to the (state dependent) model uncertainty, Entropy Regularized Q-Learning (EQL) further introduces a principled scheduling of $\beta$ by maintaining a collection of the model parameters that characterizes model uncertainty. In this paper, we present Unbiased Soft Q-Learning (UQL), which extends the work of EQL from two action, finite state spaces to multi-action, infinite state space Markov Decision Processes. We also provide a principled numerical scheduling of $\beta$, extended from SQL and using model uncertainty, during the optimization process. We show the theoretical guarantees and the effectiveness of this update method in experiments on several discrete control environments.