Path Consistency Learning in Tsallis Entropy Regularized MDPs
This work addresses the issue of sub-optimal action probabilities in entropy-regularized RL for domains with many actions, offering a more efficient solution, though it is incremental as it builds on prior path consistency learning methods.
The paper tackles the problem of sparse entropy-regularized reinforcement learning by using Tsallis entropy to produce optimal policies with non-zero probabilities for only a small number of actions, addressing the drawback of standard softmax policies that assign non-negligible probability to non-optimal actions, especially as action counts increase; it proposes sparse path consistency learning algorithms and shows empirical advantages in large-action problems.
We study the sparse entropy-regularized reinforcement learning (ERL) problem in which the entropy term is a special form of the Tsallis entropy. The optimal policy of this formulation is sparse, i.e.,~at each state, it has non-zero probability for only a small number of actions. This addresses the main drawback of the standard Shannon entropy-regularized RL (soft ERL) formulation, in which the optimal policy is softmax, and thus, may assign a non-negligible probability mass to non-optimal actions. This problem is aggravated as the number of actions is increased. In this paper, we follow the work of Nachum et al. (2017) in the soft ERL setting, and propose a class of novel path consistency learning (PCL) algorithms, called {\em sparse PCL}, for the sparse ERL problem that can work with both on-policy and off-policy data. We first derive a {\em sparse consistency} equation that specifies a relationship between the optimal value function and policy of the sparse ERL along any system trajectory. Crucially, a weak form of the converse is also true, and we quantify the sub-optimality of a policy which satisfies sparse consistency, and show that as we increase the number of actions, this sub-optimality is better than that of the soft ERL optimal policy. We then use this result to derive the sparse PCL algorithms. We empirically compare sparse PCL with its soft counterpart, and show its advantage, especially in problems with a large number of actions.