Path Consistency Learning in Tsallis Entropy Regularized MDPs
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Proceedings of the 35th International Conference on Machine Learning, PMLR 80:979988, 2018.
Abstract
We study the sparse entropyregularized 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 nonzero probability for only a small number of actions. This addresses the main drawback of the standard Shannon entropyregularized RL (soft ERL) formulation, in which the optimal policy is softmax, and thus, may assign a nonnegligible probability mass to nonoptimal 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 sparse PCL, for the sparse ERL problem that can work with both onpolicy and offpolicy data. We first derive a 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 suboptimality of a policy which satisfies sparse consistency, and show that as we increase the number of actions, this suboptimality 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.
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