Path Consistency Learning in Tsallis Entropy Regularized MDPs


We study the sparse entropy-regularized RL (ERL) problem in which the entropy term is a special form of the Tsallis entropy. The opti mal 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 standard (soft) ERL, namely having softmax optimal policy. The problem with a soft max policy is that at every state, it may assign a non-negligible probability mass to non-optimal actions. This problem is aggravated as the number of actions is increased. Lee et al. (2018) studied the properties of the sparse ERL problem and proposed value-based algorithms to solve it. 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 on-policy and off-policy data. We first derive a consistency equation for sparse ERL, called sparse consistency. We then prove that sparse consistency only implies sub-optimality (unlike the soft consistency in soft ERL). We then use the sparse consistency to derive our sparse PCL algorithms. We empirically compare sparse PCL with its soft counterpart, and show its advantage, especially in problems with large number of actions.