Sparse Markov Decision Processes with Causal Sparse Tsallis Entropy Regularization for Reinforcement Learning
This work addresses the need for efficient and robust policy regularization in reinforcement learning, offering a novel approach that is incremental but provides specific gains over prior methods.
The paper tackles the problem of inducing sparse and multi-modal optimal policies in reinforcement learning by proposing a sparse Markov decision process with causal sparse Tsallis entropy regularization, showing that it outperforms existing methods in convergence speed and performance with a constant performance error bound compared to a logarithmic increase in soft MDPs.
In this paper, a sparse Markov decision process (MDP) with novel causal sparse Tsallis entropy regularization is proposed.The proposed policy regularization induces a sparse and multi-modal optimal policy distribution of a sparse MDP. The full mathematical analysis of the proposed sparse MDP is provided.We first analyze the optimality condition of a sparse MDP. Then, we propose a sparse value iteration method which solves a sparse MDP and then prove the convergence and optimality of sparse value iteration using the Banach fixed point theorem. The proposed sparse MDP is compared to soft MDPs which utilize causal entropy regularization. We show that the performance error of a sparse MDP has a constant bound, while the error of a soft MDP increases logarithmically with respect to the number of actions, where this performance error is caused by the introduced regularization term. In experiments, we apply sparse MDPs to reinforcement learning problems. The proposed method outperforms existing methods in terms of the convergence speed and performance.