Tsallis Entropy Regularization for Linear Quadratic Regulator and Kullback-Leibler Control

Shannon entropy regularization is widely adopted in optimal control due to its ability to promote exploration and enhance robustness, e.g., maximum entropy reinforcement learning known as Soft Actor-Critic. The aim of this paper is to show that formulations based on Tsallis entropy, which is a one-parameter extension of Shannon entropy, retain many of the structural and computational advantages of Shannon-entropy-based approaches while offering additional benefits. In particular, we derive a closed-form solution for the linear quadratic regulator and an efficient computational method for the Kullback-Leibler control problem. We also demonstrate its usefulness in balancing between exploration and sparsity of the obtained control law.