  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. In this paper,
Tsallis entropy, which is a one-parameter extension of Shannon entropy, is used
for the regularization of linearly solvable MDP and linear quadratic
regulators. We derive the solution for these problems and demonstrate its
usefulness in balancing between exploration and sparsity of the obtained
control law.
