  The recently successful Munchausen Reinforcement Learning (M-RL) features
implicit Kullback-Leibler (KL) regularization by augmenting the reward function
with logarithm of the current stochastic policy. Though significant improvement
has been shown with the Boltzmann softmax policy, when the Tsallis sparsemax
policy is considered, the augmentation leads to a flat learning curve for
almost every problem considered. We show that it is due to the mismatch between
the conventional logarithm and the non-logarithmic (generalized) nature of
Tsallis entropy. Drawing inspiration from the Tsallis statistics literature, we
propose to correct the mismatch of M-RL with the help of
$q$-logarithm/exponential functions. The proposed formulation leads to implicit
Tsallis KL regularization under the maximum Tsallis entropy framework. We show
such formulation of M-RL again achieves superior performance on benchmark
problems and sheds light on more general M-RL with various entropic indices
$q$.
