Furthermore, weprove information theoretic lower bounds which establish minimax optimality of the skillparameter estimation technique usedinouralgorithm. These bounds utilize a continuum version of Fano's method along with a careful covering argument.

We study sequential decision-making problems in which each agent aims to maximize the expected total reward while satisfying a constraint on the expected total utility. We employ the natural policy gradient method to solve the discounted infinite-horizon Constrained Markov Decision Processes (CMDPs) problem. Specifically, we propose a new Natural Policy Gradient Primal-Dual (NPG-PD) method for CMDPs which updates the primal variable via natural policy gradient ascent and the dual variable via projected sub-gradient descent.