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The canonical solution methodology for finite constrained Markov decisionprocesses (CMDPs), where the objective is to maximize the expectedinfinite-horizon discounted rewards subject to the expected infinite-horizondiscounted costs constraints, is based on convex linear programming. In thisbrief, we first prove that the optimization objective in the dual linearprogram of a finite CMDP is a piece-wise linear convex function (PWLC) withrespect to the Lagrange penalty multipliers. Next, we propose a novel two-levelGradient-Aware Search (GAS) algorithm which exploits the PWLC structure to findthe optimal state-value function and Lagrange penalty multipliers of a finiteCMDP. The proposed algorithm is applied in two stochastic control problems withconstraints: robot navigation in a grid world and solar-powered unmanned aerialvehicle (UAV)-based wireless network management. We empirically compare theconvergence performance of the proposed GAS algorithm with binary search (BS),Lagrangian primal-dual optimization (PDO), and Linear Programming (LP).Compared with benchmark algorithms, it is shown that the proposed GAS algorithmconverges to the optimal solution faster, does not require hyper-parametertuning, and is not sensitive to initialization of the Lagrange penaltymultiplier.

A Gradient-Aware Search Algorithm for Constrained Markov Decision Processes