A Provably-Efficient Model-Free Algorithm for Constrained Markov Decision Processes

This paper presents the first model-free, simulator-free reinforcement learning algorithm for Constrained Markov Decision Processes (CMDPs) with sublinear regret and zero constraint violation. The algorithm is named Triple-Q because it includes three key components: a Q-function (also called action-value function) for the cumulative reward, a Q-function for the cumulative utility for the constraint, and a virtual-Queue that (over)-estimates the cumulative constraint violation. Under Triple-Q, at each step, an action is chosen based on the pseudo-Q-value that is a combination of the three "Q" values. The algorithm updates the reward and utility Q-values with learning rates that depend on the visit counts to the corresponding (state, action) pairs and are periodically reset. In the episodic CMDP setting, Triple-Q achieves tildecal Oleft(frac1 δH4 S^frac12A^frac12K^frac45 right) regret, where K is the total number of episodes, H is the number of steps in each episode, S is the number of states, A is the number of actions, and δ is Slater's constant. Furthermore, Triple-Q guarantees zero constraint violation, both on expectation and with a high probability, when K is sufficiently large. Finally, the computational complexity of Triple-Q is similar to SARSA for unconstrained MDPs and is computationally efficient.