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

TL;DR

This paper introduces Triple-Q, a model-free reinforcement learning algorithm for Constrained Markov Decision Processes that achieves sublinear regret and zero constraint violation without requiring a model or simulator.

Contribution

The paper proposes the first provably-efficient, model-free algorithm for CMDPs with theoretical regret bounds and guaranteed zero constraint violations.

Findings

Achieves $ ilde{ ext{O}}(rac{1}{ ext{delta}}H^4 S^{1/2}A^{1/2}K^{4/5})$ regret.

Guarantees zero constraint violation with high probability.

Computational complexity similar to SARSA for unconstrained MDPs.

Abstract

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 $\tilde{\cal O}\left(\frac{1 }{\delta}H^4 S^{\frac{1}{2}}A^{\frac{1}{2}}K^{\frac{4}{5}} \right)$ 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 $\delta$ 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.