Quantile Constrained Reinforcement Learning: A Reinforcement Learning Framework Constraining Outage Probability

TL;DR

This paper introduces Quantile Constrained Reinforcement Learning (QCRL), a novel framework that constrains the quantile of cumulative costs to ensure outage probability constraints, with a new policy optimization algorithm and theoretical gradient approximation results.

Contribution

It proposes the first quantile-based constraint framework for RL, deriving gradient approximation methods and implementing a distributional RL algorithm for outage probability satisfaction.

Findings

The QCPO algorithm satisfies outage probability constraints after training.

Theoretical results enable gradient approximation for quantile constraints.

Distributional RL with LDP effectively estimates tail probabilities.

Abstract

Constrained reinforcement learning (RL) is an area of RL whose objective is to find an optimal policy that maximizes expected cumulative return while satisfying a given constraint. Most of the previous constrained RL works consider expected cumulative sum cost as the constraint. However, optimization with this constraint cannot guarantee a target probability of outage event that the cumulative sum cost exceeds a given threshold. This paper proposes a framework, named Quantile Constrained RL (QCRL), to constrain the quantile of the distribution of the cumulative sum cost that is a necessary and sufficient condition to satisfy the outage constraint. This is the first work that tackles the issue of applying the policy gradient theorem to the quantile and provides theoretical results for approximating the gradient of the quantile. Based on the derived theoretical results and the technique of the Lagrange multiplier, we construct a constrained RL algorithm named Quantile Constrained Policy Optimization (QCPO). We use distributional RL with the Large Deviation Principle (LDP) to estimate quantiles and tail probability of the cumulative sum cost for the implementation of QCPO. The implemented algorithm satisfies the outage probability constraint after the training period.