List Replicable Reinforcement Learning

Abstract

Replicability is a fundamental challenge in reinforcement learning (RL), as RL algorithms are empirically observed to be unstable and sensitive to variations in training conditions. To formally address this issue, we study *list replicability* in the Probably Approximately Correct (PAC) RL framework, where an algorithm must return a near-optimal policy that lies in a *small list* of policies across different runs, with high probability. The size of this list defines the *list complexity*. We introduce both weak and strong forms of list replicability: the weak form ensures that the final learned policy belongs to a small list, while the strong form further requires that the entire sequence of executed policies remains constrained. These objectives are challenging, as existing RL algorithms exhibit exponential list complexity due to their instability. Our main theoretical contribution is a provably efficient tabular RL algorithm that guarantees list replicability by ensuring the list com

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