Reinforcement Learning with Random Time Horizons

TL;DR

This paper extends reinforcement learning to include random stopping times, deriving new policy gradient formulas and demonstrating improved optimization convergence in practical experiments.

Contribution

It introduces a rigorous framework for RL with random time horizons, deriving policy gradient formulas that account for trajectory-dependent stopping times.

Findings

New policy gradient formulas for random horizons

Improved convergence in numerical experiments

Connections to optimal control theory

Abstract

We extend the standard reinforcement learning framework to random time horizons. While the classical setting typically assumes finite and deterministic or infinite runtimes of trajectories, we argue that multiple real-world applications naturally exhibit random (potentially trajectory-dependent) stopping times. Since those stopping times typically depend on the policy, their randomness has an effect on policy gradient formulas, which we (mostly for the first time) derive rigorously in this work both for stochastic and deterministic policies. We present two complementary perspectives, trajectory or state-space based, and establish connections to optimal control theory. Our numerical experiments demonstrate that using the proposed formulas can significantly improve optimization convergence compared to traditional approaches.