Reinforcement Learning with Random Time Horizons
This work addresses a limitation in reinforcement learning for real-world applications with random stopping times, though it appears incremental as it extends existing frameworks rather than introducing a new paradigm.
The authors tackled the problem of reinforcement learning with random time horizons, extending the standard framework to handle trajectory-dependent stopping times. They derived rigorous policy gradient formulas for both stochastic and deterministic policies, and numerical experiments showed significant improvements in optimization convergence compared to traditional approaches.
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.