Reinforcement Learning with Random Time Horizons
This paper addresses realistic reinforcement learning scenarios where trajectory termination times are both stochastic and policy-dependent—challenging the conventional assumptions of fixed or infinite horizons. Method: We develop a dual modeling framework integrating trajectory- and state-space perspectives, grounded in stochastic process theory and optimal control principles, and propose a Monte Carlo–based gradient estimation scheme. Contribution/Results: (1) We derive the first unbiased policy gradient theorem for policy-dependent stochastic horizons; (2) we unify the theoretical foundations of policy optimization across finite-, infinite-, and stochastic-horizon settings; and (3) empirical evaluations demonstrate that the proposed gradient estimator significantly improves convergence speed and training stability compared to classical methods—including those assuming fixed or discounted infinite horizons—thereby enabling more robust and efficient learning in real-world sequential decision-making problems with uncertain termination.