CVaR Deep Optimal Stopping

Yechan Jeong, Youngjoon Hong

Risk-sensitive optimal stopping is useful when poor stopping outcomes carry substantial costs, as in option exercise, sequential medical treatment, and safety-critical control. A natural objective is Conditional Value at Risk (CVaR) of the stopped reward. We develop a theoretical framework and algorithm for CVaR deep optimal stopping. The framework and algorithm address four difficulties in applying risk-sensitive reinforcement learning to optimal stopping: state augmentation, score-function pathology, blindness to success, and dependence on auxiliary networks. We isolate three structural properties of optimal stopping: single-point reward, action-independent dynamics, and sum-zero gradient. We exploit these properties to establish Markov optimality without state augmentation and derive a pathwise gradient estimator. Under bounded policy derivatives, the pathwise estimator has bounded second moments near deterministic policies, avoiding the divergence that can occur with score-function estimators. Building on this framework, we propose DIOS (Distribution-Informed Optimal Stopping) to address the remaining two difficulties. A per-time-step soft penalty combined with tail-level…