← 研踪 PaperTrailarXiv:2611.11332 · v1
CVaR Deep Optimal Stopping
首次提交 2026-11-08 20:12
版本更新 2026-11-08 20:12
雷达观测 2026-11-10 12:16
摘要
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 annealing mitigates blindness to success. Estimating the reward quantile directly from each batch removes the need for an auxiliary critic. For a fixed tail level, we establish a finite-time stationarity guarantee under regularity assumptions along the training iterates. Across the 24 main Bermudan max-call configurations, DIOS achieves the highest mean CVaR and the shortest recorded training time among the tested CVaR baselines.
作者备注：Neurips 2026
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v1 · 2026-11-08 20:12 · 最新观测版本
CVaR Deep Optimal Stopping
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 annealing mitigates blindness to success. Estimating the reward quantile directly from each batch removes the need for an auxiliary critic. For a fixed tail level, we establish a finite-time stationarity guarantee under regularity assumptions along the training iterates. Across the 24 main Bermudan max-call configurations, DIOS achieves the highest mean CVaR and the shortest recorded training time among the tested CVaR baselines.
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