Tail-Risk Cross-Entropy for Robust Generative Decision-Focused Learning

Robust generative *decision-focused learning* (*DFL*) seeks to learn predictive distributions that induce reliable decisions under adverse outcome uncertainty. Existing *Conditional Value-at-Risk* (*CVaR*)-based methods, however, rely on estimated CVaR values or CVaR-optimal decisions as supervision, which depend on the conditional tail distribution and are not directly available from standard single-outcome data. We propose *Tail-Risk Cross-Entropy* (*TRCE*), a decision-focused surrogate that bypasses robust-supervision reconstruction and enables CVaR-aware generative learning directly from single-outcome observations. Our key insight is that, although CVaR is a distribution-level risk measure, the ideal CVaR-weighted objective admits an equivalent sample-wise representation through the Rockafellar–Uryasev (RU) formulation. TRCE learns the corresponding conditional Value-at-Risk (VaR) threshold from observed input–outcome pairs and uses it to construct sample-wise tail-risk signals, eliminating the need for explicit ground-truth CVaR estimates or CVaR-optimal decision labels. We establish finite-sample guarantees connecting model approximation, threshold-estimation, and generalization errors to downstream CVaR decision regret. Experiments under both light- and heavy-tailed uncertainty demonstrate consistent improvements over deterministic and generative DFL baselines.