Geometric Identification in Predict-Then-Optimize Learning
Decision-focused surrogates can recover downstream decisions without identifying the quotient report. We characterize the equality set of the convex Smart Predict-then-Optimize surrogate (SPO+) population risk. Under central symmetry, the centered mean class is the unique Bayes minimizer exactly when every nonzero effective displacement makes the old optimizer leave the shifted optimal face with positive probability. This condition separates face crossing from selected-oracle disagreement and gives quantitative local coercivity. Without symmetry, strict crossing alone need not identify the mean; selection balance with reflected crossing restores quotient-report identification, and conditi...
| Authors | Jiaxiao Xu, Changhong Mou, Keji Liu et al. |
|---|---|
| Primary category | cs.LG |
| Published | 27 September 2026 |
| Last updated at source | 27 September 2026 |
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