The Curvature of Regret in Contextual Linear Optimization
Decision-focused learning for linear optimization is complicated by the discontinuity of the optimizer, where small cost errors may leave the decision unchanged or move it to a different vertex. We show that this non-smooth pointwise behavior becomes locally quadratic after averaging over the data distribution, and we derive the curvature in closed form, specifically, a matrix-valued measure supported on the walls of the normal fan. This measure depends only on the feasible set, with the data distribution entering only as a weight. We then offer a tractable approximation for this curvature, computable with just one projection to the feasible set. We prove that the approximation weakly con...
| Authors | Konstantinos Ziliaskopoulos, Alexander Vinel, Alice E. Smith |
|---|---|
| Primary category | cs.LG |
| Published | 1 October 2026 |
| Last updated at source | 1 October 2026 |
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