Geometric conditions identify predictions in decision-focused learning
Geometric Identification in Predict-Then-Optimize Learning
Machine Learning
Summary
When computers make decisions based on predicted numbers, sometimes the exact predicted values don't need to be perfectly right to still make good decisions. The authors studied a particular method (called SPO+) to understand when and how the true average predictions can be uniquely found based on decision outcomes. They found that under certain symmetry conditions and geometric properties, it is possible to recover the exact predictions that lead to optimal decisions. Their work clarifies the difference between making decisions that change versus those that stay stable when predictions shift.
What this means in practice
- •For portfolio managers: Use geometric conditions to better understand prediction shifts and decision stability in portfolio optimization models.
- •For energy system planners: Improve interpretation of predictive models in energy storage and dispatch when optimizing operational decisions under uncertainty.
A theory result. No direct application yet.
Authors
Jiaxiao Xu, Changhong Mou, Keji Liu, Dinghua Xu, Yeyu Zhang
Abstract
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 conditional versions extend the result to measurable predictors. These are population statements, without finite-sample report-recovery or generic transfer-regret guarantees. Closed-form mechanisms reproduce the analytic identities and rates. Portfolio, complete-matrix KuaiRec, and Energy/Storage studies measure predictive fidelity, shifted regret, and fitted-report geometry. A known data-generating process (DGP) companion retains their application geometries while isolating conditional-mean recovery and crossing, without testing the original observational assumptions.