Pretrain-Then-Calibrate: Enhancing Optimality-Feasibility Tradeoff in Safe Contextual Optimization

Contextual optimization, or decision-focused learning, aims to learn context-based decision rules for downstream decision-making tasks. In addition to maintaining statistical efficiency like in conventional supervised learning, this problem entails delicate interplays with optimization tractability and the effectiveness of data-optimization integration. In this paper, we consider safe contextual optimization where, in addition to an optimality criterion, the decision rule also satisfies a high-probability-enforced risk criterion. Natural attempts to integrate chance-constraint methods such as robust optimization, with established contextual optimization pipelines such as predict-then-optimize, suffers from a high price of optimality in exchange for an adequate feasibility guarantee. This motivates us to propose a pretrain-then-calibrate framework to significantly enhance the optimality-feasibility tradeoff. Specifically, our framework translates any heuristic decision rules into rigorous statistically feasible rules via what we call a feasibility calibrator, constructed from a careful interpolation against a safe reference rule to possess certifiable joint feasibility-optimality guarantees. At a high level, our approach exploits the low-dimensional interpolation from readily obtainable good heuristics, and is advantageously model-agnostic, modular and consequently implementation-friendly. In synthetic and real-data experiments on operations management and portfolio optimization, pretrain-and-calibrate results in solutions significantly more optimal than a range of benchmarks including conformal and (distributionally) robust optimization methods without sacrificing feasibility, thus achieving demonstrably improved optimality-feasibility tradeoffs.