Reduced Cost Influence Functions for Predict-then-Optimize under Noisy Data

William Zhang, Saurabh Amin, Georgia Perakis

Machine learning models deployed in decision-making pipelines, from vehicle routing to dynamic pricing to clinical decision support, must remain reliable in the face of low-quality training data. We study a predict-then-optimize setting in which an upstream model predicts the cost vector of a downstream linear program, with a large pool of noisy training data supplemented by a small curated set of clean data. We introduce Reduced Cost Influence Functions (RCIFs), which combine influence functions from robust statistics with the geometry of linear optimization to estimate how each training point shifts downstream decisions. Building on this, we propose a reweighting algorithm that uses RCIFs to downweight harmful training points and reduce downstream regret. Experiments on random linear programs and shortest-path problems show that our approach reduces regret, and accompanying theory characterizes properties of RCIFs and identifies regimes favorable to our method relative to baselines.