Reduced Cost Influence Functions for Predict-then-Optimize under Noisy Data
Abstract
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.
Related
- Geometric Identification in Predict-Then-Optimize Learning
- Eigenvalue-Decomposition Cost Denoising for Predict-then-Optimize
- Analysis of Polynomial Threshold Functions on Random Regular Graphs: Computational Complexity of Detecting Noisy Random Lifts
- On the Fourier Entropy-Influence Conjecture for Boolean Plateaued Functions
- A Dual Representation of Influence Functions for Linearizable Models
BibTeX
@misc{zhang2026reduced,
title = {{Reduced Cost Influence Functions for Predict-then-Optimize under Noisy Data}},
author = {William Zhang and Saurabh Amin and Georgia Perakis},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.02086},
eprint = {2611.02086},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.02086},
}
RIS
TY - UNPB
TI - Reduced Cost Influence Functions for Predict-then-Optimize under Noisy Data
AU - William Zhang
AU - Saurabh Amin
AU - Georgia Perakis
PY - 2026
DA - 2026/11/01
PB - arXiv
DO - 10.48550/arxiv.2611.02086
UR - https://arxiv.org/abs/2611.02086
AB - 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.
ER -