A Proxy Matrix-based Framework for Contextual Stochastic Optimization under Confounding Effect

Yulong Huang, Shaochong Lin, Zuo-Jun Shen, Man-Chung Yue

Keywords: Contextual optimization, confounding effect, confounders, proxy matrix, semi-parametric decision framework

Abstract:

Data-driven decision-making in real-world scenarios often faces the challenge of endogeneity between decisions and outcomes, introducing confounding effects. While existing literature typically assumes unconfoundedness, this is often unrealistic. In practice, decision-making relies on high-dimensional, heterogeneous-type proxy features of confounders, leading to suboptimal decisions due to limited predictive power for uncertainty. We propose a novel semi-parametric decision framework to mitigate confounding effects.
Our approach combines exponential family matrix completion to infer the confounders matrix from proxy features, with non-parametric prescriptive methods for decision-making based on the estimated confounders. We derive a non-convergent regret bound for data-driven decisions under confounding effects and demonstrate how our framework improves this bound. Experiments on both synthetic and real datasets validate our method's efficacy in reducing confounding effects across various proxy dimensions. We also show that our approach consistently outperforms benchmarks in practical applications.

Primary Area: optimization

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Submission Number: 7247