Robust data-driven optimization for dynamic and decision-dependent systems under uncertainty

Jia, Zhuangzhuang

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https://hdl.handle.net/2142/132561 Copy

Description

Title

Robust data-driven optimization for dynamic and decision-dependent systems under uncertainty

Author(s)

Jia, Zhuangzhuang

Issue Date

2025-12-03

Director of Research (if dissertation) or Advisor (if thesis)

Hanasusanto, Grani A.

Doctoral Committee Chair(s)

Hanasusanto, Grani A.

Committee Member(s)

• Wang, Qiong
• Dong, Roy
• Nguyen, Viet Anh

Department of Study

Industrial&Enterprise Sys Eng

Discipline

Industrial Engineering

Degree Granting Institution

University of Illinois Urbana-Champaign

Degree Name

Ph.D.

Degree Level

Dissertation

Keyword(s)

• Data-driven optimization
• Robust optimization
• Stochastic dual dynamic programming
• Fair sequential selection
• Decision-dependent uncertainty

Abstract

Modern decision-making systems increasingly rely on data-driven models to guide actions in dynamic environments. However, in many real-world applications, the data available for learning is limited, biased, or influenced by previous decisions, and the resulting uncertainty can significantly degrade the performance of the models. This dissertation develops a unified framework for robust data-driven optimization in dynamic and decision-dependent systems. Across three research directions, this work introduces new algorithmic methods and theoretical results that enable decision-makers to make better decisions. The first part of the dissertation addresses multistage stochastic optimization, with a focus on situations in which uncertainty evolves according to a non-stationary, continuous-state Markov process and where the probability distribution is not known in advance. Classical solution approaches, such as scenario tree approximations or stochastic dual dynamic programming (SDDP), typically require strong assumptions, such as stagewise independence or known distributions, that limit their applicability. To move beyond these limitations, we develop a data-driven extension of SDDP that directly learns value function approximations from observed data without the need to explicitly model the underlying distribution. We establish out-of-sample performance guarantees for the resulting approximate dynamic programming strategy. However, when only limited training data are available, value estimates may suffer from optimistic bias, leading to poor performance in deployment. To mitigate this issue, we propose a distributionally robust regularization scheme based on a modified χ2 divergence and show that it is equivalent to a variance penalization of future costs. Applications in finance and energy planning demonstrate that the method substantially improves solution stability when data are scarce or structurally noisy. The second part of the dissertation focuses on sequential selection problems, such as hiring, college admissions, and loan approval, where decisions unfold across multiple stages and are made using only observational data shaped by past (potentially biased) policies. In these settings, only the covariates and outcomes of selected individuals are observed, while the performance of those screened out remains unknown. This creates selection bias and covariate shift that complicate learning, and fairness concerns arise because historical decisions may encode structural bias against certain demographic groups. To address these challenges, we propose a causal off-policy learning framework integrated with distributionally robust optimization. By constructing a Wasserstein ambiguity set around a reweighted empirical distribution, we account for both data scarcity and potential distribution shifts during deployment. Fairness is incorporated through group fairness constraints such as demographic parity or equal opportunity, and we ensure these constraints hold with high probability over all distributions in the ambiguity set. To maintain interpretability, which is essential for decisions that affect people, we restrict policies to simple linear selection rules and show that the resulting robust and fair optimization problem admits a mixed binary conic formulation solvable with off-the-shelf solvers. Empirical studies on adapted UCI datasets demonstrate that our framework significantly improves fairness and robustness while preserving high decision quality. The third part of the dissertation examines performative optimization, a setting where decisions influence the data-generating process itself. This phenomenon arises in domains such as strategic classification, pricing, and portfolio management, where behavior responds to historical decisions. Existing performative optimization methods typically assume access to an accurate model of how decisions affect future distributions; however, such models are rarely known and are often inferred from limited data. To address this, we introduce a distributionally robust performative optimization framework that explicitly models uncertainty in the decision-dependent distribution. We develop an iterative algorithm, repeated robust risk minimization, which alternates between solving a standard distributionally robust optimization problem and updating the ambiguity set based on the resulting distributional feedback. This procedure maintains computational tractability while providing theoretical guarantees on convergence and suboptimality. Numerical experiments in strategic classification, revenue management, and portfolio optimization show that the proposed method yields substantial performance improvements relative to state-of-the-art baselines, especially under model misspecification. Taken together, the contributions of this dissertation advance the theoretical and practical foundations of robust data-driven decision-making in settings where uncertainty interacts with the decision-making process itself. The frameworks developed herein provide new tools for designing reliable, interpretable, and fair policies across a wide range of dynamic systems, and highlight the importance of explicitly modeling distributional ambiguity when decisions and data are interdependent.

Graduation Semester

2025-12

Type of Resource

Thesis

Handle URL

https://hdl.handle.net/2142/132561

Copyright and License Information

Copyright 2025 Zhuangzhuang Jia

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