Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Distributionally Robust Performative Optimization

Zhuangzhuang Jia, Yijie Wang, Roy Dong, Grani A. Hanasusanto

TL;DR

This framework introduces three modeling paradigms that capture a broad range of applications in machine learning and decision-making under uncertainty and develops an iterative algorithm named repeated robust risk minimization, which alternates between solving a decision-independent distributionally robust optimization problem and updating the ambiguity set based on the previous decision.

Abstract

In performative stochastic optimization, decisions can influence the distribution of random parameters, rendering the data-generating process itself decision-dependent. In practice, decision-makers rarely have access to the true distribution map and must instead rely on imperfect surrogate models, which can lead to severely suboptimal solutions under misspecification. Data scarcity or costly collection further exacerbates these challenges in real-world settings. To address these challenges, we propose a distributionally robust framework for performative optimization that explicitly accounts for ambiguity in the decision-dependent distribution. Our framework introduces three modeling paradigms that capture a broad range of applications in machine learning and decision-making under uncertainty. This latter setting has not previously been explored in the performative optimization literature. To tackle the intractability of the resulting nonconvex objectives, we develop an iterative algorithm named repeated robust risk minimization, which alternates between solving a decision-independent distributionally robust optimization problem and updating the ambiguity set based on the previous decision. This decoupling ensures computational tractability at each iteration while enhancing robustness to model uncertainty. We provide reformulations compatible with off-the-shelf solvers and establish theoretical guarantees on convergence and suboptimality. Extensive numerical experiments in strategic classification, revenue management, and portfolio optimization demonstrate significant performance gains over state-of-the-art baselines, highlighting the practical value of our approach.

Distributionally Robust Performative Optimization

TL;DR

This framework introduces three modeling paradigms that capture a broad range of applications in machine learning and decision-making under uncertainty and develops an iterative algorithm named repeated robust risk minimization, which alternates between solving a decision-independent distributionally robust optimization problem and updating the ambiguity set based on the previous decision.

Abstract

In performative stochastic optimization, decisions can influence the distribution of random parameters, rendering the data-generating process itself decision-dependent. In practice, decision-makers rarely have access to the true distribution map and must instead rely on imperfect surrogate models, which can lead to severely suboptimal solutions under misspecification. Data scarcity or costly collection further exacerbates these challenges in real-world settings. To address these challenges, we propose a distributionally robust framework for performative optimization that explicitly accounts for ambiguity in the decision-dependent distribution. Our framework introduces three modeling paradigms that capture a broad range of applications in machine learning and decision-making under uncertainty. This latter setting has not previously been explored in the performative optimization literature. To tackle the intractability of the resulting nonconvex objectives, we develop an iterative algorithm named repeated robust risk minimization, which alternates between solving a decision-independent distributionally robust optimization problem and updating the ambiguity set based on the previous decision. This decoupling ensures computational tractability at each iteration while enhancing robustness to model uncertainty. We provide reformulations compatible with off-the-shelf solvers and establish theoretical guarantees on convergence and suboptimality. Extensive numerical experiments in strategic classification, revenue management, and portfolio optimization demonstrate significant performance gains over state-of-the-art baselines, highlighting the practical value of our approach.
Paper Structure (31 sections, 16 theorems, 154 equations, 4 figures)

This paper contains 31 sections, 16 theorems, 154 equations, 4 figures.

Table of Contents

  1. Introduction
  2. Related Work
  3. Notation and Terminology
  4. Preliminaries
  5. Repeated Robust Risk Minimization Algorithm
  6. Models and Their Tractable Reformulations
  7. Convergence Analysis
  8. Suboptimality Guarantees
  9. Experiments
  10. Strategic Classification
  11. Revenue Management
  12. Demand Response Portfolio Optimization
  13. Concluding Remarks
  14. Preliminary Definitions
  15. Background on Exponential Smoothing
  16. ...and 16 more sections

Key Result

Theorem 1

Suppose the loss functions in Models thm:reformulation1, thm:reformulation2, and thm:reformulation3 satisfy Assumptions a1, a2, and a3 respectively, and that the distribution map $\hat{{\mathbb{P}}}(\cdot)$ satisfies the $\epsilon$-sensitivity condition ass:eps. Then: Here, $\kappa = \beta / (\gamma + 2\rho L)$ for Model thm:reformulation1, $\kappa =J d k_3 \left( \frac{k_1 k_2}{\mu} + 1 \right)/

Figures (4)

  • Figure 1: Out of sample performance of different approaches
  • Figure 2: Out-of-sample performance of pricing schemes
  • Figure 3: Out-of-sample performance of DR scheduling
  • Figure 4: Out-of-sample performance as a function of the robust parameter $\rho$ and estimated on the basis of 100 simulations.

Theorems & Definitions (39)

  • Definition 1: Wasserstein metric
  • Definition 2: Robust performative optimality
  • Definition 3: Robust performative stability
  • Definition 4: Robust decoupled performative risk
  • Theorem 1
  • Theorem 2
  • Definition 5: Generalized strong convexity
  • Definition 6: Smoothness
  • Definition 7: $\epsilon$-sensitivity
  • Lemma C.1: First-order optimality condition; Section 4.2.3 in boyd2004convex
  • ...and 29 more