Projected Gradient Descent for Constrained Decision-Dependent Optimization

2025/08/12 by Zifan Wang, Wang, Zifan, Changxin Liu +7 · 1 citation
Computer Science · Decision Sciences · #FOS: Mathematics #Optimization and Control (math.OC) #Optimization and Variational Analysis #Risk and Portfolio Optimization #Stochastic Gradient Optimization Techniques

paper · pdf · doi:10.48550/arxiv.2508.08856

openalex publication_date 2025/08/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper considers the decision-dependent optimization problem, where the data distributions react in response to decisions affecting both the objective function and linear constraints. We propose a new method termed repeated projected gradient descent (RPGD), which iteratively projects points onto evolving feasible sets throughout the optimization process. To analyze the impact of varying projection sets, we show a Lipschitz continuity property of projections onto varying sets with an explicitly given Lipschitz constant. Leveraging this property, we provide sufficient conditions for the convergence of RPGD to the constrained equilibrium point. Compared to the existing dual ascent method, RPGD ensures continuous feasibility throughout the optimization process and reduces the computational burden. We validate our results through numerical experiments on a market problem and dynamic pricing problem.

Citations

• Constrained Optimization with Decision-Dependent Distributions
• Zero-Regret Performative Prediction Under Inequality Constraints
• Stochastic First-Order Algorithms for Constrained Distributionally Robust Optimization
• Stochastic Saddle Point Problems with Decision-Dependent Distributions
• Online Stochastic Optimization for Unknown Linear Systems: Data-Driven Synthesis and Controller Analysis
• Online Projected Gradient Descent for Stochastic Optimization with\n Decision-Dependent Distributions
• A New Family of Feasible Methods for Distributed Resource Allocation
• Outside the Echo Chamber: Optimizing the Performative Risk
• Stochastic optimization with decision-dependent distributions
• Stochastic Optimization for Performative Prediction
• Performative Prediction
• On Lipschitz continuity of projections onto polyhedral moving sets

Cited by

• Optimal Network Pricing for Oblivious Users under Projected Decision-Dependent Distributions

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