Decision-Dependent Distributionally Robust Optimization with Application to Dynamic Pricing

TL;DR

This paper introduces a decision-dependent distributionally robust optimization framework using Wasserstein metric and multivariate interpolation, providing finite-sample guarantees and demonstrating effectiveness in dynamic pricing with nonstationary demand.

Contribution

It develops a novel DD-DRO model with decision-dependent ambiguity sets, offering theoretical guarantees and a tractable reformulation for practical applications.

Findings

Provides finite-sample, high-probability guarantees for the true distribution.

Establishes non-asymptotic out-of-sample performance bounds.

Demonstrates improved dynamic pricing strategies with guaranteed revenue.

Abstract

We consider decision-making problems under decision-dependent uncertainty (DDU), where the distribution of uncertain parameters depends on the decision variables and is only observable through a finite offline dataset. To address this challenge, we formulate a decision-dependent distributionally robust optimization (DD-DRO) problem, and leverage multivariate interpolation techniques along with the Wasserstein metric to construct decision-dependent nominal distributions (thereby decision-dependent ambiguity sets) based on the offline data. We show that the resulting ambiguity sets provide a finite-sample, high-probability guarantee that the true decision-dependent distribution is contained within them. Furthermore, we establish key properties of the DD-DRO framework, including a non-asymptotic out-of-sample performance guarantee, an optimality gap bound, and a tractable reformulation. The practical effectiveness of our approach is demonstrated through numerical experiments on a dynamic pricing problem with nonstationary demand, where the DD-DRO solution produces pricing strategies with guaranteed expected revenue.