Strategy-robust Online Learning in Contextual Pricing

TL;DR

This paper develops a strategy-robust online learning framework for contextual pricing, addressing strategic buyer behavior and introducing a polynomial-time approximation scheme and a novel Sparse Update Mechanism to ensure robustness.

Contribution

It introduces a strategy-robust notion of regret, a PTAS for linear pricing policies, and the Sparse Update Mechanism that guarantees robustness against strategic buyers.

Findings

The PTAS efficiently learns pricing policies in adversarial environments.

The Sparse Update Mechanism ensures robustness to all Nash equilibria.

A black-box reduction from online experts to strategy-robust learners is provided.

Abstract

Learning effective pricing strategies is crucial in digital marketplaces, especially when buyers' valuations are unknown and must be inferred through interaction. We study the online contextual pricing problem, where a seller observes a stream of context-valuation pairs and dynamically sets prices. Moreover, departing from traditional online learning frameworks, we consider a strategic setting in which buyers may misreport valuations to influence future prices, a challenge known as strategic overfitting (Amin et al. 2013). We introduce a strategy-robust notion of regret for multi-buyer online environments, capturing worst-case strategic behavior in the spirit of the Price of Anarchy. Our first contribution is a polynomial-time approximation scheme (PTAS) for learning linear pricing policies in adversarial, adaptive environments, enabled by a novel online sketching technique. Building on this result, we propose our main construction: the Sparse Update Mechanism (SUM), a simple yet effective sequential mechanism that ensures robustness to all Nash equilibria among buyers. Moreover, our construction yields a black-box reduction from online expert algorithms to strategy-robust learners.