Localized exploration in contextual dynamic pricing achieves dimension-free regret

TL;DR

This paper introduces a localized exploration-then-commit algorithm for contextual dynamic pricing that achieves dimension-free regret bounds and effectively balances exploration and exploitation across different time horizons.

Contribution

The paper proposes a novel localized exploration-then-commit algorithm with a new theoretical framework and critical inequality for dynamic pricing, achieving minimax optimal regret bounds.

Findings

Achieves dimension-free regret bounds in dynamic pricing

Provides a general framework for exploration-exploitation trade-off

Validated by extensive experiments on synthetic and real data

Abstract

We study the problem of contextual dynamic pricing with a linear demand model. We propose a novel localized exploration-then-commit (LetC) algorithm which starts with a pure exploration stage, followed by a refinement stage that explores near the learned optimal pricing policy, and finally enters a pure exploitation stage. The algorithm is shown to achieve a minimax optimal, dimension-free regret bound when the time horizon exceeds a polynomial of the covariate dimension. Furthermore, we provide a general theoretical framework that encompasses the entire time spectrum, demonstrating how to balance exploration and exploitation when the horizon is limited. The analysis is powered by a novel critical inequality that depicts the exploration-exploitation trade-off in dynamic pricing, mirroring its existing counterpart for the bias-variance trade-off in regularized regression. Our theoretical results are validated by extensive experiments on synthetic and real-world data.