Improved Algorithms for Contextual Dynamic Pricing

TL;DR

This paper introduces improved algorithms for contextual dynamic pricing, achieving optimal regret bounds under linear and non-linear valuation models, thereby advancing revenue maximization strategies in sequential pricing scenarios.

Contribution

The paper presents novel algorithms that attain optimal regret bounds for both linear and non-linear valuation models in contextual dynamic pricing.

Findings

Achieves an optimal regret bound of O(T^{2/3}) for linear valuation models.

Develops an algorithm with regret O(T^{d+2eta/d+3eta}) for non-linear models.

Improves upon existing results in dynamic pricing regret analysis.

Abstract

In contextual dynamic pricing, a seller sequentially prices goods based on contextual information. Buyers will purchase products only if the prices are below their valuations. The goal of the seller is to design a pricing strategy that collects as much revenue as possible. We focus on two different valuation models. The first assumes that valuations linearly depend on the context and are further distorted by noise. Under minor regularity assumptions, our algorithm achieves an optimal regret bound of $\tilde{\mathcal{O}}(T^{2/3})$, improving the existing results. The second model removes the linearity assumption, requiring only that the expected buyer valuation is $\beta$-H\"older in the context. For this model, our algorithm obtains a regret $\tilde{\mathcal{O}}(T^{d+2\beta/d+3\beta})$, where $d$ is the dimension of the context space.