Dynamic Pricing with Adversarially-Censored Demands

TL;DR

This paper presents an online dynamic pricing algorithm that effectively manages censored demand data with adversarial inventory, achieving near-optimal regret bounds in stochastic and adversarial settings.

Contribution

Introduces a novel pricing algorithm based on optimistic derivative estimates that handles adversarially censored demand data with proven regret bounds.

Findings

Achieves ()()()()()()()()()()()()()()()()()()()()()()()()() regret bounds in adversarial demand scenarios.

Demonstrates robustness of the algorithm against adversarial inventory sequences.

Abstract

We study an online dynamic pricing problem where the potential demand at each time period $t=1,2,\ldots, T$ is stochastic and dependent on the price. However, a perishable inventory is imposed at the beginning of each time $t$, censoring the potential demand if it exceeds the inventory level. To address this problem, we introduce a pricing algorithm based on the optimistic estimates of derivatives. We show that our algorithm achieves $\tilde{O}(\sqrt{T})$ optimal regret even with adversarial inventory series. Our findings advance the state-of-the-art in online decision-making problems with censored feedback, offering a theoretically optimal solution against adversarial observations.