Toward Optimal Regret in Robust Pricing: Decoupling Corruption and Time

TL;DR

This paper introduces new regret guarantees for robust dynamic pricing that effectively separate the impact of adversarial feedback corruption from the overall time horizon, improving upon previous bounds.

Contribution

It develops a robust binary search algorithm achieving regret bounds that decouple corruption level and time horizon, advancing theoretical understanding in robust pricing.

Findings

Achieves regret +\u0x1D17T4C when corruption is known.

Achieves regret +17^2 T when corruption is unknown.

First regret guarantees to decouple corruption and time dependence in robust pricing.

Abstract

We design the first regret guarantees for robust dynamic pricing that decouple the dependence on the corruption $C$ and the time horizon $T$. In dynamic pricing, a seller with unlimited supply of a good interacts with a stream of buyers over \( T \) rounds, with the goal of maximizing revenue. At each round $t$, the seller posts a price $p_t$, and the buyer purchases the good only if their unknown valuation $v^\star$ exceeds this price. The seller observes only the binary feedback $\mathbb{I} \left\{ p_t \leq v^\star \right\}$, indicating whether a sale occurred. In the \emph{robust} pricing setting, a malicious adversary is allowed to corrupt this feedback in at most $C$ rounds. Even if the learner knows the corruption $C$, the best known regret bound is $\mathcal{O}(C\log\log T)$ by Gupta et al. [2025]. This leaves as an open problem to ``decouple'' the dependence on $C$ and $T$. In this work, we resolve this open problem. In particular, we develop a robust variant of binary search that achieves regret $\mathcal{O}(C+\log T)$ when the corruption $C$ is known and $\mathcal{O}(C+\log^2 T)$ when the corruption is unknown.