Toward Optimal Regret in Robust Pricing: Decoupling Corruption and Time
For sellers facing adversarial corruptions in buyer feedback, this provides the first regret guarantees that separate the impact of corruption from the time horizon, resolving a key open problem in robust pricing.
The paper resolves the open problem of decoupling corruption and time horizon in robust dynamic pricing, achieving regret bounds of O(C + log T) when corruption C is known and O(C + log^2 T) when unknown, improving over the previous best known bound of O(C log log T).
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.