No-Regret Learning in Partially-Informed Auctions

TL;DR

This paper develops no-regret learning algorithms for buyers in partially-informed auction settings, enabling strategic decision-making with limited information and providing theoretical regret bounds in different scenarios.

Contribution

It introduces algorithms with provable regret guarantees for buyers in auction models with incomplete information, bridging online learning and auction theory.

Findings

Regret bound of  O((Td\u00b7b7l)^{1/2}) when distribution is known and mask is SimHash.

Regret bound of  O((Tn)^{1/2}) in agnostic setting with arbitrary mask and stochastic prices.

Algorithms achieve low regret in partially-informed auction environments, extending theoretical understanding of such mechanisms.

Abstract

Auctions with partially-revealed information about items are broadly employed in real-world applications, but the underlying mechanisms have limited theoretical support. In this work, we study a machine learning formulation of these types of mechanisms, presenting algorithms that are no-regret from the buyer's perspective. Specifically, a buyer who wishes to maximize his utility interacts repeatedly with a platform over a series of $T$ rounds. In each round, a new item is drawn from an unknown distribution and the platform publishes a price together with incomplete, "masked" information about the item. The buyer then decides whether to purchase the item. We formalize this problem as an online learning task where the goal is to have low regret with respect to a myopic oracle that has perfect knowledge of the distribution over items and the seller's masking function. When the distribution over items is known to the buyer and the mask is a SimHash function mapping $\mathbb{R}^d$ to $\{0,1\}^{\ell}$, our algorithm has regret $\tilde O((Td\ell)^{1/2})$. In a fully agnostic setting when the mask is an arbitrary function mapping to a set of size $n$ and the prices are stochastic, our algorithm has regret $\tilde O((Tn)^{1/2})$.