Online Learning in a Contract Selection Problem

TL;DR

This paper introduces online learning algorithms for a contract selection problem where a seller sequentially offers contracts to buyers with unknown preferences, aiming to maximize profit with minimal regret.

Contribution

It proposes new online algorithms under the ordered preferences assumption that achieve sub-linear regret in the contract selection setting.

Findings

Algorithms achieve sub-linear regret compared to the best fixed contract set.

The approach applies to spectrum, wireless data plans, and recommendation systems.

The structural property of ordered preferences is key to the method's success.

Abstract

In an online contract selection problem there is a seller which offers a set of contracts to sequentially arriving buyers whose types are drawn from an unknown distribution. If there exists a profitable contract for the buyer in the offered set, i.e., a contract with payoff higher than the payoff of not accepting any contracts, the buyer chooses the contract that maximizes its payoff. In this paper we consider the online contract selection problem to maximize the sellers profit. Assuming that a structural property called ordered preferences holds for the buyer's payoff function, we propose online learning algorithms that have sub-linear regret with respect to the best set of contracts given the distribution over the buyer's type. This problem has many applications including spectrum contracts, wireless service provider data plans and recommendation systems.