Multi-scale Online Learning and its Applications to Online Auctions

TL;DR

This paper develops multi-scale online learning algorithms for auction pricing, achieving regret bounds that adapt to individual action ranges and improve revenue maximization strategies.

Contribution

It generalizes classical learning frameworks to multi-scale settings, providing regret bounds that depend on individual action ranges rather than the overall range.

Findings

Regret bounds scale with the best fixed price, not the overall value range.

Almost scale-free regret bounds match offline sample complexity.

Applicable to online auction and pricing problems.

Abstract

We consider revenue maximization in online auction/pricing problems. A seller sells an identical item in each period to a new buyer, or a new set of buyers. For the online posted pricing problem, we show regret bounds that scale with the best fixed price, rather than the range of the values. We also show regret bounds that are almost scale free, and match the offline sample complexity, when comparing to a benchmark that requires a lower bound on the market share. These results are obtained by generalizing the classical learning from experts and multi-armed bandit problems to their multi-scale versions. In this version, the reward of each action is in a different range, and the regret w.r.t. a given action scales with its own range, rather than the maximum range.