Improved learning rates in multi-unit uniform price auctions

TL;DR

This paper introduces a new bid modeling approach in multi-unit uniform price auctions, achieving improved online learning regret bounds, with applications to electricity markets and different feedback scenarios.

Contribution

It presents a novel bid space modeling and develops algorithms with tighter regret bounds for adversarial auction settings, including new feedback models.

Findings

Achieved regret of O(K^{4/3}T^{2/3}) under bandit feedback.

Improved regret bounds over previous literature.

Introduced a feedback model with all winning bids revealed.

Abstract

Motivated by the strategic participation of electricity producers in electricity day-ahead market, we study the problem of online learning in repeated multi-unit uniform price auctions focusing on the adversarial opposing bid setting. The main contribution of this paper is the introduction of a new modeling of the bid space. Indeed, we prove that a learning algorithm leveraging the structure of this problem achieves a regret of $\tilde{O}(K^{4/3}T^{2/3})$ under bandit feedback, improving over the bound of $\tilde{O}(K^{7/4}T^{3/4})$ previously obtained in the literature. This improved regret rate is tight up to logarithmic terms. Inspired by electricity reserve markets, we further introduce a different feedback model under which all winning bids are revealed. This feedback interpolates between the full-information and bandit scenarios depending on the auctions' results. We prove that, under this feedback, the algorithm that we propose achieves regret $\tilde{O}(K^{5/2}\sqrt{T})$.