@inproceedings{
potfer2024improved,
title={Improved learning rates in multi-unit uniform price auctions},
author={Marius Potfer and Dorian Baudry and Hugo Richard and Vianney Perchet and Cheng Wan},
booktitle={The Thirty-eighth Annual Conference on Neural Information Processing Systems},
year={2024},
url={https://openreview.net/forum?id=UN7nXLeh9D}
}
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. %by deducing a lower bound of $\Omega (T^{2/3})$ from the dynamic pricing literature, proving the optimality in $T$ of our algorithm up to log factors. 
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 $\tilde{O}(K^{5/2}\sqrt{T})$.
Improved learning rates in multi-unit uniform price auctions
Marius Potfer Dorian Baudry Hugo Richard Vianney Perchet Cheng Wan