Online Learning of Optimal Bidding Strategy in Repeated Multi-Commodity Auctions

TL;DR

This paper introduces a polynomial-time online bidding algorithm called DPDS for repeated multi-commodity auctions, achieving near-optimal regret bounds and outperforming benchmarks in electricity market simulations.

Contribution

The paper proposes a novel dynamic programming-based bidding algorithm with provable regret bounds for repeated auctions, and demonstrates its effectiveness in real-world electricity market data.

Findings

DPDS achieves regret of O(√T log T), close to the lower bound of Ω(√T).

Empirical results show DPDS outperforms benchmark heuristics in electricity trading.

The algorithm is computationally efficient and theoretically near-optimal.

Abstract

We study the online learning problem of a bidder who participates in repeated auctions. With the goal of maximizing his T-period payoff, the bidder determines the optimal allocation of his budget among his bids for $K$ goods at each period. As a bidding strategy, we propose a polynomial-time algorithm, inspired by the dynamic programming approach to the knapsack problem. The proposed algorithm, referred to as dynamic programming on discrete set (DPDS), achieves a regret order of $O(\sqrt{T\log{T}})$. By showing that the regret is lower bounded by $\Omega(\sqrt{T})$ for any strategy, we conclude that DPDS is order optimal up to a $\sqrt{\log{T}}$ term. We evaluate the performance of DPDS empirically in the context of virtual trading in wholesale electricity markets by using historical data from the New York market. Empirical results show that DPDS consistently outperforms benchmark heuristic methods that are derived from machine learning and online learning approaches.