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

We study the online learning problem of a bidder who participates in repeated auctions. With the goal of maximizing his total T-period payoff, the bidder wants to determine the optimal allocation of his fixed budget among his bids for K different goods at each period. As a bidding strategy, we propose a polynomial time algorithm, referred to as dynamic programming on discrete set (DPDS), which is inspired by the dynamic programming approach to Knapsack problems. We show that DPDS achieves the regret order of O( √ T log T ). Also, by showing that the regret growth rate is lower bounded by Ω( √ T ) for any bidding strategy, we conclude that DPDS algorithm is order optimal up to a √ log T term. We also evaluate the performance of DPDS empirically in the context of virtual bidding in wholesale electricity markets by using historical data from the New York energy market. Index Terms Repeated auctions, Online learning, Dynamic programming, Virtual bidding