No-regret Learning in Repeated First-Price Auctions with Budget Constraints

TL;DR

This paper studies online bidding strategies in repeated first-price auctions with budget constraints, proposing algorithms that achieve sublinear regret bounds and extend to general utility functions.

Contribution

It introduces RL-based algorithms for budget-constrained bidders in first-price auctions with provable regret guarantees, addressing a key open problem.

Findings

Achieves (\u221a T) regret with full bid visibility.

Achieves (T^{7/12}) regret with limited bid information.

Extends analysis to general bounded utility functions.

Abstract

Recently the online advertising market has exhibited a gradual shift from second-price auctions to first-price auctions. Although there has been a line of works concerning online bidding strategies in first-price auctions, it still remains open how to handle budget constraints in the problem. In the present paper, we initiate the study for a buyer with budgets to learn online bidding strategies in repeated first-price auctions. We propose an RL-based bidding algorithm against the optimal non-anticipating strategy under stationary competition. Our algorithm obtains $\widetilde O(\sqrt T)$-regret if the bids are all revealed at the end of each round. With the restriction that the buyer only sees the winning bid after each round, our modified algorithm obtains $\widetilde O(T^{\frac{7}{12}})$-regret by techniques developed from survival analysis. Our analysis extends to the more general scenario where the buyer has any bounded instantaneous utility function with regrets of the same order.