No-Regret Algorithms in non-Truthful Auctions with Budget and ROI Constraints

Gagan Aggarwal, Giannis Fikioris, Mingfei Zhao

Track: Economics, online markets and human computation

Keywords: repeated auctions, online learning, first-price, budget constraint, ROI constraint

TL;DR: Online learning algorithms for first-price auctions with budget and ROI constraints

Abstract:

Advertisers are increasingly using automated bidding to optimize their ad campaigns on online advertising platforms.
Autobidding allows an advertiser to optimize her objective subject to various constraints.
In this paper, we design online autobidding algorithms to optimize value subject to ROI and budget constraints.

We consider an item is being auctioned in each of $T$ rounds.
We focus on one buyer with budget and ROI constraints in the stochastic setting: her value and highest competing bid faced are drawn i.i.d. from some unknown (joint) distribution in each round.
We design low-regret bidding algorithms that bid on behalf of this buyer.
Our main result is an algorithm with full information feedback (i.e., the highest competing bid is revealed after each round) that guarantees a near-optimal $\tilde O(\sqrt T)$ regret with respect to the best Lipschitz function that maps values to bids.
The class of Lipschitz bidding functions is rich enough to best respond to many correlation structures between value and highest competing bid, e.g., positive or negative correlation.
Our result applies to a wide range of auctions, most notably any mixture of first- and second-price auctions.
In addition, our result holds for both value-maximizing buyers and quasi-linear utility-maximizing buyers.

We also study the bandit setting, where the algorithm only observes whether the bidder wins the auction or not.
In this setting, we show an $\Omega(T^{2/3})$ regret lower bound for first-price auctions, showing a significant disparity between the full information and bandit settings.
We also design an algorithm with a regret bound of $\tilde O(T^{3/4})$ when the value distribution is known and is independent of the highest competing bid.

Submission Number: 555