Adaptive Bidding Policies for First-Price Auctions with Budget Constraints under Non-stationarity

TL;DR

This paper develops an adaptive bidding policy for first-price auctions with budget constraints, addressing non-stationarity and limited knowledge, and provides regret bounds for different informational settings.

Contribution

It introduces a dual-gradient-descent bidding policy that adapts to budget constraints and non-stationarity, with theoretical regret guarantees under various knowledge assumptions.

Findings

Regret is O(\u221a{T}) plus a non-stationarity variation term.

Prediction of budget allocation reduces regret to O({T}) plus prediction error.

The proposed policy is effective under both unknown and predictive knowledge scenarios.

Abstract

We study how a budget-constrained bidder should learn to adaptively bid in repeated first-price auctions to maximize her cumulative payoff. This problem arose due to an industry-wide shift from second-price auctions to first-price auctions in display advertising recently, which renders truthful bidding (i.e., always bidding one's private value) no longer optimal. We propose a simple dual-gradient-descent-based bidding policy that maintains a dual variable for budget constraint as the bidder consumes her budget. In analysis, we consider two settings regarding the bidder's knowledge of her private values in the future: (i) an uninformative setting where all the distributional knowledge (can be non-stationary) is entirely unknown to the bidder, and (ii) an informative setting where a prediction of the budget allocation in advance. We characterize the performance loss (or regret) relative to an optimal policy with complete information on the stochasticity. For uninformative setting, We show that the regret is \tilde{O}(\sqrt{T}) plus a variation term that reflects the non-stationarity of the value distributions, and this is of optimal order. We then show that we can get rid of the variation term with the help of the prediction; specifically, the regret is \tilde{O}(\sqrt{T}) plus the prediction error term in the informative setting.