🤖 AI Summary
This paper investigates the impact of dynamic bidding pacing algorithms on group liquid welfare and individual dynamic regret in repeated ad auctions under budget constraints. To overcome the limitation of prior work—reliance on convergence assumptions about algorithmic dynamics—we propose a novel theoretical framework that makes no such assumptions. First, we establish that liquid welfare is guaranteed to be at least 50% of the optimal expected value, irrespective of convergence. Second, we derive an upper bound on dynamic regret tailored to time-varying budgets. Third, we design a gradient-based linear pacing algorithm within the core auction framework, integrating monotonic return-on-spend modeling and dynamic regret analysis to ensure broad applicability across first-price, second-price, and generalized second-price auctions. Empirical validation on Bing Ads data confirms the theoretical guarantees.
📝 Abstract
We study the aggregate welfare and individual regret guarantees of dynamic emph{pacing algorithms} in the context of repeated auctions with budgets. Such algorithms are commonly used as bidding agents in Internet advertising platforms, adaptively learning to shade bids by a tunable linear multiplier in order to match a specified budget. We show that when agents simultaneously apply a natural form of gradient-based pacing, the liquid welfare obtained over the course of the learning dynamics is at least half the optimal expected liquid welfare obtainable by any allocation rule. Crucially, this result holds emph{without requiring convergence of the dynamics}, allowing us to circumvent known complexity-theoretic obstacles of finding equilibria. This result is also robust to the correlation structure between agent valuations and holds for any emph{core auction}, a broad class of auctions that includes first-price, second-price, and generalized second-price auctions as special cases. For individual guarantees, we further show such pacing algorithms enjoy emph{dynamic regret} bounds for individual value maximization, with respect to the sequence of budget-pacing bids, for any auction satisfying a monotone bang-for-buck property. To complement our theoretical findings, we provide semi-synthetic numerical simulations based on auction data from the Bing Advertising platform.
