Budget Pacing in Repeated Auctions: Regret and Efficiency without Convergence
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.