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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 advertisingplatforms.  We show that when agents simultaneously apply a natural form ofgradient-based pacing, the liquid welfare obtained over the course of thelearning dynamics is at least half the optimal expected liquid welfareobtainable by any allocation rule.  Crucially, this result holds \emph{without requiring convergence of thedynamics}, allowing us to circumvent known complexity-theoretic obstacles offinding equilibria.  This result is also robust to the correlation structure between agentvaluations and holds for any \emph{core auction}, a broad class of auctionsthat includes first-price, second-price, and generalized second-price auctions.For individual guarantees, we further show such pacing algorithms enjoy\emph{dynamic regret} bounds for individual value maximization, with respect tothe sequence of budget-pacing bids, for any auction satisfying a monotonebang-for-buck property.

Budget Pacing in Repeated Auctions: Regret and Efficiency without Convergence