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Online advertising has recently grown into a highly competitive and complexmulti-billion-dollar industry, with advertisers bidding for ad slots at largescales and high frequencies. This has resulted in a growing need for efficient"auto-bidding" algorithms that determine the bids for incoming queries tomaximize advertisers' targets subject to their specified constraints. This workexplores efficient online algorithms for a single value-maximizing advertiserunder an increasingly popular constraint: Return-on-Spend (RoS). We quantifyefficiency in terms of regret relative to the optimal algorithm, which knowsall queries a priori.  We contribute a simple online algorithm that achieves near-optimal regret inexpectation while always respecting the specified RoS constraint when the inputsequence of queries are i.i.d. samples from some distribution. We alsointegrate our results with the previous work of Balseiro, Lu, and Mirrokni[BLM20] to achieve near-optimal regret while respecting both RoS and fixedbudget constraints.  Our algorithm follows the primal-dual framework and uses online mirrordescent (OMD) for the dual updates. However, we need to use a non-canonicalsetup of OMD, and therefore the classic low-regret guarantee of OMD, which isfor the adversarial setting in online learning, no longer holds. Nonetheless,in our case and more generally where low-regret dynamics are applied inalgorithm design, the gradients encountered by OMD can be far from adversarialbut influenced by our algorithmic choices. We exploit this key insight to showour OMD setup achieves low regret in the realm of our algorithm.

Online Bidding Algorithms for Return-on-Spend Constrained Advertisers