Online Bidding Algorithms for Return-on-Spend Constrained Advertisersĝ?FOR VERIFICATION>±

Abstract

We study online auto-bidding algorithms for a single advertiser maximizing value under the Return-on-Spend (RoS) constraint, quantifying performance in terms of regret relative to the optimal offline solution that knows all queries a priori. We contribute a simple online algorithm that achieves near-optimal regret in expectation while always respecting the RoS constraint when the input queries are i.i.d. samples from some distribution. Integrating our results with [9] achieves near-optimal regret under both RoS and fixed budget constraints. Our algorithm uses the primal-dual framework with online mirror descent (OMD) for the dual updates, and the analysis utilizes new insights into the gradient structure.