Online advertising platforms typically use auction mechanisms to allocate ad placements. Advertisers participate in a series of repeated auctions, and must select bids that will maximize their overall rewards while adhering to certain constraints. We focus on the scenario in which the advertiser has budget and return-on-investment (ROI) constraints. We investigate the problem of budget- and ROI-constrained bidding in repeated non-truthful auctions, such as first-price auctions, and present a best-of-both-worlds framework with no-regret guarantees under both stochastic and adversarial inputs. By utilizing the notion of interval regret, we demonstrate that our framework does not require knowledge of specific parameters of the problem which could be difficult to determine in practice. Our proof techniques can be applied to both the adversarial and stochastic cases with minimal modifications, thereby providing a unified perspective on the two problems. In the adversarial setting, we also show that it is possible to loosen the traditional requirement of having a strictly feasible solution to the offline optimization problem at each round.

翻译：在线广告平台通常采用拍卖机制来分配广告位。广告主参与一系列重复拍卖，需选择能最大化总体收益且满足特定约束的出价策略。本文聚焦于广告主同时受预算和投资回报率（ROI）约束的场景，研究在重复非真实拍卖（如第一价格拍卖）中受预算和ROI约束的竞价问题，并提出了一个兼具随机输入与对抗输入下无遗憾保证的“两全其美”框架。通过利用区间遗憾的概念，我们证明该框架无需预知实践中难以确定的特定问题参数。我们的证明技术可最小化修改后同时适用于对抗与随机情形，从而为两类问题提供统一视角。在对抗设定中，我们还证明可以放宽传统要求——每轮离线优化问题必须存在严格可行解。