Budget-management systems are one of the key components of modern auction markets. Internet advertising platforms typically offer advertisers the possibility to pace the rate at which their budget is depleted, through budget-pacing mechanisms. We focus on multiplicative pacing mechanisms in an online setting in which a bidder is repeatedly confronted with a series of advertising opportunities. After collecting bids, each item is then allocated through a single-item, second-price auction. If there were no budgetary constraints, bidding truthfully would be an optimal choice for the advertiser. However, since their budget is limited, the advertiser may want to shade their bid downwards in order to preserve their budget for future opportunities, and to spread expenditures evenly over time. The literature on online pacing problems mostly focuses on the setting in which the bidder optimizes an additive separable objective, such as the total click-through rate or the revenue of the allocation. In many settings, however, bidders may also care about other objectives which oftentimes are non-separable, and therefore not amenable to traditional online learning techniques. Building on recent work, we study the frequent case in which advertisers seek to reach a certain distribution of impressions over a target population of users. We introduce a novel regularizer to achieve this desideratum, and show how to integrate it into an online mirror descent scheme attaining the optimal order of sub-linear regret compared to the optimal allocation in hindsight when inputs are drawn independently, from an unknown distribution. Moreover, we show that our approach can easily be incorporated in standard existing pacing systems that are not usually built for this objective. The effectiveness of our algorithm in internet advertising applications is confirmed by numerical experiments on real-world data.

中文翻译：

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用于拍卖市场节奏的 Parity Ray 正则化器

预算管理系统是现代拍卖市场的关键组成部分之一。互联网广告平台通常通过预算调整机制为广告商提供调整其预算消耗速度的可能性。我们专注于在线环境中的乘法起搏机制，在该环境中，投标人反复面临一系列广告机会。收集出价后，每件物品都会通过单品、次价拍卖进行分配。如果没有预算限制，如实出价将是广告主的最佳选择。然而，由于他们的预算有限，广告商可能希望降低他们的出价，以便为未来的机会保留他们的预算，并随着时间的推移平均分配支出。关于在线步调问题的文献主要集中在投标者优化附加可分离目标的设置上，例如总点击率或分配收入。然而，在许多情况下，投标人可能还关心其他目标，这些目标通常是不可分离的，因此不适合传统的在线学习技术。在最近的工作的基础上，我们研究了广告商寻求在目标用户群中达到一定印象分布的常见案例。我们引入了一种新的正则化器来实现这一需求，并展示了如何将其集成到在线镜像下降方案中，与从未知分布独立抽取输入时的事后最佳分配相比，获得亚线性后悔的最佳顺序。而且，我们表明，我们的方法可以很容易地合并到通常不是为此目标而构建的标准现有起搏系统中。我们的算法在互联网广告应用中的有效性得到了对真实世界数据的数值实验的证实。