arXiv 2107.018352021-07cs.LGstat.ML

随机一次报价中的快速速率学习

Fast Rate Learning in Stochastic First Price Bidding

Université PSL（巴黎文理研究大学）；mercis Group（1000mercis集团）；CNRS（法国国家科学研究中心）；ENS Lyon（里昂高等师范学院）

Juliette Achddou, Olivier Cappé, Aurélien Garivier

发表信息：: ACML 2021 - Proceedings of Machine Learning Research 157, 2021, Nov 2021, SIngapore, Singapore

摘要：

在程序化广告中，第一价格拍卖在很大程度上取代了基于Vickrey拍卖的传统投标方法。就学习而言，第一价格拍卖更具挑战性，因为最优投标策略不仅取决于物品的价值，而且还需要其他投标的一些知识。他们已经在顺序学习中产生了一些作品，其中许多考虑了以对抗方式选择买方价值或对手最大出价的模型。即使在最简单的设置中，这也会导致算法的遗憾随着时间范围$T$的$\sqrt{T}$而增长。专注于买方发挥对一个平稳的随机环境的情况下，我们展示了如何实现显着降低遗憾：当对手的最大出价分布是已知的，我们提供了一个算法，其遗憾可以低$\log^2(T)$的情况下，分布必须学习顺序，概括该算法可以实现$T^{1/3+ ε}$遗憾，任何$ε>0$。为了获得这些结果，我们引入了两个新的想法，可以在自己的权利感兴趣。首先，通过转置在公布的价格设置中获得的结果，我们提供的条件下，第一个价格投标效用是局部二次在其最优。第二，我们利用的观察，在小的子区间，浓度的经验分布函数的变化可以更准确地控制比使用经典的Dvoretzky-Kiefer-Wolfowitz不等式。数值模拟证实，我们的算法收敛速度远远快于文献中提出的各种出价分布的替代方案，包括在实际的程序化广告平台上收集的出价。

英文摘要：

First-price auctions have largely replaced traditional bidding approaches based on Vickrey auctions in programmatic advertising. As far as learning is concerned, first-price auctions are more challenging because the optimal bidding strategy does not only depend on the value of the item but also requires some knowledge of the other bids. They have already given rise to several works in sequential learning, many of which consider models for which the value of the buyer or the opponents' maximal bid is chosen in an adversarial manner. Even in the simplest settings, this gives rise to algorithms whose regret grows as $\sqrt{T}$ with respect to the time horizon $T$. Focusing on the case where the buyer plays against a stationary stochastic environment, we show how to achieve significantly lower regret: when the opponents' maximal bid distribution is known we provide an algorithm whose regret can be as low as $\log^2(T)$; in the case where the distribution must be learnt sequentially, a generalization of this algorithm can achieve $T^{1/3+ ε}$ regret, for any $ε>0$. To obtain these results, we introduce two novel ideas that can be of interest in their own right. First, by transposing results obtained in the posted price setting, we provide conditions under which the first-price biding utility is locally quadratic around its optimum. Second, we leverage the observation that, on small sub-intervals, the concentration of the variations of the empirical distribution function may be controlled more accurately than by using the classical Dvoretzky-Kiefer-Wolfowitz inequality. Numerical simulations confirm that our algorithms converge much faster than alternatives proposed in the literature for various bid distributions, including for bids collected on an actual programmatic advertising platform.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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