Learning to Bid Optimally and Efficiently in Adversarial First-price Auctions
Courant Institute of Mathematical Sciences and the Center for Data Science, New York University（Courant数学科学研究所和数据科学中心，纽约大学）；Stern School of Business, New York University（商学院，纽约大学）；Department of Electrical Engineering, Stanford University（电气工程系，斯坦福大学）；Yahoo! Research at Verizon Media（Verizon Media的Yahoo!研究）
Yanjun Han, Zhengyuan Zhou, Aaron Flores, Erik Ordentlich, Tsachy Weissman
First-price auctions have very recently swept the online advertising industry, replacing second-price auctions as the predominant auction mechanism on many platforms. This shift has brought forth important challenges for a bidder: how should one bid in a first-price auction, where unlike in second-price auctions, it is no longer optimal to bid one's private value truthfully and hard to know the others' bidding behaviors? In this paper, we take an online learning angle and address the fundamental problem of learning to bid in repeated first-price auctions, where both the bidder's private valuations and other bidders' bids can be arbitrary. We develop the first minimax optimal online bidding algorithm that achieves an $\widetilde{O}(\sqrt{T})$ regret when competing with the set of all Lipschitz bidding policies, a strong oracle that contains a rich set of bidding strategies. This novel algorithm is built on the insight that the presence of a good expert can be leveraged to improve performance, as well as an original hierarchical expert-chaining structure, both of which could be of independent interest in online learning. Further, by exploiting the product structure that exists in the problem, we modify this algorithm--in its vanilla form statistically optimal but computationally infeasible--to a computationally efficient and space efficient algorithm that also retains the same $\widetilde{O}(\sqrt{T})$ minimax optimal regret guarantee. Additionally, through an impossibility result, we highlight that one is unlikely to compete this favorably with a stronger oracle (than the considered Lipschitz bidding policies). Finally, we test our algorithm on three real-world first-price auction datasets obtained from Verizon Media and demonstrate our algorithm's superior performance compared to several existing bidding algorithms.
Since 2019, most ad exchanges and sell-side platforms (SSPs), in the online advertising industry, shifted from second to first price auctions. Due to the fundamental difference between these auctions, demand-side platforms (DSPs) have had to update their bidding strategies to avoid bidding unnecessarily high and hence overpaying. Bid shading was proposed to adjust the bid price intended for second-price auctions, in order to balance cost and winning probability in a first-price auction setup. In this study, we introduce a novel deep distribution network for optimal bidding in both open (non-ce…
Online auctions play a central role in online advertising, and are one of the main reasons for the industry's scalability and growth. With great changes in how auctions are being organized, such as changing the second- to first-price auction type, advertisers and demand platforms are compelled to adapt to a new volatile environment. Bid shading is a known technique for preventing overpaying in auction systems that can help maintain the strategy equilibrium in first-price auctions, tackling one of its greatest drawbacks. In this study, we propose a machine learning approach of modeling optimal …
In research and policy-making guidelines, the single-bidder rate is a commonly used proxy of corruption in public procurement used but ipso facto this is not evidence of a corrupt auction, but an uncompetitive auction. And while an uncompetitive auction could arise due to a corrupt procurer attempting to conceal the transaction, but it could also be a result of geographic isolation, monopolist presence, or other structural factors. In this paper we use positive-unlabelled classification to attempt to separate public procurement auctions in the Russian Federation into auctions that are probably…
We study revenue optimization learning algorithms for repeated second-price auctions with reserve where a seller interacts with multiple strategic bidders each of which holds a fixed private valuation for a good and seeks to maximize his expected future cumulative discounted surplus. We propose a novel algorithm that has strategic regret upper bound of $O(\log\log T)$ for worst-case valuations. This pricing is based on our novel transformation that upgrades an algorithm designed for the setup with a single buyer to the multi-buyer case. We provide theoretical guarantees on the ability of a tra…
Learning to Coordinate Bidders in Non-Truthful Auctions
Shanghai University of Finance and Economics, School of Computing and Artificial Intelligence, Key Laboratory of Interdisciplinary Research of Computation and Economics（上海财经大学，计算机与人工智能学院，计算与经济学交叉研究重点实验室）；Microsoft Research & The Chinese University of Hong Kong, Shenzhen（微软研究院及香港中文大学（深圳））
With the advent and increasing consolidation of e-commerce, digital advertising has very recently replaced traditional advertising as the main marketing force in the economy. In the past four years, a particularly important development in the digital advertising industry is the shift from second-price auctions to first-price auctions for online display ads. This shift immediately motivated the intellectually challenging question of how to bid in first-price auctions, because unlike in second-price auctions, bidding one's private value truthfully is no longer optimal. Following a series of rece…
University of Maryland, College Park（马里兰大学帕克分校）；University of Zurich（苏黎世大学）
Single-shot auctions are commonly used as a means to sell goods, for example when selling ad space or allocating radio frequencies, however devising mechanisms for auctions with multiple bidders and multiple items can be complicated. It has been shown that neural networks can be used to approximate optimal mechanisms while satisfying the constraints that an auction be strategyproof and individually rational. We show that despite such auctions maximizing revenue, they do so at the cost of revealing private bidder information. While randomness is often used to build in privacy, in this context i…
The Hebrew University of Jerusalem（耶路撒冷希伯来大学）；Microsoft Research（微软研究院）
We consider the problem of bid prediction in repeated auctions and evaluate the performance of econometric methods for learning agents using a dataset from a mainstream sponsored search auction marketplace. Sponsored search auctions is a billion dollar industry and the main source of revenue of several tech giants. A critical problem in optimizing such marketplaces is understanding how bidders will react to changes in the auction design. We propose the use of no-regret based econometrics for bid prediction, modeling players as no-regret learners with respect to a utility function, unknown to t…
Although shill bidding is a common auction fraud, it is however very tough to detect. Due to the unavailability and lack of training data, in this study, we build a high-quality labeled shill bidding dataset based on recently collected auctions from eBay. Labeling shill biding instances with multidimensional features is a critical phase for the fraud classification task. For this purpose, we introduce a new approach to systematically label the fraud data with the help of the hierarchical clustering CURE that returns remarkable results as illustrated in the experiments.
We study the online learning problem of a bidder who participates in repeated auctions. With the goal of maximizing his T-period payoff, the bidder determines the optimal allocation of his budget among his bids for $K$ goods at each period. As a bidding strategy, we propose a polynomial-time algorithm, inspired by the dynamic programming approach to the knapsack problem. The proposed algorithm, referred to as dynamic programming on discrete set (DPDS), achieves a regret order of $O(\sqrt{T\log{T}})$. By showing that the regret is lower bounded by $Ω(\sqrt{T})$ for any strategy, we conclude tha…
Recently the online advertising market has exhibited a gradual shift from second-price auctions to first-price auctions. Although there has been a line of works concerning online bidding strategies in first-price auctions, it still remains open how to handle budget constraints in the problem. In the present paper, we initiate the study for a buyer with budgets to learn online bidding strategies in repeated first-price auctions. We propose an RL-based bidding algorithm against the optimal non-anticipating strategy under stationary competition. Our algorithm obtains $\widetilde O(\sqrt T)$-regre…
