Learning Reserve Prices in Second-Price Auctions

This paper proves the tight sample complexity of Second-Price Auction with Anonymous Reserve, up to a logarithmic factor, for each of all the value distribution families studied in the literature: [0,1]-bounded, [1,H]-bounded, regular, and monotone hazard rate (MHR). Remarkably, the setting-specific tight sample complexity poly(?^{-1}) depends on the precision ? ? (0, 1), but not on the number of bidders n ? 1. Further, in the two bounded-support settings, our learning algorithm allows correlated value distributions. In contrast, the tight sample complexity ??(n) ? poly(?^{-1}) of Myerson Auction proved by Guo, Huang and Zhang (STOC 2019) has a nearly-linear dependence on n ? 1, and holds only for independent value distributions in every setting. We follow a similar framework as the Guo-Huang-Zhang work, but replace their information theoretical arguments with a direct proof

Learning Reserve Prices in Second-Price Auctions

This paper proves the tight sample complexity of Second-Price Auction with Anonymous Reserve, up to a logarithmic factor, for all value distribution families that have been considered in the literature. Compared to Myerson Auction, whose sample complexity was settled very recently in (Guo, Huang and Zhang, STOC 2019), Anonymous Reserve requires much fewer samples for learning. We follow a similar framework as the Guo-Huang-Zhang work, but replace their information theoretical argument with a direct proof

Reserve price optimization in display advertising

Display advertising is the main type of online advertising, and it comes in the form of banner ads and rich media on publishers\u27 websites. Publishers sell ad impressions, where an impression is one display of an ad in a web page. A common way to sell ad impressions is through real-time bidding (RTB). In 2019, advertisers in the United States spent nearly 60 billion U.S. dollars on programmatic digital display advertising. By 2022, expenditures are expected to increase to nearly 95 billion U.S. dollars. In general, the remaining impressions are sold directly by the publishers. The only way for publishers to control the price of the impressions they sell through RTB is by setting up a reserve price, which has to be beaten by the winning bids. The two main types of RTB auction strategies are 1) first-price auctions, i.e., the winning advertiser pays the highest bid, and 2) second-price auctions, i.e., the winning advertiser pays the maximum of the second highest bid and the reserve price (the minimum price that a publisher can accept for an impression). In both types of auctions, bids lower than the reserve prices will be automatically rejected. Since both strategies are influenced by the reserve price, setting a good reserve price is an important, but challenging task for publishers. A high reserve price may lead to very few winning bids, and thus can decrease the revenue substantially. A low reserve price may devalue the impressions and hurt the revenue because advertisers do not need to bid high to beat the reserve. Reduction of ad revenue may affect the quality of free content and publishers\u27 business sustainability. Therefore, in an ideal situation, the publishers would like to set the reserve price as high as possible, while ensuring that there is a winning bid. This dissertation proposes to use machine learning techniques to determine the optimal reserve prices for individual impressions in real-time, with the goal of maximizing publishers\u27 ad revenue. The proposed techniques are practical because they use data only available to publishers. They are also general because they can be applied to most online publishers. The novelty of the research comes from both the problem, which was not studied before, and the proposed techniques, which are adapted to the online publishing domain. For second-price auctions, a survival-analysis-based model is first proposed to predict failure rates of reserve prices of specific impressions in second-price auctions. It uses factorization machines (FM) to capture feature interaction and header bidding information to improve the prediction performance. The experiments, using data from a large media company, show that the proposed model for failure rate prediction outperforms the comparative systems. The survival-analysis-based model is augmented further with a deep neural network (DNN) to capture the feature interaction. The experiments show that the DNN-based model further improves the performance from the FM-based one. For first-price auctions, a multi-task learning framework is proposed to predict the lower bounds of highest bids with a coverage probability. The model can guarantee the highest bids of at least a certain percentage of impressions are more than the corresponding predicted lower bounds. Setting the final reserve prices to the lower bounds, the model can guarantee a certain percentage of outbid impressions in real-time bidding. The experiments show that the proposed method can significantly outperform the comparison systems

Learning to bid in revenue-maximizing auctions

We consider the problem of the optimization of bidding strategies in prior-dependent revenue-maximizing auctions, when the seller fixes the reserve prices based on the bid distributions. Our study is done in the setting where one bidder is strategic. Using a variational approach, we study the complexity of the original objective and we introduce a relaxation of the objective functional in order to use gradient descent methods. Our approach is simple, general and can be applied to various value distributions and revenue-maximizing mechanisms. The new strategies we derive yield massive uplifts compared to the traditional truthfully bidding strategy

A General Theory of Sample Complexity for Multi-Item Profit Maximization

The design of profit-maximizing multi-item mechanisms is a notoriously challenging problem with tremendous real-world impact. The mechanism designer's goal is to field a mechanism with high expected profit on the distribution over buyers' values. Unfortunately, if the set of mechanisms he optimizes over is complex, a mechanism may have high empirical profit over a small set of samples but low expected profit. This raises the question, how many samples are sufficient to ensure that the empirically optimal mechanism is nearly optimal in expectation? We uncover structure shared by a myriad of pricing, auction, and lottery mechanisms that allows us to prove strong sample complexity bounds: for any set of buyers' values, profit is a piecewise linear function of the mechanism's parameters. We prove new bounds for mechanism classes not yet studied in the sample-based mechanism design literature and match or improve over the best known guarantees for many classes. The profit functions we study are significantly different from well-understood functions in machine learning, so our analysis requires a sharp understanding of the interplay between mechanism parameters and buyer values. We strengthen our main results with data-dependent bounds when the distribution over buyers' values is "well-behaved." Finally, we investigate a fundamental tradeoff in sample-based mechanism design: complex mechanisms often have higher profit than simple mechanisms, but more samples are required to ensure that empirical and expected profit are close. We provide techniques for optimizing this tradeoff