Regret Minimization for Reserve Prices in Second-Price Auctions

Cesa-Bianchi, Nicolò; Gentile, Claudio; Mansour, Yishay

doi:10.1137/1.9781611973105.86

Cited by 71 publications

(115 citation statements)

References 11 publications

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“…Our main theorem implies generalization bounds for many auction classes, such as second price auctions, which are fundamentally important in economics and beyond (e.g., (Vickrey, 1961;Cesa-Bianchi et al, 2015;Daskalakis and Syrgkanis, 2016)). We also study generalized VCG auctions, such as affine maximizer auctions, virtual valuations combinatorial auctions, and mixed-bundling auctions, which have been studied in AI and economics (e.g., (Sandholm and Likhodedov, 2015;Roberts, 1979;Lavi et al, 2003;Dobzinski and Sundararajan, 2008;Jehiel et al, 2007)).…”

Section: Our Contributionsmentioning

confidence: 92%

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

Balcan

Sandholm

Vitercik

2018

Proceedings of the 2018 ACM Conference on Economics and Computation

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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 "wellbehaved." 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. arXiv:1705.00243v4 [cs.LG] 8 Aug 2018 * We generalize to multiple buyers in Section 2.1.2.

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Section: Our Contributionsmentioning

confidence: 92%

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

Balcan

Sandholm

Vitercik

2018

Proceedings of the 2018 ACM Conference on Economics and Computation

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“…The complexity of g affects the computational complexity of the algorithm and there is a tradeoff between the computational complexity and the regret of the algorithm. For our computations here, we will set g + 1 = T C(T P ) + 1 α (16) where 0 < α < 1 is a constant. Now, we are ready to compute the components of the regret: where 2 ∈ (0, 1) is a constant.…”

Section: F1 Switching Regret and Poamentioning

confidence: 99%

Learning to Bid Without Knowing your Value

Feng

Podimata

Syrgkanis

2018

Proceedings of the 2018 ACM Conference on Economics and Computation

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We address online learning in complex auction settings, such as sponsored search auctions, where the value of the bidder is unknown to her, evolving in an arbitrary manner and observed only if the bidder wins an allocation. We leverage the structure of the utility of the bidder and the partial feedback that bidders typically receive in auctions, in order to provide algorithms with regret rates against the best fixed bid in hindsight, that are exponentially faster in convergence in terms of dependence on the action space, than what would have been derived by applying a generic bandit algorithm and almost equivalent to what would have been achieved in the full information setting. Our results are enabled by analyzing a new online learning setting with outcome-based feedback, which generalizes learning with feedback graphs. We provide an online learning algorithm for this setting, of independent interest, with regret that grows only logarithmically with the number of actions and linearly only in the number of potential outcomes (the latter being very small in most auction settings). Last but not least, we show that our algorithm outperforms the bandit approach experimentally 1 and that this performance is robust to dropping some of our theoretical assumptions or introducing noise in the feedback that the bidder receives.

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“…Bandit algorithms were already designed and studied for repeated auctions, including RTB auctions. For instance, in repeated second-price auctions, [33] construct a bandit algorithm to optimize a given bidder's revenue, while [5] design a bandit algorithm to optimize the seller's reserve price.…”

Section: Related Workmentioning

confidence: 99%

Optimization of a SSP's Header Bidding Strategy using Thompson Sampling

Jauvion¹,

Grislain²,

Sielenou

et al. 2018

Proceedings of the 24th ACM SIGKDD International Conference on Knowledge Discovery &Amp; Data Mining

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Over the last decade, digital media (web or app publishers) generalized the use of real time ad auctions to sell their ad spaces. Multiple auction platforms, also called Supply-Side Platforms (SSP), were created. Because of this multiplicity, publishers started to create competition between SSPs. In this setting, there are two successive auctions: a second price auction in each SSP and a secondary, first price auction, called header bidding auction, between SSPs.In this paper, we consider an SSP competing with other SSPs for ad spaces. The SSP acts as an intermediary between an advertiser wanting to buy ad spaces and a web publisher wanting to sell its ad spaces, and needs to define a bidding strategy to be able to deliver to the advertisers as many ads as possible while spending as little as possible. The revenue optimization of this SSP can be written as a contextual bandit problem, where the context consists of the information available about the ad opportunity, such as properties of the internet user or of the ad placement.Using classical multi-armed bandit strategies (such as the original versions of UCB and EXP3) is inefficient in this setting and yields a low convergence speed, as the arms are very correlated. In this paper we design and experiment a version of the Thompson Sampling algorithm that easily takes this correlation into account. We combine this bayesian algorithm with a particle filter, which permits to handle non-stationarity by sequentially estimating the distribution of the highest bid to beat in order to win an auction. We apply this methodology on two real auction datasets, and show that it significantly outperforms more classical approaches.The strategy defined in this paper is being developed to be deployed on thousands of publishers worldwide.

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Regret Minimization for Reserve Prices in Second-Price Auctions

Cited by 71 publications

References 11 publications

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

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

Learning to Bid Without Knowing your Value

Optimization of a SSP's Header Bidding Strategy using Thompson Sampling

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