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## The sample complexity of revenue maximization (2014)

Venue: | In Proceedings of the 46th Annual ACM Symposium on Theory of Computing |

Citations: | 9 - 4 self |

### Citations

1979 | A theory of learnable, in
- Valiant
- 1984
(Show Context)
Citation Context ... — i.e., over m + 1 i.i.d. samples from F. The expected revenue of an optimal auction is with respect to a single sample (the input) from F. Our formalism is inspired by computational learning theory =-=[38]-=-. The answer to the question (*) could be a function of up to three different parameters: the error tolerance , the number k of bidders, and the set D of allowable distributions2. It is clear that so... |

1603 |
Optimal auction design
- Myerson
- 1981
(Show Context)
Citation Context ...n F that is known a priori, Myerson’s optimal auction gives the item to the bidder with the highest virtual valuation ϕi(vi) = vi− 1−Fi(vi)fi(vi) , or to no one if all virtual valuations are negative =-=[33]-=-. The empirical Myerson auction is the obvious analog when one has data rather than distributional knowledge: define F̄i as the empirical distribution of the samples from Fi, and run the optimal aucti... |

530 |
Probability and computing, Randomized algorithms and probabilistic analysis
- Mitzenmacher, Upfal
- 2005
(Show Context)
Citation Context ...amples have q values that are at most (1 +γ)tli . As the expected number of such samples is (1+γ)tlim, a Chernoff bound gives the following upper bound on the probability that q(ui) > (1 + γ)tli (cf. =-=[31]-=-): exp{− γ 2tlim 2(1 + γ) }. Similarly, the probability that q(ui) < tli/(1 + γ) is bounded by exp{− γ 2tlim 3(1 + γ) }. It will be helpful to bound both tl1m and [tli+1 − tli ]m. As ξ̂m ≥ 1, tl1m = (... |

416 |
Neural Network Learning – Theoretical Foundations
- Anthony, Bartlett
- 1999
(Show Context)
Citation Context ... is called α-strongly regular if each Fi is α-strongly regular. For the lower bound, we take the set D of allowable distributions in (*) to be the α-strongly regular distributions for a parameter α ∈ =-=[0, 1]-=-. 1.3 Our Results Our main result is that m = poly(k, 1 ) samples are necessary and sufficient for the existence of an m-sample auction strategy that, for every strongly regular distribution F, has e... |

218 |
Optimal Selling Strategies under Uncertainty for a Discriminating Monopolist when Demands are Interdependent
- Cr¶emer, McLean
- 1985
(Show Context)
Citation Context ...ich differ in various respects from our model, see [4, 29]. For other uses of samples in auction design that differ from ours, see Fu et al. [21], who use samples to extend the Crémer-McLean theorem =-=[15]-=- to partially known valuation distributions, and Chawla et al. [10], who design non-truthful auctions that both have equilibrium revenue within a constant of optimal and enable accurate inference abou... |

178 | Auctions versus Negotiations
- Bulow, Klemperer
- 1996
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Citation Context ... [18, Theorem 4.3]. • If only a 14 -approximation of the optimal expected revenue is required, then only a single sample is required. This follows from a generalization of the Bulow-Klemperer theorem =-=[7]-=- to non-i.i.d. bidders [26, Theorem 4.4]. Thus, the necessary dependence on k fundamentally involves the interplay between bidder competition, non-identical distributions, and a very close (but still ... |

113 | Competitive auctions.
- Goldberg, Hartline, et al.
- 2006
(Show Context)
Citation Context ...d revenue of some auction of interest (e.g., second-price) approaches the optimal with an increasing number of (i.i.d.) bidders, see Neeman [34], Segal [37], Baliga and Vohra [6], and Goldberg et al. =-=[22]-=-. For applications of learning theory concepts to prior-free auction design in unlimited-supply settings, see Balcan et al. [5]. Finally, the technical issue of ironing from samples comes up also in H... |

85 | Optimal marketing strategies over social networks.
- Hartline, Mirrokni, et al.
- 2008
(Show Context)
Citation Context ...ensions; we are confident that many others are possible, as has been shown subsequently by Cole and Shravas [14]. The following property of MHR distributions is well known [27, Lemma 4.1]. Lemma 4.1 (=-=[27]-=-). Let F be an MHR distribution with monopoly price r. If q(r) is the quantile of valuation r in the distribution F , then q(r) ≥ 1e . We next show how to generalize this result to α-strongly regular ... |

76 | Simple versus optimal mechanisms
- Hartline, Roughgarden
- 2009
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Citation Context ...dest constants like 14 . For example, previous work has demonstrated that auctions with reasonably good approximation factors are possible with minimal dependence on the valuation distributions (e.g. =-=[9, 26, 2]-=-) or even, when there is no bidder with a unique valuation distribution, with no dependence on the valuation distributions [17, 18, 36]. Another interpretation of some previous results, such as [11, 9... |

75 | Optimal pricing mechanisms with unknown demand,”
- Segal
- 2003
(Show Context)
Citation Context ...hich identify conditions under which the expected revenue of some auction of interest (e.g., second-price) approaches the optimal with an increasing number of (i.i.d.) bidders, see Neeman [34], Segal =-=[37]-=-, Baliga and Vohra [6], and Goldberg et al. [22]. For applications of learning theory concepts to prior-free auction design in unlimited-supply settings, see Balcan et al. [5]. Finally, the technical ... |

67 | The value of knowing a demand curve: bounds on regret for online posted-price auctions
- Kleinberg, Leighton
- 2003
(Show Context)
Citation Context ...y with the papers most closely related to the present work. For previously studied models about revenue-maximization with an unknown distribution, which differ in various respects from our model, see =-=[4, 29]-=-. For other uses of samples in auction design that differ from ours, see Fu et al. [21], who use samples to extend the Crémer-McLean theorem [15] to partially known valuation distributions, and Chawl... |

56 | Algorithmic Pricing via Virtual Valuations
- Chawla, Hartline, et al.
- 2007
(Show Context)
Citation Context ...dest constants like 14 . For example, previous work has demonstrated that auctions with reasonably good approximation factors are possible with minimal dependence on the valuation distributions (e.g. =-=[9, 26, 2]-=-) or even, when there is no bidder with a unique valuation distribution, with no dependence on the valuation distributions [17, 18, 36]. Another interpretation of some previous results, such as [11, 9... |

55 | Reserve Prices in Internet Advertising Auctions: A Field Experiment. EC,
- Ostrovsky, Schwarz
- 2011
(Show Context)
Citation Context ...an analysis was used to provide guidance on how to set per-click reserve prices, and the valuation distributions used in this analysis are derived straightforwardly from bid data from the recent past =-=[35]-=-. This is a natural approach, but how well does it work? 1.1 The Model The goal of this paper is to understand how much data is necessary and sufficient to guarantee near-optimal expected revenue. Our... |

40 |
Revenue maximization with a single sample
- Dhangwatnotai, Roughgarden, et al.
- 2015
(Show Context)
Citation Context ...sible with minimal dependence on the valuation distributions (e.g. [9, 26, 2]) or even, when there is no bidder with a unique valuation distribution, with no dependence on the valuation distributions =-=[17, 18, 36]-=-. Another interpretation of some previous results, such as [11, 9], is the existence of constant-factor approximate auctions that derive no benefit from bidder competition. Our lower bound identifies,... |

35 | The effectiveness of English auctions,”
- Neeman
- 2003
(Show Context)
Citation Context ... settings, which identify conditions under which the expected revenue of some auction of interest (e.g., second-price) approaches the optimal with an increasing number of (i.i.d.) bidders, see Neeman =-=[34]-=-, Segal [37], Baliga and Vohra [6], and Goldberg et al. [22]. For applications of learning theory concepts to prior-free auction design in unlimited-supply settings, see Balcan et al. [5]. Finally, th... |

28 | Market research and market design
- Baliga, Vohra
(Show Context)
Citation Context ...s under which the expected revenue of some auction of interest (e.g., second-price) approaches the optimal with an increasing number of (i.i.d.) bidders, see Neeman [34], Segal [37], Baliga and Vohra =-=[6]-=-, and Goldberg et al. [22]. For applications of learning theory concepts to prior-free auction design in unlimited-supply settings, see Balcan et al. [5]. Finally, the technical issue of ironing from ... |

22 | Sequential posted pricing and multi-parameter mechanism design. In:
- Chawla, Hartline, et al.
- 2010
(Show Context)
Citation Context ...26, 2]) or even, when there is no bidder with a unique valuation distribution, with no dependence on the valuation distributions [17, 18, 36]. Another interpretation of some previous results, such as =-=[11, 9]-=-, is the existence of constant-factor approximate auctions that derive no benefit from bidder competition. Our lower bound identifies, for the first time, a constant approximation threshold beyond whi... |

22 |
Profit Maximization in Mechanism Design.
- Hartline, Karlin
- 2007
(Show Context)
Citation Context ...ghest expected revenue. The optimal auction depends on the assumed distribution, in some cases in a detailed way. While there is now a significant body of work on worst-case revenue maximization (see =-=[25]-=-), a majority of modern computer science research on revenue-maximizing auctions uses Bayesian analysis to measure auction performance (see [24]). Since the comparison between auctions depends fundame... |

19 | Reducing mechanism design to algorithm design via machine learning
- Balcan, Blum, et al.
(Show Context)
Citation Context ... see Neeman [34], Segal [37], Baliga and Vohra [6], and Goldberg et al. [22]. For applications of learning theory concepts to prior-free auction design in unlimited-supply settings, see Balcan et al. =-=[5]-=-. Finally, the technical issue of ironing from samples comes up also in Ha and Hartline [23], in the context of prior-free mechanism design, and the aforementioned Chawla et al. [10]. Our goal of obta... |

19 | Supply-limiting mechanisms
- Roughgarden, Talgam-Cohen, et al.
- 2012
(Show Context)
Citation Context ...sible with minimal dependence on the valuation distributions (e.g. [9, 26, 2]) or even, when there is no bidder with a unique valuation distribution, with no dependence on the valuation distributions =-=[17, 18, 36]-=-. Another interpretation of some previous results, such as [11, 9], is the existence of constant-factor approximate auctions that derive no benefit from bidder competition. Our lower bound identifies,... |

14 | Regret minimization for reserve prices in second-price auctions.
- Cesa-Bianchi, Gentile, et al.
- 2013
(Show Context)
Citation Context ...3) for MHR and regular distributions, respectively.6 As our results show, the learning problem is quite different and more delicate with multiple non-i.i.d. bidders. The papers of Cesa-Bianchi et al. =-=[8]-=- and Medina and Mohri [30] give algorithms for learning the optimal reserve-price-based single-item auction. Our problem of learning the best singleitem auction — whether reserve-based or otherwise — ... |

11 | Priorindependent multi-parameter mechanism design. InWINE
- Devanur, Hartline, et al.
- 2011
(Show Context)
Citation Context ...sible with minimal dependence on the valuation distributions (e.g. [9, 26, 2]) or even, when there is no bidder with a unique valuation distribution, with no dependence on the valuation distributions =-=[17, 18, 36]-=-. Another interpretation of some previous results, such as [11, 9], is the existence of constant-factor approximate auctions that derive no benefit from bidder competition. Our lower bound identifies,... |

9 | Learning theory and algorithms for revenue optimization in second price auctions with reserve.
- Mohri, Medina
- 2014
(Show Context)
Citation Context ...stributions, respectively.6 As our results show, the learning problem is quite different and more delicate with multiple non-i.i.d. bidders. The papers of Cesa-Bianchi et al. [8] and Medina and Mohri =-=[30]-=- give algorithms for learning the optimal reserve-price-based single-item auction. Our problem of learning the best singleitem auction — whether reserve-based or otherwise — is harder. With non-i.i.d.... |

8 | Optimal and efficient parametric auctions
- Azar, Daskalakis, et al.
- 2013
(Show Context)
Citation Context ...venue within a constant of optimal and enable accurate inference about the valuation distribution from samples. For other ways to parameterize partial knowledge about valuations, see e.g. Azar et al. =-=[3]-=- and Chiesa et al. [12]. For asymptotic optimality results in various symmetric settings, which identify conditions under which the expected revenue of some auction of interest (e.g., second-price) ap... |

8 | Designing and learning optimal finite support auctions.
- Elkind
- 2007
(Show Context)
Citation Context ...nd the aforementioned Chawla et al. [10]. Our goal of obtaining a (1− )- approximation of the maximum revenue achieved by any auction is impossible in the more demanding settings of [23, 10]. Elkind =-=[20]-=- studies a learning problem closely related to ours, in the restricted setting of discrete distributions with known finite supports but with unknown probabilities. In the model in [20], learning is do... |

8 | Mechanism design via consensus estimates, cross checking, and profit extraction
- Ha, Hartline
- 2012
(Show Context)
Citation Context ...ons of learning theory concepts to prior-free auction design in unlimited-supply settings, see Balcan et al. [5]. Finally, the technical issue of ironing from samples comes up also in Ha and Hartline =-=[23]-=-, in the context of prior-free mechanism design, and the aforementioned Chawla et al. [10]. Our goal of obtaining a (1− )- approximation of the maximum revenue achieved by any auction is impossible i... |

5 | Posting prices with unknown distributions
- Babaioff, Blumrosen, et al.
- 2011
(Show Context)
Citation Context ...y with the papers most closely related to the present work. For previously studied models about revenue-maximization with an unknown distribution, which differ in various respects from our model, see =-=[4, 29]-=-. For other uses of samples in auction design that differ from ours, see Fu et al. [21], who use samples to extend the Crémer-McLean theorem [15] to partially known valuation distributions, and Chawl... |

5 | Mechanism design with approximate valuations
- Chiesa, Micali, et al.
- 2012
(Show Context)
Citation Context ...t of optimal and enable accurate inference about the valuation distribution from samples. For other ways to parameterize partial knowledge about valuations, see e.g. Azar et al. [3] and Chiesa et al. =-=[12]-=-. For asymptotic optimality results in various symmetric settings, which identify conditions under which the expected revenue of some auction of interest (e.g., second-price) approaches the optimal wi... |

5 | Sampling and representation complexity of revenue maximization.
- Dughmi, Han, et al.
- 2014
(Show Context)
Citation Context ...blem is information-theoretically easy (meaning polynomial sample complexity) yet computationally hard (under complexity assumptions)? 4. Identify multi-parameter problems, less general than those in =-=[19]-=-, where a near-optimal mechanism can be learned from a polynomial number of samples. 29 5. For problems where a (1 − )-approximate mechanism cannot be learned from a polynomial number of samples, ide... |

5 |
Mechanism design and approximation
- Hartline
- 2013
(Show Context)
Citation Context ...nt body of work on worst-case revenue maximization (see [25]), a majority of modern computer science research on revenue-maximizing auctions uses Bayesian analysis to measure auction performance (see =-=[24]-=-). Since the comparison between auctions depends fundamentally on the assumed distribution, an obvious question is: where does this prior distribution come from, anyway? In most applications, and espe... |

4 | Prophet inequalities with limited information
- Azar, Kleinberg, et al.
- 2014
(Show Context)
Citation Context ...dest constants like 14 . For example, previous work has demonstrated that auctions with reasonably good approximation factors are possible with minimal dependence on the valuation distributions (e.g. =-=[9, 26, 2]-=-) or even, when there is no bidder with a unique valuation distribution, with no dependence on the valuation distributions [17, 18, 36]. Another interpretation of some previous results, such as [11, 9... |

4 | Mechanism design for data science
- Chawla, Hartline, et al.
- 2014
(Show Context)
Citation Context ...er uses of samples in auction design that differ from ours, see Fu et al. [21], who use samples to extend the Crémer-McLean theorem [15] to partially known valuation distributions, and Chawla et al. =-=[10]-=-, who design non-truthful auctions that both have equilibrium revenue within a constant of optimal and enable accurate inference about the valuation distribution from samples. For other ways to parame... |

3 | Optimal auctions for correlated buyers with sampling
- Fu, Haghpanah, et al.
- 2014
(Show Context)
Citation Context ...about revenue-maximization with an unknown distribution, which differ in various respects from our model, see [4, 29]. For other uses of samples in auction design that differ from ours, see Fu et al. =-=[21]-=-, who use samples to extend the Crémer-McLean theorem [15] to partially known valuation distributions, and Chawla et al. [10], who design non-truthful auctions that both have equilibrium revenue with... |

3 | Making the most of your samples.
- Huang, Mansour, et al.
- 2015
(Show Context)
Citation Context .... The paper also contains positive results for restricted classes of mechanisms. 1.6 Subsequent Related Work The preliminary version of this paper [13] motivated several follow-up works. Huang et al. =-=[28]-=- study the single-bidder version of our problem, studied implicitly in [18], and give optimal sample complexity bounds under several different distributional assumptions. Both the upper and lower boun... |

1 |
Applications of α-strongly regular distributions to bayesian auctions
- Cole, Rao
(Show Context)
Citation Context ...], but the learning algorithm is computationally efficient and also accommodates regular distributions. Finally, Cole and Shravas investigated further applications of α-strongly regular distributions =-=[14]-=-. 2 Preliminaries This section reviews Myerson’s optimal single-item auction [33] for the case of known distributions. There are k bidders, and for each bidder i there is a distribution Fi from which ... |

1 |
Psomas. Sample complexity of auctions with side information. Working paper
- Devanur, Huang, et al.
- 2015
(Show Context)
Citation Context ...ngle-item auctions), but unlike the present work, their results do not apply to regular distributions and do not result in computationally efficient learning algorithms. Very recently, Devanur et al. =-=[16]-=- devised a different learning algorithm for our problem which provides a strict improvement on our upper bound. The sample complexity bound in [16] is roughly the same as in [32], but the learning alg... |

1 |
The psuedo-dimension of near-optimal auctions
- Morgenstern, Roughgarden
- 2015
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Citation Context ...s of the dependence on −1, over those implied by the present work. This is also the only paper other than the present work that proves any sample complexity lower bounds. Morgenstern and Roughgarden =-=[32]-=- adapt tools from statistical learning theory [1] to give general sample complexity upper bounds that cover all single-parameter settings for bounded or MHR valuation distributions. The results in [32... |