Settling the sample complexity of single-parameter revenue maximization

Guo, Chenghao; Huang, Zhiyi; Zhang, Xinzhi

doi:10.1145/3313276.3316325

Cited by 38 publications

(98 citation statements)

References 21 publications

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“…Concretely, we propose a model where the seller may access the prior of each buyer via a targeted sampling oracle, which takes a quantile interval as input and returns a sample value within the interval. For example consider the lower bound instance by Guo et al [14]. Targeted sampling allows us to directly collect samples conditioned on being in the top 1 n portion and thus, reducing the number of samples by a factor n.…”

Section: Our Contributionsmentioning

confidence: 99%

“…On the other hand, the lower bound instance by Guo et al [14] suggests that i.i.d. samples are wasteful in the sense that most samples are irrelevant for learning a near optimal auction.…”

Section: Introductionmentioning

confidence: 96%

“…samples per buyer are sufficient and necessary for learning an auction that is optimal up to ϵ? Culminating in a series of studies, Guo et al [14] recently pinned down the optimal sample complexity up to logarithmic factors. For instance, if the values are bounded between 0 and 1, the optimal sample complexity isΘ nϵ −2 .…”

Section: Introductionmentioning

confidence: 99%

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Targeting Makes Sample Efficiency in Auction Design

Huang

Shen

et al. 2021

Proceedings of the 22nd ACM Conference on Economics and Computation

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This paper introduces the targeted sampling model in optimal auction design. In this model, the seller may specify a quantile interval and sample from a buyer's prior restricted to the interval. This can be interpreted as allowing the seller to, for example, examine the top 40% bids from previous buyers with the same characteristics. The targeting power is quantified with a parameter ∆ ∈ [0, 1] which lower bounds how small the quantile intervals could be. When ∆ = 1, it degenerates to Cole and Roughgarden's model of i.i.d. samples; when it is the idealized case of ∆ = 0, it degenerates to the model studied by Chen et al. [7]. For instance, for n buyers with bounded values in [0, 1],Õ (ϵ −1 ) targeted samples suffice while it is known that at leastΩ(nϵ −2 ) i.i.d. samples are needed. In other words, targeted sampling with sufficient targeting power allows us to remove the linear dependence in n, and to improve the quadratic dependence in ϵ −1 to linear. In this work, we introduce new technical ingredients and show that the number of targeted samples sufficient for learning an ϵ-optimal auction is substantially smaller than the sample complexity of i.i.d. samples for the full spectrum of ∆ ∈ [0, 1). Even with only mild targeting power, i.e., whenever ∆ = o(1), our targeted sample complexity upper bounds are strictly smaller than the optimal sample complexity of i.i.d. samples. CCS Concepts: • Theory of computation → Algorithmic game theory; Algorithmic mechanism design; Convergence and learning in games; Computational pricing and auctions.

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Section: Our Contributionsmentioning

confidence: 99%

“…On the other hand, the lower bound instance by Guo et al [14] suggests that i.i.d. samples are wasteful in the sense that most samples are irrelevant for learning a near optimal auction.…”

Section: Introductionmentioning

confidence: 96%

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Targeting Makes Sample Efficiency in Auction Design

Huang

Shen

et al. 2021

Proceedings of the 22nd ACM Conference on Economics and Computation

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“…(See Section 5 for details on this line of work.) Only recently, the optimal sample complexity of single item auctions has been resolved Guo et al (2019). In this paper, we consider the sample complexity of market segmentation.…”

Section: A4 Unbounded Sample Complexity In the General Casementioning

confidence: 99%

“…E 1 is within a [−2 S , 0] window. Distribution E 1 is dominated by the true distribution in the sense of first-order stochastic dominance and, hence, is called the dominated empirical distribution (e.g., Guo et al (2019); Roughgarden and Schrijvers (2016)).…”

Section: Algorithm 3 Robustify a Segmentationmentioning

confidence: 99%

Algorithmic Price Discrimination

Cummings¹,

Devanur²,

Huang³

et al. 2020

Proceedings of the Fourteenth Annual ACM-SIAM Symposium on Discrete Algorithms

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We consider a generalization of the third degree price discrimination problem studied in Bergemann et al. (2015), where an intermediary between the buyer and the seller can design market segments to maximize any linear combination of consumer surplus and seller revenue. Unlike in Bergemann et al. (2015), we assume that the intermediary only has partial information about the buyer's value. We consider three different models of information, with increasing order of difficulty. In the first model, we assume that the intermediary's information allows him to construct a probability distribution of the buyer's value. Next we consider the sample complexity model, where we assume that the intermediary only sees samples from this distribution. Finally, we consider a bandit online learning model, where the intermediary can only observe past purchasing decisions of the buyer, rather than her exact value. For each of these models, we present algorithms to compute optimal or near optimal market segmentation. * Clearly, we need certain assumptions on the seller's behavior for any nontrivial result; there is not much we can do if the seller picks prices randomly all the time. Our assumptions can accommodate natural no regret learning algorithms on the seller side, including the Upper-Confidence-Bound (UCB) algorithm and the Explore-then-Commit (ETC) algorithm. Contributions to the Sample Complexity of Mechanism DesignPioneered by Balcan et al. (2005), Elkind (2007), and Dhangwatnotai et al. (2015), and formalized by Cole and Roughgarden (2014), the sample complexity of mechanism design, in particular, the revenue maximization problem, has been a focal point in algorithmic game theory in the last few years Morgenstern and Roughgarden (2015); Balcan et al. (2016); Devanur et al. (2016); Morgenstern and Roughgarden (2016); Hartline and Taggart (2019); Cai and Daskalakis (2017); Gonczarowski and Nisan (2017); Gonczarowski and Weinberg (2018); Huang et al. (2018b); Guo et al. (2019).This paper adds to the literature of sample complexity of mechanism design in two-folds. The first one is conceptual: we formulate the first sample complexity problem from the viewpoint of an intermediary rather than the seller, and for the task of designing information dispersion rather than allocations and payments. We show impossibility results for the general case and, more importantly, identify sufficient conditions under which we derive positive algorithmic results.Conceptually new models often lead to new technical challenges. Our second contribution is an algorithmic ingredient that tackles such a new challenge. Let us start with a thought experiment: consider a more powerful intermediary who knows the true distributions; the seller, however, still acts according to some beliefs formed from the observed samples. Does the problem become trivial? Can the intermediary simply run the optimal segmentation w.r.t. the true distributions and expect near optimal outcomes?The answers turn out to be negative. Consider a segment for which there are two price...

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Improved Two Sample Revenue Guarantees via Mixed-Integer Linear Programming

Ahunbay

Vetta

2021

Algorithmic Game Theory

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We study the performance of the Empirical Revenue Maximizing (ERM) mechanism in a single-item, single-seller, single-buyer setting. We assume the buyer's valuation is drawn from a regular distribution F and that the seller has access to two independently drawn samples from F . By solving a family of mixed-integer linear programs (MILPs), the ERM mechanism is proven to guarantee at least .5914 times the optimal revenue in expectation. Using solutions to these MILPs, we also show that the worst-case efficiency of the ERM mechanism is at most .61035 times the optimal revenue. These guarantees improve upon the best known lower and upper bounds of .558 and .642, respectively, of Daskalakis and Zampetakis [4].

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Settling the sample complexity of single-parameter revenue maximization

Cited by 38 publications

References 21 publications

Targeting Makes Sample Efficiency in Auction Design

Targeting Makes Sample Efficiency in Auction Design

Algorithmic Price Discrimination

Improved Two Sample Revenue Guarantees via Mixed-Integer Linear Programming

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