Efficient Algorithms for Learning Revenue-Maximizing Two-Part Tariffs

Balcan, Maria-Florina; Prasad, Siddharth; Sandholm, Tüomas

doi:10.24963/ijcai.2020/47

Cited by 3 publications

(14 citation statements)

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“…A two-part tariff consists of a fixed price p 1 and a price p 2 per unit of item sold. For N samples of the auction and K units of the auctioned item, [8] give an algorithm for computing the revenue maximizing tariff in O(N 3 K 3 ) time for a two-part tariff scheme. In this work we provide a more efficient algorithm with output-sensitive time complexity of O(RN K), where R is the number of pieces in the total dual class function U x (•) = x∈x u x (•), where the sum is over N auction samples denoted by x.…”

Section: Efficient Revenue-maximizing Two-part Tariff Auction Designmentioning

confidence: 99%

“…The algorithmic parameter we want to select is the price ρ = p 1 , p 2 , and the problem instances are specified by the valuations v i . [8] also consider a generalization of the above scheme: instead of just a single two-part tariff (TPT), suppose the seller provides a menu of TPTs (p 1 1 , p 1 2 ), . .…”

Section: Setupmentioning

confidence: 99%

“…aligning DNAs or RNAs), the pair of species being compared, or the purpose of the alignment. Similarly, item prices are natural parameters in auction design [10,8]. On the other hand, for linkage-based clustering, one usually chooses from a set of different available heuristics, such as single or complete linkage.…”

Section: Introductionmentioning

confidence: 99%

“…3. For designing auctions with two-part tariffs [8], we provide an efficient algorithm which gives a first output-sensitive algorithm for this setting, and improves the worst-case running time complexity of prior best results (even for worst-case output sizes). Our algorithm adapts techniques developed for the linkage-based clustering problem.…”

Section: Introductionmentioning

confidence: 99%

“…We also extend our algorithm to a more general setting with 2L tariff parameters and again obtain improved, output-polynomial runtime guarantees. In practice, L is a small constant [8].…”

Section: Introductionmentioning

confidence: 99%

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Faster algorithms for learning to link, align sequences, and price two-part tariffs

Balcan¹,

Seiler²,

Sharma³

2022

Preprint

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Data-driven algorithm configuration [16,1] is a promising, learning-based approach for beyond worst-case analysis of algorithms with tunable parameters. An important open problem is the design of efficient data-driven algorithms for algorithm families with more than one parameter. In this work we provide algorithms for efficient (output-polynomial) multidimensional parameter tuning, i.e. for families with a small constant number of parameters, for three very different combinatorial problems -linkage-based clustering, dynamic programming for sequence alignment, and auction design for two-part tariff schemes. We extend the single-parameter clustering algorithm of [4] to multiple parameters and to the sequence alignment problem by proposing an execution graph which compactly represents all the states the algorithm could attain for all possible parameter values. A key problem-specific challenge is to efficiently compute how the partition of the parameter space (into regions with unique algorithmic states) changes with a single algorithmic step. We give algorithms which improve on the runtime of previously best known results for linkage-based clustering, sequence alignment and two-part tariff pricing.

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Section: Efficient Revenue-maximizing Two-part Tariff Auction Designmentioning

confidence: 99%

Section: Setupmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…We also extend our algorithm to a more general setting with 2L tariff parameters and again obtain improved, output-polynomial runtime guarantees. In practice, L is a small constant [8].…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Faster algorithms for learning to link, align sequences, and price two-part tariffs

Balcan¹,

Seiler²,

Sharma³

2022

Preprint

Self Cite

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Learning Revenue Maximizing Menus of Lotteries and Two-Part Tariffs

Balcan¹,

Beyhaghi²

2023

Preprint

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We study learnability of two important classes of mechanisms, menus of lotteries and two-part tariffs. A menu of lotteries is a list of entries where each entry is a pair consisting of probabilities of allocating each item and a price. Menus of lotteries is an especially important family of randomized mechanisms that are known to achieve revenue beyond any deterministic mechanism. A menu of two-part tariffs, on the other hand, is a pricing scheme (that consists of an up-front fee and a per unit fee) that is commonly used in the real world, e.g., for car or bike sharing services.We study learning high-revenue menus of lotteries and two-part tariffs from buyer valuation data in both distributional settings, where we have access to buyers' valuation samples up-front, and online settings, where buyers arrive one at a time and no distributional assumption is made about their values. Our main contribution is proposing the first online learning algorithms for menus of lotteries and two-part tariffs with strong regret bound guarantees. Furthermore, we provide algorithms with improved running times over prior work for the distributional settings.The key difficulty when deriving learning algorithms for these settings is that the relevant revenue functions have sharp transition boundaries. In stark contrast with the recent literature on learning such unstructured functions, we show that simple discretization-based techniques are sufficient for learning in these settings. * Some online learning algorithms, including those proved via the dispersion method, explained later, still make distributional assumptions; however, unlike the distributional learning setting, the draws are not necessarily from identical distributions.

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Bicriteria Multidimensional Mechanism Design with Side Information

Balcan¹,

Prasad²,

Sandholm³

2023

Preprint

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We develop a versatile new methodology for multidimensional mechanism design that incorporates side information about agent types with the bicriteria goal of generating high social welfare and high revenue simultaneously. Side information can come from a variety of sourcesexamples include advice from a domain expert, predictions from a machine-learning model trained on historical agent data, or even the mechanism designer's own gut instinct-and in practice such sources are abundant. In this paper we adopt a prior-free perspective that makes no assumptions on the correctness, accuracy, or source of the side information. First, we design a meta-mechanism that integrates input side information with an improvement of the classical VCG mechanism. The welfare, revenue, and incentive properties of our meta-mechanism are characterized by a number of novel constructions we introduce based on the notion of a weakest competitor, which is an agent that has the smallest impact on welfare. We then show that our meta-mechanism-when carefully instantiated-simultaneously achieves strong welfare and revenue guarantees that are parameterized by errors in the side information. When the side information is highly informative and accurate, our mechanism achieves welfare and revenue competitive with the total social surplus, and its performance decays continuously and gradually as the quality of the side information decreases. Finally, we apply our meta-mechanism to a setting where each agent's type is determined by a constant number of parameters. Specifically, agent types lie on constant-dimensional subspaces (of the potentially high-dimensional ambient type space) that are known to the mechanism designer. We use our meta-mechanism to obtain the first known welfare and revenue guarantees in this setting.

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Efficient Algorithms for Learning Revenue-Maximizing Two-Part Tariffs

Cited by 3 publications

References 4 publications

Faster algorithms for learning to link, align sequences, and price two-part tariffs

Faster algorithms for learning to link, align sequences, and price two-part tariffs

Learning Revenue Maximizing Menus of Lotteries and Two-Part Tariffs

Bicriteria Multidimensional Mechanism Design with Side Information

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