Algorithms for Distributed Winner Determination in Combinatorial Auctions

We are interested by the problem of combinatorial auctions in which multiple items are sold and bidders submit bids on packages. First, we present a multi-objective formulation for a combinatorial auctions problem extending the existing single-objective models. Indeed, the bids may concern several specifications of the item, involving not only its price, but also its quality, delivery conditions, delivery deadlines, the risk of not being paid after a bid has been accepted and so on. The seller expresses his preferences upon the suggested items and the buyers are in competition with all the specified attributes done by the seller. Second, we develop and implement a metaheuristic algorithm based on a tabu search method.

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Learning Within an Instance for Designing High-Revenue Combinatorial Auctions

Proceedings of the Thirtieth International Joint Conference on Artificial Intelligence ◽

10.24963/ijcai.2021/5 ◽

2021 ◽

Author(s):

Maria-Florina Balcan ◽

Siddharth Prasad ◽

Tuomas Sandholm

Keyword(s):

Random Sampling ◽

Combinatorial Auctions ◽

Complexity Measure ◽

Revenue Maximization ◽

Learning Groups ◽

Winner Determination ◽

Unlimited Supply ◽

Intrinsic Complexity ◽

Limited Supply ◽

New Framework

We develop a new framework for designing truthful, high-revenue (combinatorial) auctions for limited supply. Our mechanism learns within an instance. It generalizes and improves over previously-studied random-sampling mechanisms. It first samples a participatory group of bidders, then samples several learning groups of bidders from the remaining pool of bidders, learns a high-revenue auction from the learning groups, and finally runs that auction on the participatory group. Previous work on random-sampling mechanisms focused primarily on unlimited supply. Limited supply poses additional significant technical challenges, since allocations of items to bidders must be feasible. We prove guarantees on the performance of our mechanism based on a market-shrinkage term and a new complexity measure we coin partition discrepancy. Partition discrepancy simultaneously measures the intrinsic complexity of the mechanism class and the uniformity of the set of bidders. We then introduce new auction classes that can be parameterized in a way that does not depend on the number of bidders participating, and prove strong guarantees for these classes. We show how our mechanism can be implemented efficiently by leveraging practically-efficient routines for solving winner determination. Finally, we show how to use structural revenue maximization to decide what auction class to use with our framework when there is a constraint on the number of learning groups.

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Deep Learning—Powered Iterative Combinatorial Auctions

Proceedings of the AAAI Conference on Artificial Intelligence ◽

10.1609/aaai.v34i02.5606 ◽

2020 ◽

Vol 34 (02) ◽

pp. 2284-2293

Author(s):

Jakob Weissteiner ◽

Sven Seuken

Keyword(s):

Deep Learning ◽

Deep Neural Networks ◽

Preference Elicitation ◽

Integer Program ◽

Combinatorial Auctions ◽

Prediction Performance ◽

Mixed Integer ◽

Mixed Integer Program ◽

Support Vector ◽

Winner Determination

In this paper, we study the design of deep learning-powered iterative combinatorial auctions (ICAs). We build on prior work where preference elicitation was done via kernelized support vector regressions (SVRs). However, the SVR-based approach has limitations because it requires solving a machine learning (ML)-based winner determination problem (WDP). With expressive kernels (like gaussians), the ML-based WDP cannot be solved for large domains. While linear or quadratic kernels have better computational scalability, these kernels have limited expressiveness. In this work, we address these shortcomings by using deep neural networks (DNNs) instead of SVRs. We first show how the DNN-based WDP can be reformulated into a mixed integer program (MIP). Second, we experimentally compare the prediction performance of DNNs against SVRs. Third, we present experimental evaluations in two medium-sized domains which show that even ICAs based on relatively small-sized DNNs lead to higher economic efficiency than ICAs based on kernelized SVRs. Finally, we show that our DNN-powered ICA also scales well to very large CA domains.

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A Graph-Based Ant Algorithm for the Winner Determination Problem in Combinatorial Auctions

Information Systems Research ◽

10.1287/isre.2021.1031 ◽

2021 ◽

Author(s):

Abhishek Ray ◽

Mario Ventresca ◽

Karthik Kannan

Keyword(s):

Exact Algorithms ◽

Combinatorial Auctions ◽

Ant Colony ◽

Superior Performance ◽

Winner Determination Problem ◽

Winner Determination ◽

Anytime Algorithm ◽

Open Test ◽

Valid Solution ◽

Graph Pruning

Iterative combinatorial auctions are known to resolve bidder preference elicitation problems. However, winner determination is a known key bottleneck that has prevented widespread adoption of such auctions, and adding a time-bound to winner determination further complicates the mechanism. As a result, heuristic-based methods have enjoyed an increase in applicability. We add to the growing body of work in heuristic-based winner determination by proposing an ant colony metaheuristic–based anytime algorithm that produces optimal or near-optimal winner determination results within specified time. Our proposed algorithm resolves the speed versus accuracy problem and displays superior performance compared with 20 past state-of-the-art heuristics and two exact algorithms, for 94 open test auction instances that display a wide variety in bid-bundle composition. Furthermore, we contribute to the literature in two predominant ways: first, we represent the winner determination problem as one of finding the maximum weighted path on a directed cyclic graph; second, we improve upon existing ant colony heuristic–based exploration methods by implementing randomized pheromone updating and randomized graph pruning. Finally, to aid auction designers, we implement the anytime property of the algorithm, which allows auctioneers to stop the algorithm and return a valid solution to the winner determination problem even if it is interrupted before computation ends.

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