Learning What’s Going on
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Published:2018-11-26
Issue:3-4
Volume:6
Page:1-20
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ISSN:2167-8375
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Container-title:ACM Transactions on Economics and Computation
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language:en
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Short-container-title:ACM Trans. Econ. Comput.
Author:
Blum Avrim1,
Mansour Yishay2,
Morgenstern Jamie3
Affiliation:
1. Toyota Technological Institute at Chicago, USA
2. Tel Aviv University
3. Georgia Institute of Technology
Abstract
We consider a setting where
n
buyers, with combinatorial preferences over
m
items, and a seller, running a priority-based allocation mechanism, repeatedly interact. Our goal, from observing limited information about the results of these interactions, is to reconstruct both the preferences of the buyers and the mechanism of the seller. More specifically, we consider an online setting where at each stage, a subset of the buyers arrive and are allocated items, according to some unknown priority that the seller has among the buyers. Our learning algorithm observes only which buyers arrive and the allocation produced (or some function of the allocation, such as just which buyers received positive utility and which did not), and its goal is to predict the outcome for future subsets of buyers. For this task, the learning algorithm needs to reconstruct both the priority among the buyers and the preferences of each buyer. We derive mistake bound algorithms for additive, unit-demand and single-minded buyers. We also consider the case where buyers’ utilities for a fixed bundle can change between stages due to different (observed) prices. Our algorithms are efficient both in computation time and in the maximum number of mistakes (both polynomial in the number of buyers and items).
Funder
Israeli Ministry of Science
National Science Foundation
Simons Award for Graduate Students in Theoretical Computer Science
Israeli Centers of Research Excellence (I-CORE) program
Israel Science Foundation
United States-Israel Binational Science Foundation
Publisher
Association for Computing Machinery (ACM)
Subject
Computational Mathematics,Marketing,Economics and Econometrics,Statistics and Probability,Computer Science (miscellaneous)
Reference11 articles.
1. Kareem Amin Rachel Cummings Lili Dworkin Michael Kearns and Aaron Roth. 2014. Online learning and profit maximization from revealed preferences. arXiv (2014). Kareem Amin Rachel Cummings Lili Dworkin Michael Kearns and Aaron Roth. 2014. Online learning and profit maximization from revealed preferences. arXiv (2014).
2. Maria-Florina Balcan Amit Daniely Ruta Mehta Ruth Urner and Vijay V. Vazirani. 2014. Learning economic parameters from revealed preferences. arXiv abs/1407.7937 (2014). Maria-Florina Balcan Amit Daniely Ruta Mehta Ruth Urner and Vijay V. Vazirani. 2014. Learning economic parameters from revealed preferences. arXiv abs/1407.7937 (2014).
3. Learning from revealed preference
4. On the conductance of order Markov chains
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