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LEARNING IN RANDOM UTILITY MODELS VIA ONLINE DECISION PROBLEMS

Emerson Melo ()
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Emerson Melo: Indiana University, Bloomington

CAEPR Working Papers from Center for Applied Economics and Policy Research, Department of Economics, Indiana University Bloomington

Abstract: This paper studies the Random Utility Model (RUM) in environments where the decision maker is imperfectly informed about the payoffs associated to each of the alternatives he faces. By embedding the RUM into an online decision problem, we make four contributions. First, we propose a gradient-based learning algorithm and show that a large class of RUMs are Hannan consistent (Hannan [1957]); that is, the average difference between the expected payoffs generated by a RUM and that of the best fixed policy in hindsight goes to zero as the number of periods increase. Second, we show that the class of Generalized Extreme Value (GEV) models can be implemented with our learning algorithm. Examples in the GEV class include the Nested Logit, Ordered, and Product Differentiation models among many others. Third, we show that our gradient-based algorithm is the dual, in a convex analysis sense, of the Follow the Regularized Leader (FTRL) algorithm, which is widely used in the Machine Learning literature. Finally, we discuss how our approach can incorporate recency bias and be used to implement prediction markets in general environments.javascript:void(0);

Keywords: Random utility models; Multinomial Logit Model; Generalized Nested Logit models; GEV class; Online optimization; Online learning; Hannan consistency; no-regret learning (search for similar items in EconPapers)
Pages: 51 pages
Date: 2021-08
New Economics Papers: this item is included in nep-big, nep-dcm and nep-upt
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