A new paper on robust learning

[Yeon-Koo Che]

Hi all, 

My new paper with Longjian Li (NYU) and Tianling Luo (Columbia) may be of interest to you:

Learning Against Nature: Minimax Regret and the Price of Robustness

Abstract:  We study how a decision-maker (DM) learns from data of unknown quality to form robust, “general-purpose” posterior beliefs. We develop a framework for robust learning and belief formation under a minimax-regret criterion, cast as a zero-sum game: the DM chooses posterior beliefs to minimize ex-ante regret, while an adversarial Nature selects the data-generating process (DGP). We show that, in large samples of n signal draws, Nature optimally induces ambiguity by choosing a process whose precision converges to the uninformative signals at the rate 1/ √ n. As a result, learning against the adversarial DGP is nontrivial as well as incomplete: the DM’s ex-ante regret remains strictly positive even with an infinite amount of data. However, when the true DGP is fixed and informative (even if only slightly), our DM with a robust updating rule eventually learns the state with enough data. Still, learning occurs at a sub-exponential rate—quantifying the asymptotic price of robustness—and it exhibits “under-inference” bias. Our framework provides a decision-theoretic dual to the local alternatives method in asymptotic statistics, deriving the characteristic 1/ √ n-scaling endogenously from the signal ambiguity.

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Yeon-Koo Che

Kelvin J. Lancaster Professor of Economic Theory

420 W. 118th Street, IAB 1029

Columbia University

New York, NY 10027

https://www.yeonkooche.com/