Optimal Learning from Multiple Information Sources

76 Pages Posted: 13 Mar 2017  

Annie Liang

Microsoft Research

Xiaosheng Mu

Harvard University - Department of Economics

Vasilis Syrgkanis

Microsoft Corporation - Microsoft Research New England

Date Written: March 12, 2017

Abstract

Decision-makers often learn by acquiring information from distinct sources that possibly provide complementary information. We consider a decision-maker who sequentially samples from a finite set of Gaussian signals, and wants to predict a persistent multi-dimensional state at an unknown final period. What signal should he choose to observe in each period? Related problems about optimal experimentation and dynamic learning tend to have solutions that can only be approximated or implicitly characterized. In contrast, we find that in our problem, the dynamically optimal path of signal acquisitions generically:

(1) eventually coincides at every period with the myopic path of signal acquisitions, and

(2) eventually achieves "total optimality," so that at every large period, the decision-maker will not want to revise his previous signal acquisitions, even if given this opportunity.

In special classes of environments that we describe, these properties attain not only eventually, but from period 1. Finally, we characterize the asymptotic frequency with which each signal is chosen, and how this depends on primitives of the informational environment.

Keywords: learning, information, dynamic

Suggested Citation

Liang, Annie and Mu, Xiaosheng and Syrgkanis, Vasilis, Optimal Learning from Multiple Information Sources (March 12, 2017). Available at SSRN: https://ssrn.com/abstract=2931845 or http://dx.doi.org/10.2139/ssrn.2931845

Annie Liang (Contact Author)

Microsoft Research ( email )

One Memorial Drive, 14th Floor
Cambridge, MA 02142
United States

Xiaosheng Mu

Harvard University - Department of Economics ( email )

1875 Cambridge Street
Cambridge, MA 02138
United States

Vasilis Syrgkanis

Microsoft Corporation - Microsoft Research New England ( email )

One Memorial Drive, 14th Floor
Cambridge, MA 02142
United States

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