Optimal Learning from Multiple Information Sources

73 Pages Posted: 13 Mar 2017 Last revised: 2 Jun 2017

Annie Liang

Microsoft Research

Xiaosheng Mu

Harvard University - Department of Economics

Vasilis Syrgkanis

Microsoft Corporation - Microsoft Research New England

Date Written: June 1, 2017

Abstract

Consider a decision-maker who sequentially acquires Gaussian signals from distinct and possibly complementary sources for a future decision. Which sources should he choose to observe in each period? In environments that we characterize, it turns out that the dynamically optimal path of signal acquisitions:

(1) exactly coincides at every period with the myopic path of signal acquisitions, and
(2) achieves "total optimality," so that at every late period, the decision-maker will not want to revise his previous signal acquisitions even if given this opportunity.

We show that generically, these properties hold at all sufficiently late times, so that the dynamically optimal path and myopic path are eventually equivalent. Moreover, these results hold independently of the decision problem and the timing of the decision, so that the optimal rule is robust to these specifications. These results stand in contrast to a large body of dynamic learning and optimal experimentation problems in which the dynamically optimal solution can only be approximated or implicitly characterized.

Keywords: learning, information, dynamic

Suggested Citation

Liang, Annie and Mu, Xiaosheng and Syrgkanis, Vasilis, Optimal Learning from Multiple Information Sources (June 1, 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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