Optimal Learning under Robustness and Time-Consistency

TL;DR

This paper develops a continuous-time model for optimal learning under ambiguity and time-consistency, providing closed-form solutions for stopping problems in robust settings, including applications to Ellsberg's experiment and hypothesis testing.

Contribution

It introduces a novel robust, time-consistent learning framework in continuous time with explicit solutions for optimal stopping problems.

Findings

Closed-form solutions for robust optimal stopping problems.

Demonstrates the link between robustness and learning demand.

Applies the model to classical problems like Ellsberg's experiment and hypothesis testing.

Abstract

We model learning in a continuous-time Brownian setting where there is prior ambiguity. The associated model of preference values robustness and is time-consistent. It is applied to study optimal learning when the choice between actions can be postponed, at a per-unit-time cost, in order to observe a signal that provides information about an unknown parameter. The corresponding optimal stopping problem is solved in closed-form, with a focus on two specific settings: Ellsberg's two-urn thought experiment expanded to allow learning before the choice of bets, and a robust version of the classical problem of sequential testing of two simple hypotheses about the unknown drift of a Wiener process. In both cases, the link between robustness and the demand for learning is studied.