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When and what to learn in a changing world

César Barilla

Published 2025 in ACM Conference on Economics and Computation

ABSTRACT

The world is constantly changing, yet decision makers do not continuously update their worldview. When should one acquire new information and what should they learn? This paper develops a tractable framework to study the tradeoff between the timing and content of information acquisition. A decision maker sequentially choose times at which to acquire information (entailing a fixed cost) and what to learn (entailing a variable cost) about a changing state. I characterize optimal policies, using an appropriate Bellman equation that decomposes the problem into a static optimal information acquisition problem and an optimal stopping problem. Optimal information acquisition must eventually either stop or settle into a simple cycle in which information is acquired at regular intervals (when uncertainty reaches specific thresholds) and updates lead to two possible outcomes, captured by two target posterior beliefs. The convergence result enables the study of properties of long run optimal information acquisition. Optimal policies may exhibit path dependency in the form of "learning traps". The world becoming more volatile has generically ambiguous effects on the frequency of information acquisition. In the limit as fixed costs vanish, the agent optimally either waits or acquires infinitesimal amounts of information so as to confirm the current belief until rare news prompts a jump to an alternative belief; in the long run, the agent's belief jumps between two possible beliefs (and actions). In an application to a portfolio problem, optimal behavior exhibits continuous rebalancing towards diversification, punctuated by periodic shifts to more extreme allocations. With asymmetry between a safe and a risky action, optimal information acquisition can generate distortions between good and bad news, typically leading to better quality but more frequent updating for information which suggests undertaking risky actions. Link to full paper: https://cesarbarilla.com/files/Barilla_When-And-What.pdf

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