One and Done? Optimal Decisions From Very Few Samples
Article first published online: 28 JAN 2014
© 2014 Cognitive Science Society, Inc.
Volume 38, Issue 4, pages 599–637, May/June 2014
How to Cite
Vul, E., Goodman, N., Griffiths, T. L. and Tenenbaum, J. B. (2014), One and Done? Optimal Decisions From Very Few Samples. Cognitive Science, 38: 599–637. doi: 10.1111/cogs.12101
- Issue published online: 1 JUN 2014
- Article first published online: 28 JAN 2014
- Manuscript Accepted: 7 MAY 2013
- Manuscript Revised: 29 MAR 2013
- Manuscript Received: 1 JUL 2011
- ONR MURI. Grant Number: N00014-07-1-0937
- Air Force Office of Scientific Research. Grant Number: FA9550-07-1-0351
- Department of the Interior
- Bounded rationality
In many learning or inference tasks human behavior approximates that of a Bayesian ideal observer, suggesting that, at some level, cognition can be described as Bayesian inference. However, a number of findings have highlighted an intriguing mismatch between human behavior and standard assumptions about optimality: People often appear to make decisions based on just one or a few samples from the appropriate posterior probability distribution, rather than using the full distribution. Although sampling-based approximations are a common way to implement Bayesian inference, the very limited numbers of samples often used by humans seem insufficient to approximate the required probability distributions very accurately. Here, we consider this discrepancy in the broader framework of statistical decision theory, and ask: If people are making decisions based on samples—but as samples are costly—how many samples should people use to optimize their total expected or worst-case reward over a large number of decisions? We find that under reasonable assumptions about the time costs of sampling, making many quick but locally suboptimal decisions based on very few samples may be the globally optimal strategy over long periods. These results help to reconcile a large body of work showing sampling-based or probability matching behavior with the hypothesis that human cognition can be understood in Bayesian terms, and they suggest promising future directions for studies of resource-constrained cognition.