A model for learning based on the joint estimation of stochasticity and volatility
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Abstract
Previous research has stressed the importance of uncertainty for controlling the speed of learning, and how such control depends on the learner inferring the noise properties of the environment, especially volatility: the speed of change. However, learning rates are jointly determined by the comparison between volatility and a second factor, moment-to-moment stochasticity. Yet much previous research has focused on simplified cases corresponding to estimation of either factor alone. Here, we introduce a learning model, in which both factors are learned simultaneously from experience, and use the model to simulate human and animal data across many seemingly disparate neuroscientific and behavioral phenomena. By considering the full problem of joint estimation, we highlight a set of previously unappreciated issues, arising from the mutual interdependence of inference about volatility and stochasticity. This interdependence complicates and enriches the interpretation of previous results, such as pathological learning in individuals with anxiety and following amygdala damage.
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Real-world agents need to detect and distinguish dynamic changes in both volatility and observation noise at the same time.
“While existing modelling approaches have focused on either accounting for changes in volatility (Behrens et al., 2007; Mathys et al., 2011; Piray & Daw, 2020) or block-wise changes in stochasticity or noise (Lee et al., 2020; Nassar et al., 2010, 2012, 2016), it has recently been pointed out that real-world agents need to able to detect (and distinguish) dynamic changes in both at the same time (”
From The generalized Hierarchical Gaussian Filter (2026) · cites this paper as Piray & Daw, 2021
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The generalized Hierarchical Gaussian Filter
Weber, L. A., Waade, P. T., Legrand, N., Møller, A. H., Stephan, K. E., & Mathys, C. (2026) · eLife · doi:10.7554/elife.110174
- Authors
- Piray, P., & Daw, N. D.
- Affiliations
- Princeton University (US)
- Corresponding author
- Piray, Payam
- Venue
- Nature Communications
- Published
- 2021-11-15
- Volume
- 12
- Issue
- 1
- Pages
- 6587-6587
- ISSN
- 2041-1723 (ISSN-L)
- PMC
- PMC8592992
- OpenAlex
- W3211391129
- Cited by
- 153
- References
- 17
- Citations by year
- 2026: 26 · 2025: 51 · 2024: 31 · 2023: 26 · 2022: 14 · 2021: 5
- FWCI
- 9.99
- Type
- journal article
- Language
- en
- Open access
- gold
- doi.org
- Locations
- Nature Communications (publishedVersion, cc-by)
- bioRxiv (Cold Spring Harbor Laboratory) (acceptedVersion, cc-by-nc-nd)
- PubMed Central (publishedVersion, cc-by)
- PubMed (publishedVersion)
- RePEc: Research Papers in Economics (submittedVersion)
- DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion, cc-by-sa)
- Funders
- National Science Foundation (1822571)
- John Templeton Foundation (61454)
- Topics
- Life Sciences › Neuroscience › Cognitive Neuroscience › Memory and Neural Mechanisms
- Life Sciences › Neuroscience › Cognitive Neuroscience › Neural and Behavioral Psychology Studies
- Life Sciences › Neuroscience › Cognitive Neuroscience › Neural dynamics and brain function
- Keywords
- learning rate, volatility estimation, uncertainty, Bayesian inference, simultaneous estimation, learning models, anxiety, amygdala damage
- MeSH terms
- Algorithms, Animals, Haplorhini, Anxiety, Anxiety Disorders, Decision Making, Humans, Learning, Volatilization, Uncertainty
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