Imprecise neural computations as a source of adaptive behaviour in volatile environments


In everyday life, humans face environments that feature uncertain and volatile or changing situations. Efficient adaptive behaviour must take into account uncertainty and volatility. Previous models of adaptive behaviour involve inferences about volatility that rely on complex and often intractable computations. Because such computations are presumably implausible biologically, it is unclear how humans develop efficient adaptive behaviours in such environments. Here, we demonstrate a counterintuitive result: simple, low-level inferences confined to uncertainty can produce near-optimal adaptive behaviour, regardless of the environmental volatility, assuming imprecisions in computation that conform to the psychophysical Weber law. We further show empirically that this Weber-imprecision model explains human behaviour in volatile environments better than optimal adaptive models that rely on high-level inferences about volatility, even when considering biologically plausible approximations of such models, as well as non-inferential models like adaptive reinforcement learning.

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Fig. 1: Inferential models of adaptive behaviour.
Fig. 2: Models’ maximal performances in stable, changing and unstable environments.
Fig. 3: Models’ versatility across environments.
Fig. 4: Model fits to human performances in closed, unstable environments.
Fig. 5: Human and model adaptive behaviour following contingency reversals.
Fig. 6: Model fits to human performances in open-ended, changing environments.

Data availability

All the data that support the findings of the present study are available from the corresponding author upon request.

Code availability

All program codes are freely available at


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We thank J. Drevet for her help in collecting human data. Supported by a European Research Council Grant (ERC-2009-AdG #250106) to E.K. and a DGA-INSERM PhD fellowship to C.F. The funders had no role in study design, data collection and analysis, decision to publish or preparation of the manuscript.

Author information




E.K. and C.F. conceived the study and designed the models. C.F. and N.C. developed the models. C.F. programmed the models, performed computer simulations and collected human data. E.K. and C.F. analysed human and simulation data. E.K. and C.F. wrote the paper.

Corresponding author

Correspondence to Etienne Koechlin.

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The authors declare no competing interests

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Peer review information Primary Handling Editor: Marike Schiffer

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Extended data

Extended Data Fig. 1 Examples of five volatility trajectories in unstable environments.

Environment volatility follows a bounded gaussian random walk between 0.03 and 0.2 with variance 0.0001 (see Methods).

Extended Data Fig. 2 Relation between the Weber noise component λ in the Weber imprecision model and external volatility.

The figure shows the entropy of posterior beliefs about current combinations (latent state posteriors) for the exact varying-volatility and Weber imprecision model. Each model is simulated N = 50 times in a closed environment (K=2, two-armed bandit), which alternates between high and low-volatility periods. Left, simulations when Weber component λ is set to 0 and constant component μ is large (μ = 0.2). Right, simulations when Weber component λ is large (λ = 1.5) and constant component μ is low (μ = 0.02). Note that the entropies of posterior beliefs are similar between the Weber-imprecision and varying-volatility model only when the Weber component is large enough.

Extended Data Fig. 3 Full generative model of varying-volatility models.

This model is exactly the process generating unstable environments. This generative model assumes that volatility τt follows a bounded random walk with constant variance ν. zt represents the current correct combination. γ represents the probabilities of combination occurrence whenever the correct combination changes. η represents feedback noise. In every trial, observables are stimuli st, actions at and binary feedback rt. See Methods for details.

Extended Data Fig. 4 Full generative model of constant-volatility models.

This model is exactly the process generating changing environments. This generative model assumes that volatility τ is constant. zt represents the current correct combination. γ represents the probabilities of combination occurrence whenever the correct combination changes. η represents feedback noise. In every trial, observables are stimuli st, actions at and binary feedback rt. See Methods for details.

Extended Data Fig. 5 Full generative model of zero-volatility models.

This model is exactly the process generating stable environments. This generative model assumes that volatility is null and that observations are all equally informative. z represents the correct combination. γ represents combinations’ probabilities. η represents feedback noise. In every trial, observables are stimuli st, actions at and binary feedback rt. See Methods for details.

Extended Data Fig. 6

Means (s.e.m) of parameters fitted across participants for exact and forward volatility models.

Extended Data Fig. 7

Means (s.e.m.) of parameters fitted across participants for the Weber-imprecision model.

Extended Data Fig. 8

Means (s.e.m.) of parameters fitted across participants for Reinforcement Learning models.

Supplementary information

Supplementary Information

Supplementary Discussion, Supplementary Methods, Supplementary Figs. 1–5 and Supplementary Refs. 1–5.

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Findling, C., Chopin, N. & Koechlin, E. Imprecise neural computations as a source of adaptive behaviour in volatile environments. Nat Hum Behav (2020).

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