Computational noise in reward-guided learning drives behavioral variability in volatile environments

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When learning the value of actions in volatile environments, humans often make seemingly irrational decisions that fail to maximize expected value. We reasoned that these ‘non-greedy’ decisions, instead of reflecting information seeking during choice, may be caused by computational noise in the learning of action values. Here using reinforcement learning models of behavior and multimodal neurophysiological data, we show that the majority of non-greedy decisions stem from this learning noise. The trial-to-trial variability of sequential learning steps and their impact on behavior could be predicted both by blood oxygen level-dependent responses to obtained rewards in the dorsal anterior cingulate cortex and by phasic pupillary dilation, suggestive of neuromodulatory fluctuations driven by the locus coeruleus–norepinephrine system. Together, these findings indicate that most behavioral variability, rather than reflecting human exploration, is due to the limited computational precision of reward-guided learning.

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Fig. 1: Experimental paradigm and noisy RL model.
Fig. 2: Contributions of learning noise and choice stochasticity to non-greedy decisions.
Fig. 3: Decomposition of learning noise into ultimately predictable and unpredictable terms.
Fig. 4: Characterization of decision effects predicted by learning noise.
Fig. 5: Neural correlates of learning noise in the human brain.
Fig. 6: Neural correlates of learning noise in choice-free, cued trials.
Fig. 7: Brain–behavior and pupillometric analyses.
Fig. 8: Proposed payoff–cost trade-off on learning precision.

Data availability

The data (behavioral, neuroimaging and pupillometric) that support these findings are available from the corresponding author upon request.

Code availability

Python and C++ code for fitting all computational models described in the article are available at The algorithmic backbone of the Monte Carlo procedures used to fit models can be found in Supplementary Modeling Note.


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We thank C. Summerfield (University of Oxford; Google DeepMind) for comments on an earlier version of the manuscript. This work was supported by a starting grant from the European Research Council awarded to V.W. (ERC-StG-759341), a junior researcher grant from the Agence Nationale de la Recherche awarded to V.W. (ANR-14-CE13-0028) and two department-wide grants from the Agence Nationale de la Recherche (ANR-10-LABX-0087 and ANR-10-IDEX-0001-02 PSL). C.F. was supported by a graduate research fellowship from the Direction Générale de l’Armement (2015-60-0041). S.P. was supported by a CNRS-Inserm ATIP-Avenir grant (R16069JS) and a research grant from the Programme Emergence(s) of the City of Paris.

Author information

S.P. and V.W. were responsible for conceptualization. C.F., V.W. and S.P. were responsible for the methodology. C.F., V.S. and V.W. performed the formal analysis. V.S. and R.D. carried out the investigations. C.F., V.S. and V.W. wrote the original draft. C.F., V.S., S.P. and V.W. reviewed and edited the report. V.W. supervised the study and acquired funding.

Correspondence to Valentin Wyart.

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The authors declare no competing interests.

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Peer review information Nature Neuroscience thanks Samuel Gershman, Yonatan Loewenstein, and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Integrated supplementary information

Supplementary Figure 1 Additional model comparisons across experiments 1 and 2 (N = 59 participants).

(a) Knock-out procedure. The top panel shows models that varied based on the presence or absence of learning noise (ζ) in addition to the softmax choice policy (β). The bottom panel shows models that varied based on the presence or absence of a softmax choice policy (β) on top of learning noise (ζ). (b) Results of the model comparison in the partial and complete feedback conditions for models described in panel a pooled across experiment 1 (N = 29) and experiment 2 (N = 30). Similarly to the main behavioral results, these comparisons revealed that participants featured both learning noise (fixed-effects: BF≈1050.3, random-effects: exceedance p=0.99) and choice stochasticity (fixed-effects: BF≈1082.4, random-effects: exceedance p=0.999) in the partial feedback condition (left panel). In the complete feedback condition, the model with learning noise better explained the data than the exact model (fixed-effects: BF≈10100.3, random-effects: exceedance p=0.999). Furthermore, a model with learning noise and an argmax action selection policy fitted the data decisively better than a model with learning noise and a softmax policy (fixed-effects: BF≈1015.8, random-effects: exceedance p=0.999) (right panel). Error bars for model frequencies correspond to the s.d. of estimated Dirichlet distributions.

Supplementary Figure 2 Results of the parameter recovery procedure.

Implementation of the parameter recovery procedure in experiment 1 (in the partial feedback condition). For a given set of parameter values, we simulated the model 29 times (once for each of the N = 29 different realizations of the task). Obtained simulated actions were fitted using the same exact procedure used to fit human data, to quantify the extent to which we could recover the simulated (ground-truth) parameters values. (a) Parameter recovery for the learning noise parameter ζ, with other parameters (softmax temperature 1/β and learning rates) fixed. (b) Parameter recovery for the softmax temperature 1/β with other parameters (learning noise ζ and learning rates) fixed. Fixed parameter values were set to group-level mean estimates obtained using a fixed-effects approach. For the single parameter whose value was varied, we considered 11 values logarithmically distributed around the group-level mean estimate. Horizontal lines represent the subjects’ group mean with the 99% confidence interval. Each dot represents the recovered parameter averaged across simulations (N=29) with vertical lines showing s.d.m. The results shown indicate that ground-truth parameter values are well recovered by our fitting procedure. Also, it shows that the fitting procedure is robust to changes of learning noise and softmax temperature parameters. Recovered parameters do not saturate within the range values parameters considered for learning noise (a) and start to saturate only when the softmax temperature parameter is set to about three times the group-level mean value (b).

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Supplementary Figures 1 & 2, Supplementary Tables 1 & 2, Supplementary Modeling Note, and Supplementary Note

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Findling, C., Skvortsova, V., Dromnelle, R. et al. Computational noise in reward-guided learning drives behavioral variability in volatile environments. Nat Neurosci (2019) doi:10.1038/s41593-019-0518-9

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