Dopamine reward prediction errors reflect hidden-state inference across time


Midbrain dopamine neurons signal reward prediction error (RPE), or actual minus expected reward. The temporal difference (TD) learning model has been a cornerstone in understanding how dopamine RPEs could drive associative learning. Classically, TD learning imparts value to features that serially track elapsed time relative to observable stimuli. In the real world, however, sensory stimuli provide ambiguous information about the hidden state of the environment, leading to the proposal that TD learning might instead compute a value signal based on an inferred distribution of hidden states (a 'belief state'). Here we asked whether dopaminergic signaling supports a TD learning framework that operates over hidden states. We found that dopamine signaling showed a notable difference between two tasks that differed only with respect to whether reward was delivered in a deterministic manner. Our results favor an associative learning rule that combines cached values with hidden-state inference.

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Figure 1: Task design.
Figure 2: Averaged dopamine activity in tasks 1 and 2 shows different patterns of modulation over a range of ISIs.
Figure 3: Individual dopamine neurons show opposing patterns of post-reward firing in tasks 1 and 2.
Figure 4: TD with CSC model, with or without reset, is inconsistent with our data.
Figure 5: Belief-state model is consistent with our data.
Figure 6: Value signals in the belief-state model of tasks 1 and 2.
Figure 7: Hazard and subjective hazard functions for tasks 1 and 2.


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We thank R. Born, J. Assad and C. Harvey for discussions, members of the Uchida lab for discussions and C. Dulac for sharing resources. This work was supported by National Science Foundation grant CRCNS 1207833 (S.J.G.), US National Institutes of Health grants R01MH095953 (N.U.), R01MH101207 (N.U.), T32 MH020017 (C.K.S.) and T32GM007753 (C.K.S.), a Harvard Brain Science Initiative Seed grant (N.U.), a Harvard Mind Brain and Behavior faculty grant (S.J.G. and N.U.) and Fondation pour la Recherche Medicale grant SPE20150331860 (B.M.B.).

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C.K.S. and N.U. designed the recording experiments and behavioral task; C.K.S. collected and analyzed data; C.K.S. and S.J.G. constructed the computational models; and C.K.S., B.M.B., S.J.G. and N.U. wrote the manuscript.

Corresponding authors

Correspondence to Naoshige Uchida or Samuel J Gershman.

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The authors declare no competing financial interests.

Integrated supplementary information

Supplementary Figure 1 Task 2b.

a, Task 2b was identical to Task 2, except for the constant ISI trial type. Odor B trials had a constant ISI of 2.0 s. b, The trough of the dopamine omission ‘dip’ was slightly later for 2s variable ISI omission trials than for 2s constant ISI omission trials, as indicated by the arrows. c, This slightly later omission dip is consistent with our belief state TD model. If our belief state TD model was adjusted to incorporate timing uncertainty (see Supplementary Fig. 12), the ‘dip’ for reward omission would be more blurred in time, particularly for the 2s constant ISI omission response.

Supplementary Figure 2 Mice learn to lick in anticipation of rewarded odors.

a-c, Anticipatory lick rate increased above baseline for all rewarded trial types (n = 26 sessions, F1,50 > 150, P < 6 × 10-17 for odors A-C in Task 1, 1-way ANOVA; n = 9 sessions, F1,16 > 60, P < 1 × 10-6 for odors A-C in Task 2, 1-way ANOVA; n = 22 sessions, F1,42 > 100, P < 5 × 10-13 for odors A-C in Task 2b, 1-way ANOVA). Anticipatory lick rate did not increase above baseline for odor D trials (P > 0.10 for all Tasks, odor D, 1-way ANOVA). d, Average licking PSTH for all sessions across all animals trained on Task 1. e, Average licking PSTH for all sessions across all animals trained on Task 2 (including Task 2b).

Supplementary Figure 3 Are any aspects of licking behavior correlated with temporal modulation of dopamine RPEs?

Because the trends of licking behavior across time appeared to be different between Tasks 1 and 2 (see Supplementary Figure 2d,e), we asked whether licking patterns during each session were at all predictive of temporal modulation of dopamine RPEs recorded during that session. a,c, Example fits of logistic function to lick data during individual sessions (see Methods ). b,d, Correlations between various parameters of these logistic functions and the slope of phasic dopamine RPEs across time in Task 1 (b) and Task 2 (d). e, Correlations between the slope k of the logistic function and the slope of phasic dopamine RPEs across time as an aggregate in both Task 1 and Task 2 cohorts. f, Correlations between the slope of licking behavior across time just prior to reward delivery (200ms-0ms) and the slope of phasic dopamine RPEs across time. Our analysis revealed a relationship between the steepness, k, of the logistic licking function and negative modulation over time for post-reward firing in Task 1 (b), and in an aggregate analysis of both Task 1 and Task 2 cohorts (e). However, the steepness of the logistic function in Task 1 is determined in the time prior to reward delivery (see a). None of these analyses revealed a behavior correlate of shifting temporal expectation during the interval in which rewards could be delivered.

Supplementary Figure 4 Recording sites.

a,b, Schematic of recording sites for animals used in Task 1(a) and Task 2 (b)

Supplementary Figure 5 Optogenetic identification of dopamine neurons.

a, Raw trace for single example neuron, demonstrating laser pulses and laser-evoked spikes. b, Near-identical match between waveform of average laser-evoked spike (blue) and average spontaneous spike (black) for same example neuron. c, Histogram of latencies to spike for same example neuron. d, Light-evoked spikes for 10Hz and 50Hz pulses, for same example neuron. e,f, Mean latency and standard deviation of light-evoked spikes, for all identified dopamine neurons. g, Waveform correlation between laser-evoked and spontaneous spikes, for all identified dopamine neurons.

Supplementary Figure 6 Onset of phasic post-reward RPEs begin 50 ms following water-valve opening.

Non-normalized PSTH for Tasks 1 (a) and 2 (b) aligned to the time of reward with only a 20ms box used for smoothing. Although water valve opens at 0ms, phasic dopaminergic response does not begin until 50ms following water valve opening.

Supplementary Figure 7 Visualization of belief-state model parameters (see Computational Methods for details).

a,b, Schematic of the difference between modeling Task 1 and 2. Whereas cue can never lead back to the ITI sub-state in Task 1, this ‘hidden’ transition occurs in 10% of trials (omission trials) in Task 2. c,d, Observation matrices for Task 1 and 2. In a tiny percentage of cases in Task 2 (see Computational Methods), the animal observes ‘cue’ when in fact it transitions from the ITI back to the ITI during an omission trial. This occurs in such a small proportion of sub-state 15→15 transitions that it cannot be visualized in this map, so we have indicated values that differ between Tasks directly below the matrices. See Methods for how these values were computed. e,f, Transition matrices for Task 1 and 2. The probability of transitioning from the sub-state 15 back to the sub-state 15 is slightly higher in Task 2 (see Computational Methods), due to the presence of omission trials. The baseline probability of transitioning out of the ITI in either task is so small that it cannot be visualized here, so we have indicated values that differ between Tasks directly below the matrices. See Methods for how these values were computed.

Supplementary Figure 8 Belief-state model reproduces modulation of pre-reward and post-reward RPEs over variable ISI interval.

a,c, Pre-reward (a) and post-reward (c) RPEs generated by belief state model for different ISIs in Task 1. b,d, Pre-reward (b) and post-reward (d) RPEs generated by belief state model across different ISIs in Task 2.

Supplementary Figure 9 Post-reward RPEs normalized to free-water response.

In order to compare the magnitude of dopamine RPEs across different populations of neurons, post-reward RPEs must be normalized to the free water response (see Eshel et al., 2016). a, Post-reward RPEs in Task 1 are suppressed to about 60% of the free water response at the beginning of the interval (1.2s), and are suppressed to about 40% of the free water response at the end of the interval (2.8s). RPEs plotted are from the 29 neurons for which we included 2-5 free water deliveries during recording. b, Post-reward RPEs in Task 2 are suppressed to about 60% of the free water response at the beginning of the interval (1.2s), and are suppressed to about 90% of the free water response at the end of the interval (2.8s). RPEs plotted are from the 34 neurons for which we included 2-5 free water deliveries during recording. c, Schematic of data in (a) and (b), highlighting that the opposing trends of temporal modulation in Tasks 1 and 2 arise mostly from diverging patterns towards the end of the interval.Citation for Eshel et al., 2016: Eshel N, Tian J, Bukwich M, Uchida N. Dopamine neurons share a common response function for reward prediction error. Nat Neurosci. 19, 479-486 (2016)

Supplementary Figure 10 Belief-state model result is agnostic to precise shape of trained distribution.

When we trained our belief state TD model on a uniform distribution, the model produced negative modulation of post-reward RPEs over time in the 100% rewarded condition, and positive modulation of post-reward RPEs over time in the 90% rewarded condition. Therefore, while an assumption of our model is that mice perfectly learned the Gaussian distribution of reward timings, relaxing this assumption produces the same qualitative result.

Supplementary Figure 11 Testing belief-state TD model and TD with CSC and Reset model on other studies’ data.

a, Other studies trained animals to anticipate rewarding or reward-predicting events during a variable ISI interval in which the ISI was drawn from a flat probability distribution10-12. In these studies, reward was delivered in 100% of trials. b,c, Both the belief state model (b) and TD with CSC and Reset model (c) produce negative modulation of RPEs over time. d, Exponential distribution of ISIs, similar to Fiorillo et al, 2008 Figure 5d, on which we trained our belief state TD model. e, Post-reward RPEs decreased over time for belief state model trained on exponential distribution of ISIs, similar to data in Fiorillo et al, 2008 Figure 5e.

Supplementary Figure 12 Belief-state model can be adapted to incorporate temporal uncertainty.

a, Belief state at time t was blurred by a Gaussian distribution with standard deviation proportional to t, in order to capture temporal uncertainty. b,c, Belief state model with temporal uncertainty captures our data well. Post-reward RPEs are less suppressed for Odor C than for Odor B in both tasks, due to temporal uncertainty that grows with elapsed time.

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Starkweather, C., Babayan, B., Uchida, N. et al. Dopamine reward prediction errors reflect hidden-state inference across time. Nat Neurosci 20, 581–589 (2017).

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