doi: 10.1371/journal.pcbi.1002055.
Epub 2011 May 26.
Speed/accuracy trade-off between the habitual and the goal-directed processes
Affiliations
- PMID: 21637741
- PMCID: PMC3102758
- DOI: 10.1371/journal.pcbi.1002055
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Speed/accuracy trade-off between the habitual and the goal-directed processes
PLoS Comput Biol.
2011 May.
Abstract
Instrumental responses are hypothesized to be of two kinds: habitual and goal-directed, mediated by the sensorimotor and the associative cortico-basal ganglia circuits, respectively. The existence of the two heterogeneous associative learning mechanisms can be hypothesized to arise from the comparative advantages that they have at different stages of learning. In this paper, we assume that the goal-directed system is behaviourally flexible, but slow in choice selection. The habitual system, in contrast, is fast in responding, but inflexible in adapting its behavioural strategy to new conditions. Based on these assumptions and using the computational theory of reinforcement learning, we propose a normative model for arbitration between the two processes that makes an approximately optimal balance between search-time and accuracy in decision making. Behaviourally, the model can explain experimental evidence on behavioural sensitivity to outcome at the early stages of learning, but insensitivity at the later stages. It also explains that when two choices with equal incentive values are available concurrently, the behaviour remains outcome-sensitive, even after extensive training. Moreover, the model can explain choice reaction time variations during the course of learning, as well as the experimental observation that as the number of choices increases, the reaction time also increases. Neurobiologically, by assuming that phasic and tonic activities of midbrain dopamine neurons carry the reward prediction error and the average reward signals used by the model, respectively, the model predicts that whereas phasic dopamine indirectly affects behaviour through reinforcing stimulus-response associations, tonic dopamine can directly affect behaviour through manipulating the competition between the habitual and the goal-directed systems and thus, affect reaction time.
Conflict of interest statement
The authors have declared that no competing interests exist.
Figures
(A) The agent is at state 
and three choices are available: 
, 
and 
. The habitual system, as shown, has an estimate for the value of each action in the form of probability distribution functions, based on its previous experiences. These uncertain estimated values are then compared to each other in order to calculate the expected gain of having the exact value of each action (
). In the case of this example, action 
has the highest mean value, according to the uncertain knowledge in the habitual system. However, it is probable that the exact value of this action be less than the mean value of action 
. In that case, the best strategy would be to choose action 
, rather that 
. Thus, it is worth knowing the exact value of 
(
has a high value). (B) The exact value of actions is supposed to be attainable if a tree search is performed in the decision tree, by the goal-directed system. However, the benefit of search must be higher than its cost. The benefit of deliberation for each action is equal to its 
signal, whereas the cost of deliberation is equal to 
, which is the total reward that could be potentially acquired during the deliberation time, 
(
is the average over acquired rewards during some past actions). Since for action 
, the benefit of deliberation has exceeded its cost, the goal-directed system is engaged in value estimation. (C) Finally, action selection is carried out based on the estimated values for actions, which have come from either the habitual (for actions 
and 
) or the goal-directed (for action 
) system. For those actions that are not deliberated, the mean value of their distribution function is used for action selection.
and three choices are available: , and . The habitual system, as shown, has an estimate for the value of each action in the form of probability distribution functions, based on its previous experiences. These uncertain estimated values are then compared to each other in order to calculate the expected gain of having the exact value of each action (). In the case of this example, action has the highest mean value, according to the uncertain knowledge in the habitual system. However, it is probable that the exact value of this action be less than the mean value of action . In that case, the best strategy would be to choose action , rather that . Thus, it is worth knowing the exact value of ( has a high value). (B) The exact value of actions is supposed to be attainable if a tree search is performed in the decision tree, by the goal-directed system. However, the benefit of search must be higher than its cost. The benefit of deliberation for each action is equal to its signal, whereas the cost of deliberation is equal to , which is the total reward that could be potentially acquired during the deliberation time, ( is the average over acquired rewards during some past actions). Since for action , the benefit of deliberation has exceeded its cost, the goal-directed system is engaged in value estimation. (C) Finally, action selection is carried out based on the estimated values for actions, which have come from either the habitual (for actions and ) or the goal-directed (for action ) system. For those actions that are not deliberated, the mean value of their distribution function is used for action selection.
(A) In the training phase, the animal is put in a Skinner box where pressing the lever 
followed by a nose-poke entry in the food magazine (enter-magazine: 
) leads to obtaining the food reward. Other action sequences, like entering the magazine before pressing the lever (i.e. 
) result in no reward. As the task is supposed to be cyclic, the agent will return back to the initial state, 
, after taking each sequence of responses. (B) In the second phase, the devaluation phase, the food outcome which used to be acquired during the training period is devalued by being paired with illness. (C) The animal's behaviour is then tested in the same Skinner box used for training, with the difference that no outcome is delivered to the animal anymore, in order to avoid changes in behaviour due to new reinforcement. (D) Behavioural results (adopted from ref [22]) show that the rate of pressing the lever decreases significantly after devaluation for the case of moderate pre-devaluation training. In contrast, it doesn't show a significant change, when the training period has been extensive. Error bars represent 
(standard error of the mean).
followed by a nose-poke entry in the food magazine (enter-magazine: ) leads to obtaining the food reward. Other action sequences, like entering the magazine before pressing the lever (i.e. ) result in no reward. As the task is supposed to be cyclic, the agent will return back to the initial state, , after taking each sequence of responses. (B) In the second phase, the devaluation phase, the food outcome which used to be acquired during the training period is devalued by being paired with illness. (C) The animal's behaviour is then tested in the same Skinner box used for training, with the difference that no outcome is delivered to the animal anymore, in order to avoid changes in behaviour due to new reinforcement. (D) Behavioural results (adopted from ref [22]) show that the rate of pressing the lever decreases significantly after devaluation for the case of moderate pre-devaluation training. In contrast, it doesn't show a significant change, when the training period has been extensive. Error bars represent (standard error of the mean).
The model is simulated under two scenarios: moderate training (left column), and extensive training (right column). In the moderate training scenario, the agent has experienced the environment for 40 trials before devaluation treatment, whereas in the extensive training scenario, 240 pre-devaluation training trials have been provided. In sum, the figure shows that after extensive training, but not moderate training, the 
signal is below 
at the time of devaluation (Plot 
against 
). Thus, the behaviour in the second scenario, but not the first, doesn't change right after devaluation (Plot 
against 
. Also, plot 
against 
). The low value of the 
signal at the time of devaluation for the second scenario is because there is little overlap between the distribution functions of the values of the two available choices (Plots 
and 
). The opposite is true for the first scenario (Plots 
and 
). Numbers along the horizontal axis in plots 
to 
, and 
to 
, represent trial numbers. Each “trial” ends when the simulated agent receives a reward; e.g. in the schedule of Figure 2 , each time the agent chooses 
at state 
, the trial number is counted up. Plots 
and 
show the distribution functions of the habitual system over its estimated 
-values, at one trial before devaluation. Bar charts 
and 
show the average probability of performing 
at 10 trials before (filled bars) and 10 trials after (empty bars) devaluation. All data reported are means over 3000 runs. The 
for all bar charts is close to zero and thus, not illustrated.
signal is below at the time of devaluation (Plot against ). Thus, the behaviour in the second scenario, but not the first, doesn't change right after devaluation (Plot against . Also, plot against ). The low value of the signal at the time of devaluation for the second scenario is because there is little overlap between the distribution functions of the values of the two available choices (Plots and ). The opposite is true for the first scenario (Plots and ). Numbers along the horizontal axis in plots to , and to , represent trial numbers. Each “trial” ends when the simulated agent receives a reward; e.g. in the schedule of Figure 2 , each time the agent chooses at state , the trial number is counted up. Plots and show the distribution functions of the habitual system over its estimated -values, at one trial before devaluation. Bar charts and show the average probability of performing at 10 trials before (filled bars) and 10 trials after (empty bars) devaluation. All data reported are means over 3000 runs. The for all bar charts is close to zero and thus, not illustrated.
(A) In the training phase, either pressing lever one 
or pressing lever two 
, if followed by entering the magazine 
, results in acquiring one unit of either of the two rewards, 
or 
, respectively. The reinforcing value of the two rewards is equal to one. Other action sequences lead to no reward. As in the task of Figure 2 , this task is also assumed to be cyclic. (B) In the devaluation phase, the outcome of one of the responses (
) is devalued (
), whereas the rewarding value of the outcome of the other response (
) has remained unchanged. After the devaluation phase, the animal's behaviour is tested in extinction (for space consideration, this phase is not illustrated). Similar to the task of Figure 2 , neither 
nor 
is delivered to the animal in the test phase.
or pressing lever two , if followed by entering the magazine , results in acquiring one unit of either of the two rewards, or , respectively. The reinforcing value of the two rewards is equal to one. Other action sequences lead to no reward. As in the task of Figure 2 , this task is also assumed to be cyclic. (B) In the devaluation phase, the outcome of one of the responses () is devalued (), whereas the rewarding value of the outcome of the other response () has remained unchanged. After the devaluation phase, the animal's behaviour is tested in extinction (for space consideration, this phase is not illustrated). Similar to the task of Figure 2 , neither nor is delivered to the animal in the test phase.
The results show that since the reinforcing value of the two outcomes is equal, there is a huge overlap between the distribution functions over the 
-values of actions 
and 
, at state 
, even after extensive training (240 trials) (Plots 
and 
). Accordingly, the 
signals (benefit of goal-directed deliberation) for these two actions remain higher than the 
signal (cost of deliberation) (Plot 
) and thus, the goal-directed system is always engaged in value-estimation for these two choices. The behaviourally observable result is that responding remains sensitive to revaluation of outcomes, even though devaluation has happened after a prolonged training period (Plots 
and 
).
-values of actions and , at state , even after extensive training (240 trials) (Plots and ). Accordingly, the signals (benefit of goal-directed deliberation) for these two actions remain higher than the signal (cost of deliberation) (Plot ) and thus, the goal-directed system is always engaged in value-estimation for these two choices. The behaviourally observable result is that responding remains sensitive to revaluation of outcomes, even though devaluation has happened after a prolonged training period (Plots and ).
(A) When each trial begins, one of the two stimuli, 
or 
, is presented in random on a screen. The subject can then choose whether to touch the screen (
action) or not (
action). The task is performed in three phases: training, reversal, and extinction. During the training phase, the subject will receive a reward if the stimulus 
is presented and the action 
is performed by the subject, or if the stimulus 
is presented and the action 
is selected (
). During the reversal phase, the reward function is reversed, meaning that the 
action must be chosen when the stimulus 
is presented, and vice versa (
). Finally, during the extinction phase, regardless of the presented stimulus, only the 
action leads to a reward (
). (B) During both the training and reversal phases, subjects' reaction time is high at the early stages when they don't have enough experience with the new conditions yet. However, after some trials, the reaction time declines significantly. Error bars represent 
.
or , is presented in random on a screen. The subject can then choose whether to touch the screen ( action) or not ( action). The task is performed in three phases: training, reversal, and extinction. During the training phase, the subject will receive a reward if the stimulus is presented and the action is performed by the subject, or if the stimulus is presented and the action is selected (). During the reversal phase, the reward function is reversed, meaning that the action must be chosen when the stimulus is presented, and vice versa (). Finally, during the extinction phase, regardless of the presented stimulus, only the action leads to a reward (). (B) During both the training and reversal phases, subjects' reaction time is high at the early stages when they don't have enough experience with the new conditions yet. However, after some trials, the reaction time declines significantly. Error bars represent .
Since the 
signals have high values at the early stages of learning (plot 
), the goal-directed system is active and thus, the deliberation time is relatively high (plot 
). After further training, the habitual system takes control over behaviour (plot 
) and as a result, the model's reaction time decreases (plot 
). After reversal, it takes some trials for the habitual system to realize that the cached 
-values are not precise anymore (equivalent to an increase in the variance of 
). Thus, after some trials after reversal, the 
signal increases again (plot 
), which results in re-activation of the goal-directed system. As a result, the model's reaction time increases again (plot 
). A similar explanation holds for the rest of the trials. In sum, consistent with the experimental data, the reaction time is higher during the searching period, than the applying period.
signals have high values at the early stages of learning (plot ), the goal-directed system is active and thus, the deliberation time is relatively high (plot ). After further training, the habitual system takes control over behaviour (plot ) and as a result, the model's reaction time decreases (plot ). After reversal, it takes some trials for the habitual system to realize that the cached -values are not precise anymore (equivalent to an increase in the variance of ). Thus, after some trials after reversal, the signal increases again (plot ), which results in re-activation of the goal-directed system. As a result, the model's reaction time increases again (plot ). A similar explanation holds for the rest of the trials. In sum, consistent with the experimental data, the reaction time is higher during the searching period, than the applying period.
In this example, at each trial, one of the four stimuli is presented with equal probabilities. After observing the stimulus, only one of four available choices lead to a reward (
). The task structure is verbally instructed to the subjects before they start performing the task. The interval between the appearance of the stimulus and the initiation of a response is measured as “reaction time”. The experiment is performed under different numbers of stimulus-response pairs; e.g. some subjects perform the task when only one stimulus-response pair is available (
), whereas for other subjects the number of stimulus-response pairs might be different.
). The task structure is verbally instructed to the subjects before they start performing the task. The interval between the appearance of the stimulus and the initiation of a response is measured as “reaction time”. The experiment is performed under different numbers of stimulus-response pairs; e.g. some subjects perform the task when only one stimulus-response pair is available (), whereas for other subjects the number of stimulus-response pairs might be different.
Consistent with the behavioural data, the results show that as the number of stimulus-response pairs increase, the reaction time also increases. Moreover, if extensive training is provided to the subjects, the reaction time decreases and becomes independent from the number of choices.
The proposed model predicts that manipulating the knowledge acquired by the goal-directed system should not affect the goal-directedness of behaviours. To test this prediction, a place/response task can be used. (A) In the first phase, the animal is moderately trained to acquire food reward in a T-maze. Since this training is moderate, the goal-directed system is expected to control behaviour during this phase. (B) In the second phase, the uncertainty of the goal-directed system is increased by putting the animal inside the right arm for some few trials, while the food reward comes at random or is totally removed. (C) Since the second phase doesn't have any effect on the habitual system, our model predicts that the arbitration between the system must have remained intact and thus, responding should still be goal-directed in the third phase. For that, the animal should still chose turning toward the window, even though its starting point is at the opposite end of the maze.
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