Institute for Theoretical Physics and Mathematics Tehran January, 2006 Value based decision making: behavior and theory

Greg Corrado Leo Sugrue

SENSORY INPUT DECISION MECHANISMS ADAPTIVE BEHAVIOR low level sensory analyzers motor output structures

SENSORY INPUT DECISION MECHANISMS ADAPTIVE BEHAVIOR low level sensory analyzers motor output structures REWARD HISTORY representation of stimulus/ action value

How do we measure value? Herrnstein RJ, 1961

The Matching Law Choice Fraction

Behavior: What computation does the monkey use to ‘match’? Theory: Can we build a model that replicates the monkeys’ behavior on the matching task? How can we validate the performance of the? model? Why is a model useful? Physiology: What are the neural circuits and signal transformations within the brain that implement the computation?

An eye movement matching task Baiting Fraction 1:11:1 6:16:1 1:61:6 6:16:1 1:21:2 2:12:1 1:21:2

Dynamic Matching Behavior

Rewards Dynamic Matching Behavior

Responses Rewards Dynamic Matching Behavior

Relation Between Reward and Choice is Local Responses Rewards

How do they do this? What local mechanism underlies the monkey’s choices in this game? To estimate this mechanism we need a modeling framework.

Linear-Nonlinear-Poisson (LNP) Models of choice behavior Strategy estimation is straightforward

How do animals weigh past rewards in determining current choice? Estimating the form of the linear stage

How is differential value mapped onto the animal’s instantaneous probability of choice? Estimating the form of the nonlinear stage Differential Value

Differential Value (rewards) Monkey F Monkey G Probability of Choice (red)

Our LNP Model of Choice Behavior Model Validation Can the model predict the monkey’s next choice? Can the model generate behavior on its own?

Can the model predict the monkey’s next choice?

Predicting the next choice: single experiment

Predicting the next choice: all experiments

Can the model generate behavior on its own?

Model generated behavior: single experiment

Distribution of stay durations summarizes behavior across all experiments Stay Duration (trials)

Model generated behavior: all experiments Stay Duration (trials)

Model generated behavior: all experiments Stay Duration (trials)

1.Explore second order behavioral questions 2.Explore neural correlates of valuation Ok, now that you have a reasonable model what can you do with it?

1.Explore second order behavioral questions 2.Explore neural correlates of valuation Ok, now that you have a reasonable model what can you do with it?

choice history: Surely ‘not getting a reward’ also has some influence on the monkey’s behavior? reward history: Choice of Model Input

choice history: reward history:  the value of an unrewarded choice hybrid history:  Choice of Model Input

Systematically vary the value of  Estimate new L and N stages for the model Test each new model’s ability to a) predict choice and b) generate behavior hybrid history:  Can we build a better model by taking unrewarded choices into account?

Value of Unrewarded Choices (  ) Predictive Performance Generative Performance Unrewarded choices: The value of nothin’

Value of Unrewarded Choices (  ) Predictive Performance Generative Performance Stay Duration Histogram Overlap (%) Unrewarded choices: The value of nothin’

Contrary to our intuition inclusion of information about unrewarded choices does not improve model performance Choice of Model Input

Optimality of Parameters

Weighting of past rewards Is there an ‘optimal’ weighting function to maximize the rewards a player can harvest in this game?

The tuning of the  2 (long) component of the L- stage affects foraging efficiency. Monkeys have found this optimum. Weighting of past rewards The  1 (short) component of the L-stage does not affect foraging efficiency. Why do monkeys overweight recent rewards? The tuning of the , the nonlinear function relating value to p(choice) affects foraging efficiency. The monkeys have found this optimum also.

The differential model is a better predictor of monkey choice

Monkeys match; best LNP model Model predicts and generates choices Monkeys find optimal  2 and  ;  1 not critical Unrewarded choices have no effect Differential value predicts choices better than fractional value

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Best LNP model: Candidate decision variable, differential value: g(v1 - v2) = pc

Aside: what would Bayes do? 1) maintain beliefs over baiting probabilities 2) be greedy or use dynamic programming

Firing rates in LIP are related to target value on a trial-by-trial basis LIP gm020b into RF out of RF Target Value

The differential model also accounts for more variance in LIP firing rates

How we control/measure value An experimental task based on that principle A simple model of value based choice How we validate that model How we use the model to explore behavior How we use the model to explore value related signals in the brain What I’ve told you: Our Linear-Nonlinear-Poisson model Hybrid models, optimality of reward weights Neural firing in area LIP correlates with ‘differential value’ on a trial-by-trial basis A dynamic foraging task The matching law Predictive and generative validation

Foraging Efficiency Varies as a Function of  2

Foraging Efficiency Does Not Vary as a Function of  1

What do animals do? Matching is a probabilistic policy: Matching is almost optimal within the set of probabilistic policies. Animals match.

+ the change over delay

Greg Corrado

How do we implement the change over delay? only one ‘live’ target at a time