Institute for Theoretical Physics and MathematicsTehran

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

representationof stimulus/action value

How do we measure value?

Herrnstein RJ, 1961

The Matching Law

Ch

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e F

ract

ion

Behavior: What computation does the monkey use to ‘match’?

Theory: Can we build a model that replicatesthe 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

Bai

ting

Fra

ctio

n1:1

6:1

1:6

6:1

1:2

2:1

1:2

Dynamic Matching Behavior

Rewards

Dynamic Matching Behavior

ResponsesRewards

Dynamic Matching Behavior

Relation Between Reward and Choice is Local

ResponsesRewards

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

DifferentialValue

Differential Value (rewards)

Monkey F Monkey G

Pro

babi

lity

of

Cho

ice

(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?

0000111110011choice history:

Surely ‘not getting a reward’ also has some influence on the monkey’s behavior?

0000010100001reward history:

Choice of Model Input

0000111110011choice history:

0000010100001reward history:

the value of an unrewarded choice

hybrid history: 0000010100001

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: 0000010100001

Can we build a better model by taking unrewarded choices into account?

Value of Unrewarded Choices () Value of Unrewarded Choices ()

Predictive Performance Generative Performance

Unrewarded choices: The value of nothin’

Value of Unrewarded Choices () Value of Unrewarded Choices ()

Predictive Performance Generative Performance

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Du r

atio

n H

i sto

gram

Ov e

r lap

(%

)

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 monkeysoverweight 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

?

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

http://brainmap.wustl.edu/vanessen.html

gm020b

intoRF

outof 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:

€

pchoose = f pbait , pbait( )

Matching is almost optimal within the set of probabilistic policies.

Animals match.

+ the changeover delay

Greg Corrado

How do we implement the change over delay?

only one ‘live’ target at a time