brook moldoveanu april16

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Intelligent Artificialityand an Economics of Mental Behavior

Mihnea Moldoveanu

University of Toronto

Brooks Lecture, Institute for Cognitive Science

Ottawa

April 16, 2013


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What I Am Not (A Partial List, Part I)

I am not an economist (though I work alongside a few);

I am not a neuroscientist, of either wet or dry kinds (though I will

work with many of both, soon);

I am not a psychologist (though I used to work with one, andeven tried to impersonate one for 18 months);

I am not an AI guy (or, gal) (though my post docs/RAs comefrom a computer science and artificial intelligence lab);

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What I Am Not (A Partial List, Part II)

I am not a neuro-economist (I do not understand what that means);

I am not a neuropsychologist (they dont understand what thatmeans);

I am not an empiricist (but, who is, really?);

I am not a theorist (see I am not an empiricist);

I am not an epistemologist or impartial observer of scientificpractice (an incoherent concept).

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A Gap(ing Hole) in the Core of Rational

Choice Models

Choice-theoretic conditions on rational choice (antisymmetry,acyclicity, completeness, identity) guarantee existence of objectivefunction economic agents are said to maximize in virtue of choosing.

How are we to interpret maximization (optimization)? As a real processwhose temporal dynamics refer to something?

If, so, what is it running on? Brains?

Researchers desktops? Laptops? iPads?

Turing Machines? (i.e. an imaginary process running on an imaginary device?)

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Predict how this Creature

will choose from among N

options:

Predict behavior of this

device:

INPUTS:

Past choices among

similar options

Revealed preference modelRationalityconditions

OUTPUTS:

Prediction of choice/behavior

INPUTS:

Newton Laws

Measured values of g, l,, m

2

21

d

mmGFg

OUTPUTS:

Prediction of movement trajectory,transient and static

m

g

l

The Predictive Apparatus Is Faulty


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(Not) A Trick Question(Illuminative of the question: How does optimization happen?

Suppose Bob must choosebetween two lotteries:

Lottery A pays $1MMwith probability0.1and $0with probability 0.9.

Lottery B pays $1MM if the 7thdigit inthe decimal expansion of sqrt(2)is an 3and $0 otherwise.

No calculator, SmartPhone or

computer;

Needs to choose in 2 min.

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Bobs

Choice

Lottery A

Lottery B

P($1MM)=0.1

P($0)=0.9;

$1MM if

dig7(sqrt(2))=3;

Else, $0.


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What If We Know Bob KnowsThis?

Depends on whether or not Bobsees the problem as one solvable bythe algorithm;

Depends on whether or not Bob cancorrectly perform requiredoperations quickly enough togenerate answer in under 2 minutes.

Depends on whether or not Bobthinkshe can correctly perform theoperations quickly enough togenerate the answer in under 2minutes.

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Problem: Given x such that x = 2, find x

[NEWTONS METHOD]

Step 1: Formf(x) = x - 2

Step 2: Computef (x) = 2x

Step 3: Make first guess at x: x= 1Step 4: (Repeat as necessary)Xk+1= xk

e.g. x= 1 - = 1.5x= 1.416667:

:

Calculator says x= 1.4142135. (requires 5 steps)


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The Computational Process Model Matters

to Whether We Ascribe Rationality to Bob

Each calculation generates

new information (2 bits)

that reduces Bobs

uncertainty regarding the truevalue of the answer

on account of the fact that

it actually reduces theinstantaneous search space ofthe problem he is trying toosolve.

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A3

A2

A1

A4

A5

AA

A represents the exact answer,is the diameter of an

acceptable error region

aroundA. {Ak}are successive

approximations of A, outputsof successive iterations of the

solution algorithm.


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and the Logical Depth of Calculative Thinking

Matters to Strategic Payoffs[Cournot-Nash Duopoly Without Logical Omniscience]

Firm 1s quantity

choice/best response

Firm 2s quantity

choice/best response

a-c2

a-c2

a-c4

a-c4

3(a-c)8 3(a-c)8

5(a-c)16

5(a-c)16

11(a-c)

32

11(a-c)

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Generate using series

qN= a-c - qN-1 ;

2 2qo=0

Which results from jointmaximization of profits

i= (a-c-qi-qj)qi

So, if firm 1 says, I willsell a-c , firm 2 will

2credibly retort, I will sella-c ; which would

4Lead to losses relative to

the a-c , a-c

3 3solution

a-c3

NASH EQUILIBRIUM

Moldoveanu, 2009, Thinking Strategically About Thinking Strategically


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Computational Landscapes for Interactive

Problem Solving (Duopoly)

Computational Landscape ofCournot Nash Equilibrium, 2firms, a=3, c=1.

Horizontal axes represent numberof iterations for each firm. Verticalaxis is the profit level of firm 1.Profit levels of firm 2 are

symmetrical.

Landscape converges to NashEquilibrium output of (a-c)/3.

10Moldoveanu, 2009, Thinking Strategically About Thinking Strategically


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If All Problem Solving Processes Had These

Dynamics, We Would Be Programming on Brains

Right Now.


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What if Bob Had to Make a Different

Choice with Procedural Implications?

$1MM for finding the shortest

Path connecting Canadas 4663 cities in1 day of less, OR

One days consulting fees guaranteed.

Total number of operations required

K ~ 2 ~ 5 x 10His computational prowess R ~ 10 ops/second

His computational budget

(10 ops / second) (3600 sec / H) (24h / day)

x(365 days / yr) ~ 3 x 10 ops

He can solve this problem in 1.6 x 10years

not worth it!

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UNLESS, Bob Had Some Kind of a

Short Cut

Non-exhaustive

Non-deterministic

Non-universal (will not be optimalfor other NP-hard optimizationproblems)

Locally exportable (to other TSPs)

Hardware-adaptable (more/lessRAM, and operations per I/Ocycle);

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4663 city TSP, solvedusing Lin-Kernighan (meta) algorithm


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The NP Class Reads like a Whos Who of Everyday

Problems (Solved by Creatures with Brains)

Optimalscheduling withlumpy activitiesand constraints,

Optimal pathcalculation via

Traveling

Salesman

problem

Optimal taskdesign, viaKnapsack

Nash Equilibriumcalculation for

minimum payoff

Circle of trustdiscovery, cliquediscovery (social

reasoning)

kSAT(Cook, 1976)

3 SAT

Partition Vertex Cover

CliqueHamiltonian

circuit

reduces to reduces to

reduces to reduces to

models models

models models

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Generalized Problem Solver, Version 2.X

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Modeling Toolkit for Problem Solving

Processes: An Associative Map

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kSAT/MaxSAT

TSP Vertex Cover

Clique

Cover Knapsack

Evolutionary Search

Divide and ConquerLocal Neighborhood Search

Brunch and Bound

Scholastic Hill Climbing

?

?

Payoffs [Problems x Procedures]


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What Could Computational Payoffs Look

Like? Two Separate Payoff Structures

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Accuracy

of

Solution

(proximity

to

optimum)

A(a,s)

Speed of Convergence

(inverse of time to achievement)

Algorithmic advantage: , a, SA

(a,s)B

(a,s)

B(a,s)

S

a

Accuracy

of

Solution

Probability of achieving

solution of requisite accuracy within maximum allowable

time x resource window

Algorithmic advantage: , a, pA

(a,p)B

(a,p)

B(a,p)

A(a,p)

p

a


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Combine into One 3D Measure

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a=Accuracy of solution

B(a,s,p)

A(a,s,p)

P=Probability of Convergence

S = Speed of convergence

Algorithmic Advantage: , a,s,pA

(a,s,p)B

(a,s,p)


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Getting Closer: How Would a Chip Designer

Think About Embodied Problem Solving?

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Using Application-Specific Chip Design as a

Paradigm for Mind-Brain Investigation

No operation without implementation;

No algorithmic change without architecturalconsequence;

Capacity limit (Ops/sec,M) part of everyhardware decision;

Hardware Adaptable to Algorithm/I-Orequirements (more/less RAM, operations

per I/O cycle, precision of internalrepresentation of coefficients);

Average-case performance far moreimportant than worst case performance(e.g.dynamic range extremes of the input x[n]).

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Simulation Is NotJust Modeling:

It Has Bite, Which Is Why We Call It EMULATION

21

,

@,

@,


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Decision

Point 1

Algorithm 2

Decisionpoint 3 yes

no

operation

Estimate

Algorithm 1

DecisionPoint 2

no

yes

stop

Estimate

Of Course, Humans Can Choose Whether or

Not to Proceed with an Algorithmic Computation at

Many Points

uncertainty

Information gain

Along the way

anxiety cost

uncertainty threshold

Threshold test for engaging

in next operation


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A Goal for Intelligent Artificiality:

A Brain Emulator/Co-Processor

No model of mental behavior withoutarchitectural and behavioral consequences;

Brain states on which mental states supervene

can be tracked, not only modelled:prediction/control supersedes explanation asregulative goal.

Hardware changes (TMS, ECT, stimulus

protocols, psycho-pharm) can be emulated,enabling point predictions about mentalbehavior.

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We Need an Anatomically Informed Model

of Brainware Layered connectivity for the associative

cortices;

Cross-layer forward and backwardconnections (sparser), intra-layer

connections (denser);

Some (parametrizable) asymmetry betweenforward and backward connections;

Architectural levers include strength ofsynaptic connections, plastic formationof new circuits.

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That Is Emulable via a Well Understood

Structure (Recurrent Neural Network)

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Dynamically Adaptive Nodes

Sensory Nodes

Prediction

Errors

Predictions


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Which Extremizes an Objective Function Familiar to

Self-Organizing (Entropy-Increase-Defying) Systems

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*

min,

, ln , + ln ,

Kullback-Leiblerdivergence of p,q

Spread of q(ENTROPY)

actions

internal states

causes

problems(inputs,causes)Sensory states


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to Provide an Extremisand That Works at Different

Space-Time Scales and in Different Domains of Being.

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, ln , + ln ,

min* min*,() min*,()

actions sampling inference

, (,) ( , )

pico:synaptic weight

changes

micro:attentional

shifts

macro


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Now, If We Could Only Explain Away

Complexity Mismatches Which We Can!

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(,())

2() -

()log 2

()

():

"Efficient coding":

(,)(,):

=()


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We Can Rebuild a Theory of Computation

Using Brainware as the Computational Substrate

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Stimulus

Response

State (n+1)

State (n)

< ( ) >


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and Fill in the Gaps of Both Symbolic Representation

and Rational Choice Approaches

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max,,, , , , . , , , ; :

PROCEDURALLY OPAQUE;ARCHITECTURALLY INDETERMINATE;

PHYSICALLY UNREALIZABLE IN MANY CASES OF INTEREST

max ,* (, , /, ) . ( )

PROCEDURALLY UNREALISTIC;ARCHITECTURALLY INAPPLICABLE;WORST CASE EMPHASIS UNREASONABLE IN MOST CASES OF INTEREST


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Circumventing Logically Deep Equilibrium

Calculations: BeautyContest Example

Nplayers, 1 period game;

Each player submits number from 0to Nto a(n honest) clearing house.

Winner (gets $N x $1000) of the

game is the player that submits thenumber that is closest to 2/3 of theaverage of all the other numbers.

Iterated dominance reasoning:

ifI submit x andothers submit

(y,z,w,) then winner would havehad to havesubmitted z, soI shouldhave submitted y.

Equilibrium submission (strategy) is

0: (2/3)(0)=0

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, 2

3

=

2

1

N

. . 1 0 0 , ~0,100- 5 0 , , 33.33

+,

2

3 ,

0


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Circumventing Logically Deep Equilibrium

Calculations: BeautyContest Example

Encode othersvia Types (Ho, 2004)

Type 0players do not think of whatothers think;

Type 1players think only of whatothers think;

Type 2players think of whatType 0and Type 1 players think only;

Type k players think of what

Type (k-1, k-2,) players think only.

Define Q(this group type set) as

estimate of density ofType kplayers inthis group.

RefineQ(types) (mode, spread) according tocues.

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Q(Type/Group)

Q(Type)

Type1 2 3

Group 1

Q(Type)

Type1 2 3

Group 2

Q(Type)

Type1 2 3

Group 3Q(Type)

Type1 2 3

Group 4

Poisson (Type/Group)

4


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Intelligent

Artificiality

A Foundation for Mind-Brain Design,

Diagnostics and Development

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