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Transcript of 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.
6
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.
7
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)
32
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);
13
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
18
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)
25
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
26
*
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.
27
, 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!
28
(,())
2() -
()log 2
()
():
"Efficient coding":
(,)(,):
=()
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We Can Rebuild a Theory of Computation
Using Brainware as the Computational Substrate
29
Stimulus
Response
State (n+1)
State (n)
< ( ) >
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and Fill in the Gaps of Both Symbolic Representation
and Rational Choice Approaches
30
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
31
, 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.
32
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