Competent Program Evolution
Dissertation Defense
Moshe Looks
December 11th, 2006
1
Synopsis

Competent optimization requires adaptive
decomposition

This is problematic in program spaces

Thesis: we can do it by exploiting semantics
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Results: it works!
2
General Optimization



Find a solution s in S
Maximize/minimize f(s)
 f:S
To solve this faster than O(|S|),
make assumptions about f
3
Near-Decomposability
Complete separability would be nice…
Weaker Interactions
Stronger Interactions
Near-decomposability (Simon, 1969) is more realistic
4
Exploiting Separability

Separability = independence assumptions

Given a prior over the solution space

represented as a probability vector
3.
Sample solutions from the model
Update model toward higher-scoring points
Iterate...

Works well when interactions are weak
1.
2.
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Exploiting Near-Decomposability

Bayesian optimization algorithm (BOA)



represent problem decomposition as a Bayesian Network
learned greedily, via a network scoring metric
Hierarchical BOA

uses Bayesian networks with local structure



restricted tournament replacement
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allows smaller model-building steps
leads to more accurate models
promotes diversity
Solves the linkage problem
Competence: solving hard problems quickly,
accurately, and reliably
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Program Learning

Solutions encode executable programs

execution maps programs to behaviors



find a program p in P
maximize/minimize f(exec(p))


exec:PB
f:B
To be useful, make assumptions about
exec, P, and B
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Properties of Program Spaces

Open-endedness

Over-representation


Compositional hierarchy


many programs map to the same behavior
intrinsically organized into subprograms
Chaotic Execution

similar programs may have very different
behaviors
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Properties of Program Spaces
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Simplicity prior

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Simplicity preference


smaller programs are preferable
Behavioral decomposability


simpler programs are more likely
f:B is separable / nearly decomposable
White box execution

execution function is known and constant
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Thesis

Program spaces not directly decomposable

Leverage properties of program spaces as
inductive bias
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Leading to competent program evolution
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Representation-Building
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Organize programs in terms of commonalities
Ignore semantically meaningless variation
Explore plausible variations
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Representation-Building


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Common regions must be aligned
Redundancy must be identified
Create knobs for plausible variations
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Representation-Building

What about…



changing the phase?
averaging two input instead of picking one?
…
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behavior (semantic) space
program (syntactic) space
Statics & Dynamics
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Representations span a limited subspace of programs

Conceptual steps in representation-building:
1.
2.
3.

reduction to normal form (x, x + 0 → x)
neighborhood enumeration (generate knobs)
neighborhood reduction (get rid of some knobs)
Create demes to maintain a sample of many representations



deme: a sample of programs living in a common representation
intra-deme optimization: use the hBOA
inter-deme:

based on dominance relationships
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Meta-Optimizing Semantic
Evolutionary Search (MOSES)
1.
Create an initial deme based on a small set of knobs (i.e.,
empty program) and random sampling in knob-space
2.
Select a deme and run hBOA on it
3.
Select programs from the final hBOA population meeting the
deme-creation criterion (possibly displacing existing demes)
4.
For each such program:
1.
2.
3.
5.
create a new representation centered around the program
create a new random sample within this representation
add as a deme
Repeat from step 2
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Artificial Ant
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Eat all food pellets within 600 steps
Existing evolutionary methods not
significantly than random
Space contains many regularities
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To apply MOSES:
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three reductions rules for normal form
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e.g., left, left, left → right
separate knobs for rotation,
movement, & conditionals
no neighborhood reduction
needed
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Artificial Ant
Technique


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136,000
How does MOSES do it?
Evolutionary
Programming
Searches a greatly reduced
space
Genetic
Programming
450,000
MOSES
23,000
x
x
Exploits key dependencies:



Effort
“[t]hese symmetries lead to essentially the same solutions
appearing to be the opposite of each other. E.g. either a pair of
Right or pair of Left terminals at a particular location may be
important.” – Langdon & Poli, “Why ants are hard”
hBOA modeling learns linkage between rotation knobs
Eliminate modeling and the problem still gets solved


but with much higher variance
computational effort rises to 36,000
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Elegant Normal Form (Holman, ’90)


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Hierarchical normal form for Boolean formulae
Reduction process takes time linear in formula size
99% of random 500-literal formulae reduced over 98%
18
Syntactic vs. Behavioral Distance

Is there a correlation between syntactic and behavioral distance?

5000 unique random formulae of arity 10 with 30 literals each


Computed the set of pairwise



qualitatively similar results for arity 5
behavioral distances (truth-table Hamming distance)
syntactic distances (tree edit distance, normalized by tree size)
The same computation on the same formulae reduced to ENF
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Syntactic vs. Behavioral Distance

Is there a correlation between syntactic and behavioral distance?
Random Formulae
Reduced to ENF
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Neighborhoods & Knobs

What do neighborhoods look like, behaviorally?

1000 unique random formulae, arity 5, 100 literals each


Enumerate all neighbors (edit distances <2)


qualitatively similar results for arity 10
compute behavioral distance from source
Neighborhoods in MOSES defined based on ENF


neighbors are converted to ENF, compared to original
used to heuristically reduce total neighborhood size
21
Neighborhoods & Knobs

What do neighborhoods look like, behaviorally?
Random formulae
Reduced to ENF
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Hierarchical Parity-Multiplexer

Study decomposition in a Boolean domain

Multiplexer function of arity k1 computed
from k1 parity function of arity k2


total arity is k1k2
Hypothesis:

parity subfunctions will exhibit tighter linkages
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Hierarchical Parity-Multiplexer

Computational effort decreases 42% with modelbuilding (on 2-parity-3-multiplexer)

Parity
subfunctions
(adjacent pairs)
have tightest
linkages

Hypothesis
validated
24
Program Growth

5-parity, minimal program size ~ 53
25
Program Growth

11-multiplexer, minimal program size ~ 27
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Where do the Cycles Go?
Problem
hBOA
Representation- Program
Building
Evaluation
5-Parity
28%
43%
29%
11-multiplex
5%
5%
89%
CFS
Complexity
80%
10%
O(N·l2·a2)
O(N·l·a)
11%
O(N·l·c)
N is population size, O(n1.05)
l is program size, a is the arity of the space
n is representation size, O(a·program size)
c is number of test cases
27
Supervised Classification

Goals:

accuracies comparable to SVM

superior accuracy vs. GP

simpler classifiers vs. SVM and GP
28
Supervised Classification

How much simpler?
Consider average-sized formulae learned for the 6-multiplexer

MOSES



21 nodes
max depth 4
or(and(not(x1) not(x2) x3)
and(or(not(x2)
and(x3 x6))
x1 x4)
and(not(x1) x2 x5)
and(x1 x2 x6))

GP (after reduction to ENF!)


50 nodes
max depth 7
and(or(not(x2)
and(or(x1 x4)
or(and(not(x1) x4)
x6)))
or(and(or(x1 x4)
or(and(or(x5 x6)
or(x2
and(x1 x5)))
and(not(x1) x3)))
and(or(not(x1)
and(x2 x6))
or(not(x1) x3 x6)
or(and(not(x1) x2)
and(x2 x4)
and(not(x1) x3)))))
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Supervised Classification

Datasets taken from recent comp. bio. papers

Chronic fatigue syndrome (101 cases)



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Lymphoma (77 cases) & aging brains (19 cases)




based on 26 SNPs
genes either in homozygosis, in heterozygosis, or not expressed
56 binary features
based on gene expression levels (continuous)
50 most-differentiating genes selected
preprocessed into binary features based on medians
All experiments based on 10 independent runs of 10-fold
cross-validation
30
Quantitative Results

Classification average test accuracy:
Technique
CFS
Lymphoma Aging Brain
SVM
66.2%
97.5%
95.0%
GP
67.3%
77.9%
70.0%
MOSES
67.9%
94.6%
95.3%
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Quantitative Results

Benchmark performance:

artificial ant


parity problems



6x less computational effort vs. EP, 20x less vs. GP
1.33x less vs. EP, 4x less vs. GP on 5-parity
found solutions to 6-parity (none found by EP or GP)
multiplexer problems

9x less vs. GP on 11-multiplexer
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Qualitative Results


Requirements for competent program evolution

all requirements for competent optimization

+ exploit semantics

+ recombine programs only within bounded subspaces
Bipartite conception of problem difficulty

program-level: adapted from the optimization case

deme-level: theory based on global properties of the
space (deme-level neutrality, deceptiveness, etc.)
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Qualitative Results

Representation-building for programs:

parameterization based on semantics

transforms program space properties

to facilitate program evolution

probabilistic modeling over sets of program
transformations

models compactly represent problem structure
34
Competent Program Evolution

Competent: not just good performance



Vision: representations are important




explainability of good results
robustness
program learning is unique
representations must be specialized
based on semantics
MOSES: meta-optimizing semantic
evolutionary search

exploiting semantics and managing demes
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Committee

Dr. Ron Loui (WashU, chair)

Dr. Guy Genin (WashU)
Dr. Ben Goertzel (Virginia Tech,
Novamente LLC)
Dr. David E. Goldberg (UIUC)
Dr. John Lockwood (WashU)
Dr. Martin Pelikan (UMSL)
Dr. Robert Pless (WashU)
Dr. William Smart (WashU)
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