Hybrid Evolution of Heterogeneous Neural Networks

Transcription

Hybrid Evolution of Heterogeneous Neural Networks
Hybrid Evolution of
Heterogeneous Neural Networks
01001110 01100101
01110101 01110010
01101111 01101110
01101111 01110110
01100001 00100000
01110011 01101011
01110101 01110000
01101001 01101110
01100001 00100000
01101011 01100001
01110100 01100101
01100100 01110010
01111001 00100000
01110000 01101111
01100011 01101001
01110100 01100001
01100011 01110101
00101100 00100000
01000110 01000101
01001100 00100000
01000011 01010110
01010101 01010100
Zdeněk Buk
bukz1@fel.cvut.cz
Miroslav Šnorek
snorek@fel.cvut.cz
http://cig.felk.cvut.cz
Computational Intelligence Group
Department of Computer Science and Engineering
Faculty of Electrical Engineering
Czech Technical University in Prague
ICANN 2008
Outline
●
Continual Evolution Algorithm (CEA) description
●
Data structures – encoding of the individuals
●
Evolution process
●
Control functions
●
Testing, experiments
●
Population behavior
●
Conclusion
18th International Conference on Artificial Neural Networks
3-6 September 2008, Diplomat Hotel, Prague, Czech Republic
Zdeněk Buk, bukz1@fel.cvut.cz, http://cig.felk.cvut.cz
Continual Evolution Algorithm
●
Hybrid genetic algorithm
–
●
combination of genetic and gradient-based methods
Separate evolution of structure and parameters
of individuals (models, neural networks)
●
Variable population size
●
Sequential replacement of individuals
–
evolution in continual time dimension
–
age parameter of each individual
18th International Conference on Artificial Neural Networks
3-6 September 2008, Diplomat Hotel, Prague, Czech Republic
Zdeněk Buk, bukz1@fel.cvut.cz, http://cig.felk.cvut.cz
Individuals encoding
xi =a i , pi , si , bi 
●
Separate evolution of structure and parameters
of individuals (models, neural networks)
18th International Conference on Artificial Neural Networks
3-6 September 2008, Diplomat Hotel, Prague, Czech Republic
Zdeněk Buk, bukz1@fel.cvut.cz, http://cig.felk.cvut.cz
Individuals encoding
xi =a i , pi , si , bi 
age of the individual
18th International Conference on Artificial Neural Networks
3-6 September 2008, Diplomat Hotel, Prague, Czech Republic
Zdeněk Buk, bukz1@fel.cvut.cz, http://cig.felk.cvut.cz
Individuals encoding
xi =a i , pi , si , bi 
structural vector
18th International Conference on Artificial Neural Networks
3-6 September 2008, Diplomat Hotel, Prague, Czech Republic
Zdeněk Buk, bukz1@fel.cvut.cz, http://cig.felk.cvut.cz
Individuals encoding
xi =a i , pi , si , bi 
structural vector
topology of the network
18th International Conference on Artificial Neural Networks
3-6 September 2008, Diplomat Hotel, Prague, Czech Republic
Zdeněk Buk, bukz1@fel.cvut.cz, http://cig.felk.cvut.cz
Individuals encoding
xi =a i , pi , si , bi 
structural vector
topology of the network
activation functions
18th International Conference on Artificial Neural Networks
3-6 September 2008, Diplomat Hotel, Prague, Czech Republic
Zdeněk Buk, bukz1@fel.cvut.cz, http://cig.felk.cvut.cz
Individuals encoding
xi =a i , pi , si , bi 
parametric vector
behavioral vector
18th International Conference on Artificial Neural Networks
3-6 September 2008, Diplomat Hotel, Prague, Czech Republic
Zdeněk Buk, bukz1@fel.cvut.cz, http://cig.felk.cvut.cz
Individuals encoding
xi =a i , pi , si , bi 
parametric vector
behavioral vector
weights
18th International Conference on Artificial Neural Networks
3-6 September 2008, Diplomat Hotel, Prague, Czech Republic
Zdeněk Buk, bukz1@fel.cvut.cz, http://cig.felk.cvut.cz
Individuals encoding
xi =a i , pi , si , bi 
18th International Conference on Artificial Neural Networks
3-6 September 2008, Diplomat Hotel, Prague, Czech Republic
Zdeněk Buk, bukz1@fel.cvut.cz, http://cig.felk.cvut.cz
Evolution process
●
Hybrid genetic algorithm
–
●
combination of genetic and gradient-based methods
2 Dimensional evolution
18th International Conference on Artificial Neural Networks
3-6 September 2008, Diplomat Hotel, Prague, Czech Republic
Zdeněk Buk, bukz1@fel.cvut.cz, http://cig.felk.cvut.cz
Evolution process
18th International Conference on Artificial Neural Networks
3-6 September 2008, Diplomat Hotel, Prague, Czech Republic
Zdeněk Buk, bukz1@fel.cvut.cz, http://cig.felk.cvut.cz
Crossover and mutation
Individual 1
p1
s1
b1
p2
s2
b2
Offspring
Individual 2
18th International Conference on Artificial Neural Networks
3-6 September 2008, Diplomat Hotel, Prague, Czech Republic
Zdeněk Buk, bukz1@fel.cvut.cz, http://cig.felk.cvut.cz
Crossover and mutation
Individual 1
p1
s1
b1
p2
s2
b2
Random mutation
Offspring
Individual 2
18th International Conference on Artificial Neural Networks
3-6 September 2008, Diplomat Hotel, Prague, Czech Republic
Zdeněk Buk, bukz1@fel.cvut.cz, http://cig.felk.cvut.cz
Crossover and mutation
Individual 1
p1
s1
b1
p2
s2
b2
Random mutation
Offspring
Individual 2
18th International Conference on Artificial Neural Networks
3-6 September 2008, Diplomat Hotel, Prague, Czech Republic
Zdeněk Buk, bukz1@fel.cvut.cz, http://cig.felk.cvut.cz
Crossover and mutation
Individual 1
p1
s1
b1
p2
s2
b2
Offspring
Individual 2
18th International Conference on Artificial Neural Networks
3-6 September 2008, Diplomat Hotel, Prague, Czech Republic
Zdeněk Buk, bukz1@fel.cvut.cz, http://cig.felk.cvut.cz
Crossover and mutation
Individual 1
p1
s1
b1
p2
s2
b2
Offspring
Individual 2
18th International Conference on Artificial Neural Networks
3-6 September 2008, Diplomat Hotel, Prague, Czech Republic
Zdeněk Buk, bukz1@fel.cvut.cz, http://cig.felk.cvut.cz
Crossover and mutation
Individual 1
p1
s1
b1
p2
s2
b2
Offspring
Individual 2
Random mutation
18th International Conference on Artificial Neural Networks
3-6 September 2008, Diplomat Hotel, Prague, Czech Republic
Zdeněk Buk, bukz1@fel.cvut.cz, http://cig.felk.cvut.cz
Crossover and mutation
Individual 1
p1
s1
b1
p2
s2
b2
Offspring
Copy
Individual 2
18th International Conference on Artificial Neural Networks
3-6 September 2008, Diplomat Hotel, Prague, Czech Republic
Zdeněk Buk, bukz1@fel.cvut.cz, http://cig.felk.cvut.cz
Crossover and mutation
Individual 1
p1
s1
b1
p2
s2
b2
Offspring
pi
si
bi
Individual 2
18th International Conference on Artificial Neural Networks
3-6 September 2008, Diplomat Hotel, Prague, Czech Republic
Zdeněk Buk, bukz1@fel.cvut.cz, http://cig.felk.cvut.cz
Time dimension
●
Training the behavioral vector during time
using gradient algorithm.
Age=0
pi
si
bi
Time
18th International Conference on Artificial Neural Networks
3-6 September 2008, Diplomat Hotel, Prague, Czech Republic
Zdeněk Buk, bukz1@fel.cvut.cz, http://cig.felk.cvut.cz
Time dimension
●
Training the behavioral vector during time
using gradient algorithm.
Age=0
Age=1
pi
si
bi
Time
18th International Conference on Artificial Neural Networks
3-6 September 2008, Diplomat Hotel, Prague, Czech Republic
Zdeněk Buk, bukz1@fel.cvut.cz, http://cig.felk.cvut.cz
Time dimension
●
Training the behavioral vector during time
using gradient algorithm.
Age=0
Age=1
Age=2
pi
si
bi
Time
18th International Conference on Artificial Neural Networks
3-6 September 2008, Diplomat Hotel, Prague, Czech Republic
Zdeněk Buk, bukz1@fel.cvut.cz, http://cig.felk.cvut.cz
Probability control
●
Probability functions
●
RP – reproduction probability,
●
DP – death probability, elimination of bad solutions
in population.
●
Balancing functions
●
to keep the population size in some reasonable
limits.
18th International Conference on Artificial Neural Networks
3-6 September 2008, Diplomat Hotel, Prague, Czech Republic
Zdeněk Buk, bukz1@fel.cvut.cz, http://cig.felk.cvut.cz
Reproduction probability
●
Raw reproduction probability function
*
*
RP  xi = RP a i , F  xi 
Fitness
RP*
Age
Fitness
Age
18th International Conference on Artificial Neural Networks
3-6 September 2008, Diplomat Hotel, Prague, Czech Republic
Zdeněk Buk, bukz1@fel.cvut.cz, http://cig.felk.cvut.cz
Death probability
●
Raw death probability function
*
*
DP  xi = DP a i , F  xi 
Fitness
DP*
Age
Fitness
Age
18th International Conference on Artificial Neural Networks
3-6 September 2008, Diplomat Hotel, Prague, Czech Republic
Zdeněk Buk, bukz1@fel.cvut.cz, http://cig.felk.cvut.cz
Balancing functions
●
Computation of final probabilities.
●
Depend on raw probabilities and population size.
●
Big population grows slower,
●
small population grows faster.
*
RP  xi = BAL RP  N , RP  xi 
*
DP  xi = BAL DP  N , DP  xi 
18th International Conference on Artificial Neural Networks
3-6 September 2008, Diplomat Hotel, Prague, Czech Republic
Zdeněk Buk, bukz1@fel.cvut.cz, http://cig.felk.cvut.cz
Evolution control
18th International Conference on Artificial Neural Networks
3-6 September 2008, Diplomat Hotel, Prague, Czech Republic
Zdeněk Buk, bukz1@fel.cvut.cz, http://cig.felk.cvut.cz
Evolution control
18th International Conference on Artificial Neural Networks
3-6 September 2008, Diplomat Hotel, Prague, Czech Republic
Zdeněk Buk, bukz1@fel.cvut.cz, http://cig.felk.cvut.cz
Evolution control
18th International Conference on Artificial Neural Networks
3-6 September 2008, Diplomat Hotel, Prague, Czech Republic
Zdeněk Buk, bukz1@fel.cvut.cz, http://cig.felk.cvut.cz
Evolution control
18th International Conference on Artificial Neural Networks
3-6 September 2008, Diplomat Hotel, Prague, Czech Republic
Zdeněk Buk, bukz1@fel.cvut.cz, http://cig.felk.cvut.cz
Evolution control
18th International Conference on Artificial Neural Networks
3-6 September 2008, Diplomat Hotel, Prague, Czech Republic
Zdeněk Buk, bukz1@fel.cvut.cz, http://cig.felk.cvut.cz
Evolution control
18th International Conference on Artificial Neural Networks
3-6 September 2008, Diplomat Hotel, Prague, Czech Republic
Zdeněk Buk, bukz1@fel.cvut.cz, http://cig.felk.cvut.cz
Evolution control
18th International Conference on Artificial Neural Networks
3-6 September 2008, Diplomat Hotel, Prague, Czech Republic
Zdeněk Buk, bukz1@fel.cvut.cz, http://cig.felk.cvut.cz
Testing, experiments
●
●
●
●
Construction of the neural networks.
Universal topology based on fully recurrent
network.
Structure
–
topology → adjacency matrix
–
activation functions → parametrized Λ-functions
Behavior
–
weight matrix
18th International Conference on Artificial Neural Networks
3-6 September 2008, Diplomat Hotel, Prague, Czech Republic
Zdeněk Buk, bukz1@fel.cvut.cz, http://cig.felk.cvut.cz
Testing, experiments
●
●
Neural networks based on fully recurrent
topology construction using CEA
Activation function optimization
18th International Conference on Artificial Neural Networks
3-6 September 2008, Diplomat Hotel, Prague, Czech Republic
Zdeněk Buk, bukz1@fel.cvut.cz, http://cig.felk.cvut.cz
Testing, experiments
●
Benchmark tasks
●
Learn to oscillate experiment
18th International Conference on Artificial Neural Networks
3-6 September 2008, Diplomat Hotel, Prague, Czech Republic
Zdeněk Buk, bukz1@fel.cvut.cz, http://cig.felk.cvut.cz
Population behavior
18th International Conference on Artificial Neural Networks
3-6 September 2008, Diplomat Hotel, Prague, Czech Republic
Zdeněk Buk, bukz1@fel.cvut.cz, http://cig.felk.cvut.cz
Population behavior
18th International Conference on Artificial Neural Networks
3-6 September 2008, Diplomat Hotel, Prague, Czech Republic
Zdeněk Buk, bukz1@fel.cvut.cz, http://cig.felk.cvut.cz
Fitness
Population behavior
Iterations
18th International Conference on Artificial Neural Networks
3-6 September 2008, Diplomat Hotel, Prague, Czech Republic
Zdeněk Buk, bukz1@fel.cvut.cz, http://cig.felk.cvut.cz
Conclusion
●
●
Reduction of the number of fitness function
evaluations.
Using the probability and balancing functions it
is possible to change the CEA to behave more
–
–
–
like random search,
standard genetic algorithm,
or gradient algorithm.
18th International Conference on Artificial Neural Networks
3-6 September 2008, Diplomat Hotel, Prague, Czech Republic
Zdeněk Buk, bukz1@fel.cvut.cz, http://cig.felk.cvut.cz
Conclusion
●
CEA → universal optimization algorithm
●
mainly for problems with separate description
–
of structure
–
and behavior
→ typically neural networks.
●
Automatic control of the size of the population
–
exploitation ↔ exploration
18th International Conference on Artificial Neural Networks
3-6 September 2008, Diplomat Hotel, Prague, Czech Republic
Zdeněk Buk, bukz1@fel.cvut.cz, http://cig.felk.cvut.cz

Similar documents