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Automatic Problem Decomposition using Co-evolution and Ensembles

Vineet Khare http://www.cs.bham.ac.uk/~vrk [email protected]

Overview 1.

Automatic Problem Decomposition

2.

Issues involved

3.

Why Co-evolution and Network Ensembles?

4.

Literature review

5.

Discussion

Automatic Problem Decomposition ●

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Problem Decomposition – Types –

Functional

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Categorical

Automatic Problem Decomposition

Issues Involved •

Problem Decomposition

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Interdependencies between subcomponents

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Credit Assignment

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Maintenance of diversity

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Adding subcomponents

Why Co-evolution and Ensembles? •

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Co-evolution – evolving individuals for different roles in a common task. Ensembles •

Modular Structure easy to understand

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Can embed apriori knowledge

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Improved generalization and learning speed.

Literature Review •

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Different techniques using co-evolution and/or NN ensembles Functional/categorical decomposition Try to discover structure of knowledge represented by training patterns.

Potter Potterand andDe DeJong, Jong,2000 2000

Evolving coadapted subcomponents •

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Evolving solutions in form of interacting coadapted subcomponents subcomponents - collection of co-operating species Emergence of appropriate number of interdependent species and their roles.

Potter Potterand andDe DeJong, Jong,2000 2000

Evolving coadapted subcomponents •

Number of species f(t) - f(t-L) < G

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rewards based on collaboration

Moriarty Moriartyand andMiikkulainen, Miikkulainen,1997 1997

Symbiotic Adaptive Neuro-evolution (SANE) ●

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Each neuron tends to converge to different but overlapping role Co-operative co-evolution –

Rewards depends on how well they collaborate. Number of species

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Search not focussed on single dominant indiv.

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Network blueprint population

Yong Yongand andMiikkulainen, Miikkulainen,2000 2000

Co-op. Co-evolution of multi-agent Systems ●

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Team of several predators cooperate to capture a fast moving prey. Entire space of solutions divided into a set of simpler subtasks (one agent per subtask). Team of NNs evolved using GA to solve a cooperative task

Yong Yongand andMiikkulainen, Miikkulainen,2000 2000

Co-op. Co-evolution of multi-agent Systems ● ●

Multi-agent ESP approach ESP separate population for each hidden layer neuron

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Autonomous co-operating controllers approach

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Incremental Learning

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Number of agents fixed – at least 2

Darwen Darwenand andYao, Yao,1996 1996

Automatic Modularization by Speciation ●

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Speciated population as a complete modular system GA with implicit fitness sharing to evolve high quality strategies for IPD Gating Algorithm

Khare Khareand andYao, Yao,2001 2001

Speciated ANNs ●

EANN system with fitness sharing

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Combination of outputs

Jaksa, Jaksa,2002 2002

Automatic Modularization of ANNs ●

Structure optimization during learning modular structured defined optimal

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Also learns the structure of knowledge

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Soft module

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Multi-objective nature

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Fixed number of modules

Jacobs Jacobset. et.al., al.,1991 1991

Task Decomposition through Competition ●

Networks compete to learn training patterns

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Decomposition = partition + allocation

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Gating network determining the proportion of each output - linear combination E = || d - ∑i pioi ||

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What and where vision tasks

Jacobs Jacobset. et.al., al.,1991 1991

Adaptive Mixture of Local Experts ●

Strong coupling between experts => Many experts for one case E = < || d - ∑i pioi ||2 > = ∑i || d - oi ||2

References Mitchell A. Potter & Kenneth A. De Jong, “Cooperative Coevolution: An Architecture for Evolving Coadapted Subcomponents,” Evolutionary Computation 8(1): 1-29, 2000. Moriarty, D. E., & Miikkulainen, R., “Forming neural networks through efficient and adaptive co-evolution.” Evolutionary Computation, 5 (4), 373--399, 1998. Chern Han Yong and Risto Miikkulainen, “Cooperative Coevolution of Multi-Agent Systems”. Technical Report AI01-287, Department of Computer Sciences, University of Texas at Austin, 2001. P. Darwen and X. Yao (1996a), ``Automatic modularisation by speciation,'' Proc. of the Third IEEE International Conference on Evolutionary Computation (ICEC'96), Nagoya, Japan, 20-22 May 1996, pp.88-93. V. Khare and X. Yao, ``Artificial speciation and automatic modularisation,'' Proc. of the 4th Asia-Pacific Conference on Simulated Evolution And Learning (SEAL'02), pp.56-60, Singapore, November 2002. Rudolf Jaksa, “Automatic Modularization of ANNs Using Adaptive Critic Method,” the Third WESEAS Conference on Neural networks and Applications (NNA’02), 2002. Jacobs, R.A., Jordan, M.I., and Barto, A.G. (1991) Task decomposition through competition in a modular connectionist architecture: The what and where vision tasks. Cognitive Science, 15, 219-250. Jacobs, R.A., Jordan, M.I., Nowlan, S.J., and Hinton, G.E. (1991) Adaptive mixtures of local experts. Neural Computation, 3, 79-87.