XCSF with Local Deletion: Preventing Detrimental Forgetting

Cognitive Bodyspaces: Learning and Behavior

Department of Psychology (III)Cognitive Psychology

XCSF with Local Deletion:Preventing Detrimental Forgetting

Martin V. ButzDepartment of Psychology III

University of WürzburgRöntgenring 11, 97070 Würzburg,

[email protected]

Olivier SigaudInstitut des Systèmes Intelligents et de Robotique, Université Pierre et Marie Curie Paris 6. CNRS UMR 7222, 4 place

Jussieu, F-75005 Paris, [email protected]

mailto:[email protected]



13. 7. 2011 XCSF with Local Deletion Martin V. Butz & Olivier Sigaud

Motivation

Achieve the following goals:– Maintain a complete solution– Avoid detrimental forgetting– Enable continuous learning with selective focus

… particularly in problems where: – the problem space is non-uniformly or non-independently

sampled (not iid).– the sub-space is not fully sampled (learning in manifolds).– some problem subspaces need to be known (smaller error)

better than others (selective learning).


Observation

• XCSF reproduces locally but deletes globally.

• This is good, because we generate a generalization pressure (local classifiers are on average more general).

• This is bad, however, because non-uniformly sampled problems can lead to forgetting.

• Thus, how can we– delete locally and still– generate the

generalization pressure?

specificity

0 1accurate, maximally general

0

1

set pressure

mutation pressure

subsumption pressure


Approach:Choose local candidates for deletion without dependency on their generality.

Algorithm1. Select random classifier cl from [M].2. [D] = 3. for all c 2 [P] do4. if cl does match center of c

then5. add c to candidate list

[D]6. end if7. end for8. DELETE FROM CANDIDATE LIST [D]


The Two Evaluation Functions

Crossed-Ridge Function Diagonal Sine Function


Evaluation with Different Sampling Types

• Normal: Uniform Sampling1. Random walk sampling:

– Next sample is located in radial vicinity of previous one

2. Random walk sampling in ring (area of distance .3 to .4 of center)

3. Centered, Gaussian sampling 4. Ring-based Gaussian sampling

Parameter Settings: N = 4000, ²0 = 0.002


Crossed RidgeUniform Sampling


Crossed-Ridge ComparisonBefore Condensation

Normal XCSF XCSF with Local Deletion


Crossed-Ridge ComparisonAfter Condensation



Crossed RidgeRandom Walk Sampling


Crossed RidgeRing-based Gaussian Sampling


Sine FunctionUniform Sampling


Diagonal Sine FunctionBefore Condensation



Diagonal Sine FunctionAfter Condensation



Sine FunctionRandom Walk Sampling


Sine FunctionRandom Walk Sampling in Ring


Sine FunctionGaussian Sampling


Sine FunctionRing-based Gaussian Sampling


Summary & Conclusions

• Local deletion does not negatively affect performance.

• During condensation, local deletion can assure a better problem solution sustenance.

• Some of the results also indicate better structural development during learning.

• These results have been confirmed in various other settings.

• No apparent drawback to apply local deletion (constant overhead computationally)

• Use this mechanism also in other condition settings!

• Use it also to selectively learn higher accurate and lower accurate approximations in different problem subspaces!

Education

XCSF with Local Deletion: Preventing Detrimental Forgetting