Learning Classifier Systems

1
Learning Classifier Systems

• Navigating the fitness landscape?
• Why use evolutionary computation?
• Whats the concept of LCS?
• Early pioneers
• Competitive vs Grouped Classifiers
• Beware the Swampy bits!
• Niching
• Selection for mating and effecting
• Balance exploration with exploitation.
• Balance the pressures
• Zeroth level classifier system
• The X-factor
• Alphabet soup
• New Slants - piecewise linear approximators
• Why don't LCS rule the world?
• Simplification schemes
• Cognitive Classifiers
• Neuroscience Inspirations
• Application Domains

2
Non-piecewise Approximators

• Standard difficulties/restrictions
• Standard lcs use hyperrectangles to classify
  (divide up the input landscape into actions)
• Oblique data and function approximation cause lcs
  difficulty
• (the most appropriate kernel may not be a
  rectangle)
• The action is fixed for each condition range
• (every time classifier matches it has the same
  action)
• The prediction is eventually stable for each
  classifier
• (every time a trained classifier matches it has
  the same action)

3
Approximators

• Standard difficulties/restrictions
• The complete and accurate map philosophy of XCS
  means that actions are finite and discrete
• X x ai ? P
• A function from input vectors to scalar payoffs
  so the system approximates a separate function
  for each action
• Problem when action is continuous!
• e.g. Stock market prediction or control of robots
• Standard representations dont function in this
  manner
• ( note fuzzy logic alphabets can produce
  continuous actions, maybe also NNs)

4
XCSF

• Real valued encoding
• Concatenation of interval predicates
• Two-point Crossover crossover point can be
• between predicates
• within an interval predicates
• Mutation
• addition of an amount rand(m0)
• returns value from (0, m0 for lower bound
• Bounded random amount proved better than fixed
  amount
• Repair used as normal
• Covering lower bound
• Returns value from 0, r0

5
Piecewise CONSTANT Approximators

• Very simple approximators
• Need to approximate the function
• y f(x)
• Let x be the input and y be the payoff
• The closeness of the approximation should be
  controllable with the error threshold e0
• When e1 lt e2 evolutionary pressure forces weaker
  classifier out of population
• No pressure between classifiers with e lt e0
• Efficient distribution of classifiers in a tiling
• Need to minimise overlap as prediction sums
• Wilson, S. W., " Classifiers that approximate
  functions"
• Natural Computing, 1(2-3), 211-234 (2002).

6
Piecewise CONSTANT Approximators

• 0 to 99 in 20 steps 0 if whole step, o if part

7
Piecewise-Linear Approximators

• Linear approximators
• The action is flexible for each condition range
• (every time classifier matches it has the same
  action)
• Need to approximate the function
• y f(x)
• With h(x)
• Prediction is linear polynomial of the input
  components
• Initially approximate a 1-D function
• w1 slope of a straight line
• w0 with its intercept
• Hyperplane approximation to f(x)

8
Piecewise-Linear Approximators

• Linear approximators
• Could adapt weights through evaluation
• (weights concatenated with interval predicates)
• Much simpler to use gradient technique
• t is target, o is output
• Actual - Prediction
• Correction rate usually set to 0.4

9
Piecewise-Linear Approximators

• Correction rate usually set to 0.4

10
Piecewise-Linear Approximators

• Change error threshold, Changes accuracy

e0 10
11
Piecewise-Linear Approximators

• Linear approximators
• Can be multidimensional
• Can restrict actions to aid approximations
• Thus produce generalized classifier
• Exploit
• Explore
• a for each classifier in M
• Special cases
• 101 , P ? 1000a

12
Gene Expressions

• Gene Expression Programming (GEP)
• GEP C. Ferreira 2001
• Similar to GP S-Expressions
• Phenotype is tree of functions terminals
• Differs in
• Translation stage
• Linear chromosome
• Transparency
• Head and possible useless tail
• All chromosomes valid so RD simplified
• Restricted length to control bloat
• Wilson, S.W., " Classifier conditions using gene
  expression programming"
• Technical Report No. 2008001, Illinois Genetic
  Algorithms Laboratory,
• University of Illinois at Urbana-Champaign,
  January, 2008.

13
Gene Expressions

• Gene Expression Programming (GEP)
• -eab/cdbbaddc
• Karva encoding
• Prefix encoding

14
Gene Expressions

• Can solve complex problems, but
• Slow
• Non-compact populations as no subsumption
• Many different, but correct classifiers