Investigating Scaling of an Abstracted LCS Utilising Ternary and SExpression Alphabets

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Investigating Scaling of an Abstracted LCS
Utilising Ternary and S-Expression Alphabets

• Charalambos Ioannides Will Browne
• Cybernetics, University of Reading, UK
• siu03ci_at_rdg.ac.uk w.n.browne_at_reading.ac.uk

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Introduction

• The multiplexer problem is a common testbed for
  machine learning
• although LCS variants perform well, scaling is
  an issue
• Human beings understand the concept behind the
  multiplexer problem rather than individual
  problem instances
• Standard alphabets enable LCS to remove
  irrelevant details through generalisation
• It is hypothesised that more powerful alphabets
  could enable the abstraction of concepts.

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Motivation

• How can we use the solutions to simple problems
  to build solutions to more complex problems?
• How can we arrive at a system that solves entire
  problem spaces using few or a single classifier?
• What is involved in Machine Learning especially
  when trying to identify Abstracted Solutions to
  fully or partially discovered/solved problem
  spaces?
• How does the problem representation dictate the
  problem solution?

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Aims

• Provide solution to the Multiplexer problem by
  the use of an LCS related Abstraction Algorithm
• Investigate the usefulness of alternative
  Classifier Representations
• Provide a unified method by which LCS solve the
  MUX problems regardless of complexity

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Benefits

• To provide a mechanism that represents knowledge
  in a more human readable form
• Identify whether the LCS framework performs
  better when using alternative representation
  schemes
• Provide a compact rule-base that extracts the
  most essential (abstract) information from the
  environment

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Abstraction

• Definition of Abstraction
• The act or process of separating in thought, of
  considering a thing independently of its
  associations
• Insulate relevant characteristics from
  overwhelming detail. Drew Endy
• Achieved partly through expressively superior
  languages (alphabets)

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Abstraction
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Methodology

• Created the classical XCS framework
• Implemented a system for binary S-Expression
  representation (S_XCS)
• Developed a system using 10 diverse S-Expression
  functions (S_XCS1)
• Used Optimal Population Simulation to arrive at
  better populations faster.

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Alphabets the XCS system

• XCS shifts the main classifier metric from
  strength based to accuracy based
• XCS exhibits a powerful on-line learning
  algorithm, but struggles beyond 70-MUX
• Can use many alphabets, e.g. the Ternary Alphabet
  uses 0,1, symbols
• may be considered as a positional OR relation
• S-Expressions tested,
• but ongoing work, e.g. deletion strategy
• XCSF utilises computed predictions for
  approximating functions.

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Alternative Representations

• Messy Representation
• Integer Continuous Representation
• S-Expression Representation
• Neural Fuzzy Logic Representation
• First Order Logic Grammatical Evolution
  Approaches

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The Multiplexer Problem

• Properties
• Multimodality
• Scalability
• Epistasis

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Experimental Approach
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Contrasting the Algorithms
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Experimental Design

• Use S_XCS to assess how Binary Functions can cope
  with problem complexity
• Use S_XCS1 to determine differences with previous
  approach and assess the effect of relatively
  large diverse Function Set
• Use Optimal Population Simulation to measure its
  effect towards solution discovery

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Experimental Design

• The same, standard for the XCS literature
  initialisation parameters used throughout the
  project (i.e. N400, a0.1, ß0.2, ?0.71, e0.5,
  e010, ?5 etc.)
• For the calculation of Fitness (F) the Absolute
  Accuracy (?) is used rather than the Relative
  Accuracy (?)
• The GenerateCoveringClassifier() function is
  called when overall population fitness is below a
  threshold (i.e. FTotallt0.5)
• Numerosity ceases to play a dominant role
• There is no Subsumption Deletion

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Alphabet Symbols
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PROGRAM
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PROGRAM
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What do Classifiers look like
S_XCS1 without O.P.S.
S_XCS on 3-MUX
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Results-1
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Results-2
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Results-3
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Results-4
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Results-5
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Results-6
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Results-7
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Discussion

• Classical GP approach tends to use predefined
  training and evaluation sets
• S_XCS approach uses XCS framework, e.g. where
  consistency is emphasised over reward
• LCS provides layered learning for abstraction
• Can utilise co-operation of classifiers
• The expressiveness of S-Expressions can be used
  to make Classifiers more readable, compact and
  more capable in solving larger complexity problems

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Conclusions

• Limiting number of Variables is more effective
  than Limiting Functions
• S_XCS can select appropriate functions for a
  specific problem from a group of potential
  functions
• Problem Complexity requires potent functions to
  negate its effects
• There is a shift from Problem Complexity towards
  Functional Complexity

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Thank you for listening

• A N Y Q U E S T I O N S ?

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Different Approach - 1

• Traditional XCS
• Classifiers made up of strings of bits
• Static representation of Conditions and Actions
• Another form of Q-Learning

• Symbolic XCS
• Classifiers made up of functions and variables as
  tree structure
• Dynamic representation of Conditions and Actions
• Shift from Environmental Complexity to
  Represen-tational Complexity

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Methodology

• Identify potency of Ternary Alphabet
• Identify key strong points of the XCS learning
  paradigm
• Summarise on how Abstraction could be achieved
• Evaluate alternative representations and pick the
  best
• Identify potency of S-Expressions