[Paper Review] A Layered Learning Approach to Scaling in Learning Classifier Systems for Boolean Problems

Isidro M. Alvarez, Trung B. Nguyen+2 more|arXiv (Cornell University)|Jun 2, 2020

Evolutionary Algorithms and Applications28 references4 citations

TL;DR

This paper proposes an enhanced layered learning approach, XCSCF*, that enables Learning Classifier Systems to scale across multiple Boolean problem domains by reusing learned code fragments (CFs) and functional building blocks through transfer learning. By decomposing complex problems into hierarchical sub-problems and embedding type-safe, general-purpose functions, the system learns compact, interpretable solutions for n-bit Multiplexer, Carry-one, Majority-on, and Even-parity problems without task-specific hardcoding.

ABSTRACT

Learning classifier systems (LCSs) originated from cognitive-science research but migrated such that LCS became powerful classification techniques. Modern LCSs can be used to extract building blocks of knowledge to solve more difficult problems in the same or a related domain. Recent works on LCSs showed that the knowledge reuse through the adoption of Code Fragments, GP-like tree-based programs, into LCSs could provide advances in scaling. However, since solving hard problems often requires constructing high-level building blocks, which also results in an intractable search space, a limit of scaling will eventually be reached. Inspired by human problem-solving abilities, XCSCF* can reuse learned knowledge and learned functionality to scale to complex problems by transferring them from simpler problems using layered learning. However, this method was unrefined and suited to only the Multiplexer problem domain. In this paper, we propose improvements to XCSCF* to enable it to be robust across multiple problem domains. This is demonstrated on the benchmarks Multiplexer, Carry-one, Majority-on, and Even-parity domains. The required base axioms necessary for learning are proposed, methods for transfer learning in LCSs developed and learning recast as a decomposition into a series of subordinate problems. Results show that from a conventional tabula rasa, with only a vague notion of what subordinate problems might be relevant, it is possible to capture the general logic behind the tested domains, so the advanced system is capable of solving any individual n-bit Multiplexer, n-bit Carry-one, n-bit Majority-on, or n-bit Even-parity problem.

Motivation & Objective

• To address the scalability limit of existing Learning Classifier Systems (LCS) when solving large-scale Boolean problems.
• To extend the XCSCF* framework beyond the Multiplexer domain to support multiple heterogeneous Boolean problem domains.
• To enable transfer learning of functional building blocks (code fragments) across sub-problems to reduce search space and improve solution compactness.
• To develop a general, extensible framework that supports variable-scale problem solving without hardcoding problem size.
• To enhance interpretability by structuring solutions through intermediate, reusable functional components.

Proposed method

• Decomposing complex Boolean problems into a hierarchy of progressively more complex sub-problems to enable layered learning.
• Introducing a generalized input mechanism using an attribute list (attlst) to replace fixed-size constants, enabling variable-scale problem solving.
• Embedding type-fitting constraints to ensure compatibility between functions and code fragments, reducing invalid search space.
• Using a set of base axioms and domain-agnostic functions (e.g., StringSum, HeadList, TailList) to provide foundational building blocks for problem decomposition.
• Applying transfer learning by reusing learned code fragments (CFs) from simpler sub-problems to solve more complex target problems.
• Recasting learning as a process of building logical chains of functionality, analogous to threshold concepts in human learning.

Experimental results

Research questions

• RQ1 Can a layered learning approach in LCSs enable robust scaling across multiple distinct Boolean problem domains?
• RQ2 How can functional building blocks be reused across sub-problems to reduce search space and improve solution compactness?
• RQ3 To what extent can a system learn general, interpretable solutions without task-specific hardcoding or prior problem size constraints?
• RQ4 Can the integration of type-safe, general-purpose functions enable scalable and extensible problem solving in LCSs?
• RQ5 How does the use of transfer learning and functional composition compare to conventional tabula rasa learning in terms of solution quality and interpretability?

Key findings

• XCSCF* successfully solved n-bit versions of the Multiplexer, Carry-one, Majority-on, and Even-parity problems using only a minimal set of general-purpose functions and base axioms.
• The system achieved minimal and interpretable solutions, often requiring just one general rule per problem domain, even for large-scale problems.
• The use of an explicit attribute list (attlst) enabled variable-scale problem solving, removing the need for hardcoding problem size.
• The system demonstrated that learned code fragments and functional building blocks could be effectively transferred across sub-problems, significantly reducing the search space.
• Solutions were compact and interpretable when abstracted, though fully expanded CF trees revealed complex nested patterns, indicating effective functional composition.
• The framework supports future extension to continuous and real-valued datasets through a modular, curricula-based learning architecture.