Automated Problem Decomposition for the Boolean Domain with Genetic Programming

Researchers have been interested in exploring the regularities and modularity of the problem space in genetic programming (GP) with the aim of decomposing the original problem into several smaller subproblems. The main motivation is to allow GP to deal with more complex problems. Most previous works on modularity in GP emphasise the structure of modules used to encapsulate code and/or promote code reuse, instead of in the decomposition of the original problem. In this paper we propose a problem decomposition strategy that allows the use of a GP search to find solutions for subproblems and combine the individual solutions into the complete solution to the problem

Sequential Symbolic Regression with Genetic Programming

This chapter describes the Sequential Symbolic Regression (SSR) method, a new strategy for function approximation in symbolic regression. The SSR method is inspired by the sequential covering strategy from machine learning, but instead of sequentially reducing the size of the problem being solved, it sequentially transforms the original problem into potentially simpler problems. This transformation is performed according to the semantic distances between the desired and obtained outputs and a geometric semantic operator. The rationale behind SSR is that, after generating a suboptimal function f via symbolic regression, the output errors can be approximated by another function in a subsequent iteration. The method was tested in eight polynomial functions, and compared with canonical genetic programming (GP) and geometric semantic genetic programming (SGP). Results showed that SSR significantly outperforms SGP and presents no statistical difference to GP. More importantly, they show the potential of the proposed strategy: an effective way of applying geometric semantic operators to combine different (partial) solutions, avoiding the exponential growth problem arising from the use of these operators

Complementary Layered Learning

Layered learning is a machine learning paradigm used to develop autonomous robotic-based agents by decomposing a complex task into simpler subtasks and learns each sequentially. Although the paradigm continues to have success in multiple domains, performance can be unexpectedly unsatisfactory. Using Boolean-logic problems and autonomous agent navigation, we show poor performance is due to the learner forgetting how to perform earlier learned subtasks too quickly (favoring plasticity) or having difficulty learning new things (favoring stability). We demonstrate that this imbalance can hinder learning so that task performance is no better than that of a suboptimal learning technique, monolithic learning, which does not use decomposition. Through the resulting analyses, we have identified factors that can lead to imbalance and their negative effects, providing a deeper understanding of stability and plasticity in decomposition-based approaches, such as layered learning. To combat the negative effects of the imbalance, a complementary learning system is applied to layered learning. The new technique augments the original learning approach with dual storage region policies to preserve useful information from being removed from an agent’s policy prematurely. Through multi-agent experiments, a 28% task performance increase is obtained with the proposed augmentations over the original technique

Scalable genetic programming by gene-pool optimal mixing and input-space entropy-based building-block learning

The Gene-pool Optimal Mixing Evolutionary Algorithm (GOMEA) is a recently introduced model-based EA that has been shown to be capable of outperforming state-of-the-art alternative EAs in terms of scalability when solving discrete optimization problems. One of the key aspects of GOMEA's success is a variation operator that is designed to extensively exploit linkage models by effectively combining partial solutions. Here, we bring the strengths of GOMEA to Genetic Programming (GP), introducing GP-GOMEA. Under the hypothesis of having little problem-specific knowledge, and in an effort to design easy-to-use EAs, GP-GOMEA requires no parameter specification. On a set of well-known benchmark problems we find that GP-GOMEA outperforms standard GP while being on par with more recently introduced, state-of-the-art EAs. We furthermore introduce Input-space Entropy-based Building-block Learning (IEBL), a novel approach to identifying and encapsulating relevant building blocks (subroutines) into new terminals and functions. On problems with an inherent degree of modularity, IEBL can contribute to compact solution representations, providing a large potential for knock-on effects in performance. On the difficult, but highly modular Even Parity problem, GP-GOMEA+IEBL obtains excellent scalability, solving the 14-bit instance in less than 1 hour

Improving the Scalability of XCS-Based Learning Classifier Systems

Using evolutionary intelligence and machine learning techniques, a broad range of intelligent machines have been designed to perform different tasks. An intelligent machine learns by perceiving its environmental status and taking an action that maximizes its chances of success. Human beings have the ability to apply knowledge learned from a smaller problem to more complex, large-scale problems of the same or a related domain, but currently the vast majority of evolutionary machine learning techniques lack this ability. This lack of ability to apply the already learned knowledge of a domain results in consuming more than the necessary resources and time to solve complex, large-scale problems of the domain. As the problem increases in size, it becomes difficult and even sometimes impractical (if not impossible) to solve due to the needed resources and time. Therefore, in order to scale in a problem domain, a systemis needed that has the ability to reuse the learned knowledge of the domain and/or encapsulate the underlying patterns in the domain. To extract and reuse building blocks of knowledge or to encapsulate the underlying patterns in a problem domain, a rich encoding is needed, but the search space could then expand undesirably and cause bloat, e.g. as in some forms of genetic programming (GP). Learning classifier systems (LCSs) are a well-structured evolutionary computation based learning technique that have pressures to implicitly avoid bloat, such as fitness sharing through niche based reproduction. The proposed thesis is that an LCS can scale to complex problems in a domain by reusing the learnt knowledge from simpler problems of the domain and/or encapsulating the underlying patterns in the domain. Wilson’s XCS is used to implement and test the proposed systems, which is a well-tested, online learning and accuracy based LCS model. To extract the reusable building blocks of knowledge, GP-tree like, code-fragments are introduced, which are more than simply another representation (e.g. ternary or real-valued alphabets). This thesis is extended to capture the underlying patterns in a problemusing a cyclic representation. Hard problems are experimented to test the newly developed scalable systems and compare them with benchmark techniques. Specifically, this work develops four systems to improve the scalability of XCS-based classifier systems. (1) Building blocks of knowledge are extracted fromsmaller problems of a Boolean domain and reused in learning more complex, large-scale problems in the domain, for the first time. By utilizing the learnt knowledge from small-scale problems, the developed XCSCFC (i.e. XCS with Code-Fragment Conditions) system readily solves problems of a scale that existing LCS and GP approaches cannot, e.g. the 135-bitMUX problem. (2) The introduction of the code fragments in classifier actions in XCSCFA (i.e. XCS with Code-Fragment Actions) enables the rich representation of GP, which when couples with the divide and conquer approach of LCS, to successfully solve various complex, overlapping and niche imbalance Boolean problems that are difficult to solve using numeric action based XCS. (3) The underlying patterns in a problem domain are encapsulated in classifier rules encoded by a cyclic representation. The developed XCSSMA system produces general solutions of any scale n for a number of important Boolean problems, for the first time in the field of LCS, e.g. parity problems. (4) Optimal solutions for various real-valued problems are evolved by extending the existing real-valued XCSR system with code-fragment actions to XCSRCFA. Exploiting the combined power of GP and LCS techniques, XCSRCFA successfully learns various continuous action and function approximation problems that are difficult to learn using the base techniques. This research work has shown that LCSs can scale to complex, largescale problems through reusing learnt knowledge. The messy nature, disassociation of message to condition order, masking, feature construction, and reuse of extracted knowledge add additional abilities to the XCS family of LCSs. The ability to use rich encoding in antecedent GP-like codefragments or consequent cyclic representation leads to the evolution of accurate, maximally general and compact solutions in learning various complex Boolean as well as real-valued problems. Effectively exploiting the combined power of GP and LCS techniques, various continuous action and function approximation problems are solved in a simple and straight forward manner. The analysis of the evolved rules reveals, for the first time in XCS, that no matter how specific or general the initial classifiers are, all the optimal classifiers are converged through the mechanism ‘be specific then generalize’ near the final stages of evolution. Also that standard XCS does not use all available information or all available genetic operators to evolve optimal rules, whereas the developed code-fragment action based systems effectively use figure and ground information during the training process. Thiswork has created a platformto explore the reuse of learnt functionality, not just terminal knowledge as present, which is needed to replicate human capabilities

Bootstrap Learning Via Modular Concept Discovery

Suppose a learner is faced with a domain of problems about which it knows nearly nothing. It does not know the distribution of problems, the space of solutions is not smooth, and the reward signal is uninformative, providing perhaps a few bits of information but not enough to steer the learner effectively. How can such a learner ever get off the ground? A common intuition is that if the solutions to these problems share a common structure, and the learner can solve some simple problems by brute force, it should be able to extract useful components from these solutions and, by composing them, explore the solution space more efficiently. Here, we formalize this intuition, where the solution space is that of typed functional programs and the gained information is stored as a stochastic grammar over programs. We propose an iterative procedure for exploring such spaces: in the first step of each iteration, the learner explores a finite subset of the domain, guided by a stochastic grammar; in the second step, the learner compresses the successful solutions from the first step to estimate a new stochastic grammar. We test this procedure on symbolic regression and Boolean circuit learning and show that the learner discovers modular concepts for these domains. Whereas the learner is able to solve almost none of the posed problems in the procedure’s first iteration, it rapidly becomes able to solve a large number by gaining abstract knowledge of the structure of the solution space.Engineering and Applied Science