Improving the Scalability of XCS-Based Learning Classifier Systems

<p>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.</p>

Improving the Scalability of XCS-Based Learning Classifier Systems

<p>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.</p>

Generalized cyclic contractions and coincidence points involving a control function on partial metric spaces

PurposeIn this paper, we use the notion of cyclic representation of a nonempty set with respect to a pair of mappings to obtain coincidence points and common fixed points for a pair of self-mappings satisfying some generalized contraction- type conditions involving a control function in partial metric spaces. Moreover, we provide some examples to analyze and illustrate our main results.Design/methodology/approachTheoretical method.FindingsWe establish some coincidence points and common fixed point results in partial metric spaces.Originality/valueResults of this study are new and interesting.

The Optimal Control of Two Work-Stealing Deques, Moving One After Another in a Shared Memory

In the parallel work-stealing load balancers, each core owns personal buffer of tasks called deque. One end of the deque is used by its owner to add and retrieve tasks, while the second end is used by other cores to steal tasks. In the paper two representation methods of deques are analyzed: partitioned serial cyclic representation of deques (one of the conventional techniques); and the new approach proposed by our team, without partition of shared memory in advance between deques moving one after another in a circle. Previously we analyzed these methods for representing FIFO queues in network applications, where the “One after another” way gave the best result for some values of the system parameters. Purpose of this research is to construct and analyze models of the process of work with two circular deques located in shared memory, where they movie one after another in a circle. The mathematical model is constructed in the form of a random walk by integer points in the pyramid. The simulation model is constructed using the Monte Carlo method. The used work-stealing strategy is stealing of one element. We propose the mathematical and simulation models of this process and carry out numerical experiments.

Extending XCS with Cyclic Graphs for Scalability on Complex Boolean Problems

A main research direction in the field of evolutionary machine learning is to develop a scalable classifier system to solve high-dimensional problems. Recently work has begun on autonomously reusing learned building blocks of knowledge to scale from low-dimensional problems to high-dimensional ones. An XCS-based classifier system, known as XCSCFC, has been shown to be scalable, through the addition of expression tree–like code fragments, to a limit beyond standard learning classifier systems. XCSCFC is especially beneficial if the target problem can be divided into a hierarchy of subproblems and each of them is solvable in a bottom-up fashion. However, if the hierarchy of subproblems is too deep, then XCSCFC becomes impractical because of the needed computational time and thus eventually hits a limit in problem size. A limitation in this technique is the lack of a cyclic representation, which is inherent in finite state machines (FSMs). However, the evolution of FSMs is a hard task owing to the combinatorially large number of possible states, connections, and interaction. Usually this requires supervised learning to minimize inappropriate FSMs, which for high-dimensional problems necessitates subsampling or incremental testing. To avoid these constraints, this work introduces a state-machine-based encoding scheme into XCS for the first time, termed XCSSMA. The proposed system has been tested on six complex Boolean problem domains: multiplexer, majority-on, carry, even-parity, count ones, and digital design verification problems. The proposed approach outperforms XCSCFA (an XCS that computes actions) and XCSF (an XCS that computes predictions) in three of the six problem domains, while the performance in others is similar. In addition, XCSSMA evolved, for the first time, compact and human readable general classifiers (i.e., solving any n-bit problems) for the even-parity and carry problem domains, demonstrating its ability to produce scalable solutions using a cyclic representation.

Chain enumeration of k-divisible noncrossing partitions of classical types

International audience We give combinatorial proofs of the formulas for the number of multichains in the $k-divisible$ noncrossing partitions of classical types with certain conditions on the rank and the block size due to Krattenthaler and Müller. We also prove Armstrong's conjecture on the zeta polynomial of the poset of k-divisible noncrossing partitions of type A invariant under the 180° rotation in the cyclic representation. Nous donnons une preuve combinatoire de la formule pour le nombre de multichaînes dans les partitions $k-divisibles$ non-croisées de type classique avec certaines conditions sur le rang et la taille du bloc due à Krattenthaler et Müller. Nous prouvons aussi la conjecture d'Amstrong sur le polynôme zeta du poset des partitions k-divisibles non-croisées de type A invariantes par la rotation de 180° dans la représentation cyclique.