Autoencoders are data-specific compression algorithms learned automatically from examples. The predominant approach has been to construct single large global models that cover the domain. However, training and evaluating models of increasing size comes at the price of additional time and computational cost. Conditional computation, sparsity, and model pruning techniques can reduce these costs while maintaining performance. Learning classifier systems (LCSs) are a framework for adaptively subdividing input spaces into an ensemble of simpler local approximations that together cover the domain. LCS perform conditional computation through the use of a population of individual gating/guarding components, each associated with a local approximation. This article explores the use of an LCS to adaptively decompose the input domain into a collection of small autoencoders, where local solutions of different complexity may emerge. In addition to the benefits in convergence time and computational cost, it is shown possible to reduce the code size as well as the resulting decoder computational cost when compared with the global model equivalent.

An important strength of learning classifier systems (LCSs) lies in the combination of genetic optimization techniques with gradient-based approximation techniques. The chosen approximation technique develops locally optimal approximations, such as accurate classification estimates, Q-value predictions, or linear function approximations. The genetic optimization technique is designed to distribute these local approximations efficiently over the problem space. Together, the two components develop a distributed, locally optimized problem solution in the form of a population of expert rules, often called classifiers. In function approximation problems, the XCSF classifier system develops a problem solution in the form of overlapping, piecewise linear approximations. This paper shows that XCSF performance on function approximation problems additively benefits from: 1) improved representations; 2) improved genetic operators; and 3) improved approximation techniques. Additionally, this paper introduces a novel closest classifier matching mechanism for the efficient compaction of XCS's final problem solution. The resulting compaction mechanism can boil the population size down by 90% on average, while decreasing prediction accuracy only marginally. Performance evaluations show that the additional mechanisms enable XCSF to reliably, accurately, and compactly approximate even seven dimensional functions. Performance comparisons with other, heuristic function approximation techniques show that XCSF yields competitive or even superior noise-robust performance.

We analyze generalization in XCSF and introduce three improvements. We begin by showing that the types of generalizations evolved by XCSF can be influenced by the input range. To explain these results we present a theoretical analysis of the convergence of classifier weights in XCSF which highlights a broader issue. In XCSF, because of the mathematical properties of the Widrow-Hoff update, the convergence of classifier weights in a given subspace can be slow when the spread of the eigenvalues of the autocorrelation matrix associated with each classifier is large. As a major consequence, the system's accuracy pressure may act before classifier weights are adequately updated, so that XCSF may evolve piecewise constant approximations, instead of the intended, and more efficient, piecewise linear ones. We propose three different ways to update classifier weights in XCSF so as to increase the generalization capabilities of XCSF: one based on a condition-based normalization of the inputs, one based on linear least squares, and one based on the recursive version of linear least squares. Through a series of experiments we show that while all three approaches significantly improve XCSF, least squares approaches appear to be best performing and most robust. Finally we show how XCSF can be extended to include polynomial approximations.

The learning classifier system XCS is an iterative rule-learning system that evolves rule structures based on gradient-based prediction and rule quality estimates. Besides classification and reinforcement learning tasks, XCS was applied as an effective function approximator. Hereby, XCS learns space partitions to enable a maximally accurate and general function approximation. Recently, the function approximation approach was improved by replacing (1) hyperrectangular conditions with hyper-ellipsoids and (2) iterative linear approximation with the recursive least squares method. This paper combines the two approaches assessing the usefulness of each. The evolutionary process is further improved by changing the mutation operator implementing an angular mutation that rotates ellipsoidal structures explicitly. Both enhancements improve XCS performance in various non-linear functions. We also analyze the evolving ellipsoidal structures confirming that XCS stretches and rotates the evolving ellipsoids according to the shape of the underlying function. The results confirm that improvements in both the evolutionary approach and the gradient approach can result in significantly better performance.

This paper introduces XCSF extended with tile coding prediction: each classifier implements a tile coding approximator; the genetic algorithm is used to adapt both classifier conditions (i.e., to partition the problem) and the parameters of each approximator; thus XCSF evolves an ensemble of tile coding approximators instead of the typical monolithic approximator used in reinforcement learning. The paper reports a comparison between (i) XCSF with tile coding prediction and (ii) plain tile coding. The results show that XCSF with tile coding always reaches optimal performance, it usually learns as fast as the best parametrized tile coding, and it can be faster than the typical tile coding setting. In addition, the analysis of the evolved tile coding ensembles shows that XCSF actually adapts local approximators following what is currently considered the best strategy to adapt the tile coding parameters in a given problem.

We study how different prediction update algorithms influence the performance of XCSF. We consider three classical parameter estimation algorithms (NLMS, RLS, and Kalman filter) and four gain adaptation algorithms (K1, K2, IDBD, and IDD). The latter have been shown to perform comparably to the best algorithms (RLS and Kalman), but they have a lower complexity. We apply these algorithms to update classifier prediction in XCSF and compare the performances of the seven versions of XCSF on a set of real functions. Our results show that the best known algorithms still perform best: XCSF with RLS and XCSF with Kalman perform significantly better than the others. In contrast, when added to XCSF, gain adaptation algorithms perform comparably to NLMS, the simplest estimation algorithm, the same used in the original XCSF. Nevertheless, algorithms that perform similarly generalize differently. For instance: XCSF with Kalman filter evolves more compact solutions than XCSF with RLS and gain adaptation algorithms allow better generalization than NLMS.

This papers presents a novel representation of classifier conditions based on convex hulls. A classifier condition is represented by a sets of points in the problem space. These points identify a convex hull that delineates a convex region in the problem space. The condition matches all the problem instances inside such region. XCSF with convex conditions is applied to function approximation problems and its performance is compared to that of XCSF with interval conditions. The comparison shows that XCSF with convex hulls converges faster than XCSF with interval conditions. However, convex conditions usually do not produce more compact solutions.

Computed prediction represents a major shift in learning classifier system research. XCS with computed prediction, based on linear approximates, has been applied so far to function approximation, to single step problems involving continuous payoff functions, and to multi step problems. In this paper we take this new approach in a different direction and apply it to the learning of Boolean functions - a domain characterized by highly discontinuous 0/1000 payoff functions. We also extend it to the case of computed prediction based on functions, borrowed from neural networks, that may be more suitable for 0/1000 payoff problems: the perceptron and the sigmoid. The results we present show that XCSF with linear prediction performs optimally in typical Boolean domains and it allows more compact solutions evolving classifiers that are more general compared with XCS. In addition, perceptron based and sigmoid based prediction can converge slightly faster than linear prediction while producing slightly more compact solutions

We apply XCS with computed prediction (XCSF) to tackle multistep reinforcement learning problems involving continuous inputs. In essence we use XCSF as a method of generalized reinforcement learning. We show that in domains involving continuous inputs and delayed rewards XCSF can evolve compact populations of accurate maximally general classifiers which represent the optimal solution to the target problem. We compare the performance of XCSF with that of tabular Q-learning adapted to the continuous domains considered here. The results we present show that XCSF can converge much faster than tabular techniques while producing more compact solutions. Our results also suggest that when exploration is less effective in some areas of the problem space, XCSF can exploit effective generalizations to extend the evolved knowledge beyond the frequently explored areas. In contrast, in the same situations, the convergence speed of tabular Q-learning worsens.

XCSF is the extension of XCS in which classifier prediction is computed as a linear combination of classifier inputs and a weight vector associated to each classifier. XCSF can exploit classifiers' computable prediction to evolve accurate piecewise linear approximations of functions. In this paper, we take XCSF one step further and show how XCSF can be easily extended to allow polynomial approximations. We test the extended version of XCSF on various approximation problems and show that quadratic/cubic approximations can be used to significantly improve XCSF's generalization capabilities.

XCSF extends the typical concept of learning classifier systems through the introduction of computed classifier prediction. Initial results show that XCSF's computed prediction can be used to evolve accurate piecewise linear approximations of simple functions. In this paper, we take XCSF one step further and apply it to typical reinforcement learning problems involving delayed rewards. In essence, we use XCSF as a method of generalized (linear) reinforcement learning to evolve piecewise linear approximations of the payoff surfaces of typical multistep problems. Our results show that XCSF can easily evolve optimal and near optimal solutions for problems introduced in the literature to test linear reinforcement learning methods.

Takes initial steps toward a theory of generalization and learning in the learning classifier system XCS. We start from Wilson's generalization hypothesis, which states that XCS has an intrinsic tendency to evolve accurate, maximally general classifiers. We analyze the different evolutionary pressures in XCS and derive a simple equation that supports the hypothesis theoretically. The equation is tested with a number of experiments that confirm the model of generalization pressure that we provide. Then, we focus on the conditions, termed "challenges," that must be satisfied for the existence of effective fitness or accuracy pressure in XCS. We derive two equations that suggest how to set the population size and the covering probability so as to ensure the development of fitness pressure. We argue that when the challenges are met, XCS is able to evolve problem solutions reliably. When the challenges are not met, a problem may provide intrinsic fitness guidance or the reward may be biased in such a way that the problem will still be solved. The equations and the influence of intrinsic fitness guidance and biased reward are tested on large Boolean multiplexer problems. The paper is a contribution to understanding how XCS functions and lays the foundation for research on XCS's learning complexity.

September 01 2003 Introduction to the Special Issue: Learning Classifier Systems In Special Collection: CogNet Pier Luca Lanzi, Pier Luca Lanzi Search for other works by this author on: This Site Google Scholar Wolfgang Stolzmann, Wolfgang Stolzmann Search for other works by this author on: This Site Google Scholar Stewart W. Wilson Stewart W. Wilson Search for other works by this author on: This Site Google Scholar Author and Article Information Pier Luca Lanzi Wolfgang Stolzmann Stewart W. Wilson Online Issn: 1530-9304 Print Issn: 1063-6560 © 2003 Massachusetts Institute of Technology2003 Evolutionary Computation (2003) 11 (3): iii–iv. https://doi.org/10.1162/106365603322365270 Cite Icon Cite Permissions Share Icon Share Facebook Twitter LinkedIn MailTo Views Icon Views Article contents Figures & tables Video Audio Supplementary Data Peer Review Search Site Citation Pier Luca Lanzi, Wolfgang Stolzmann, Stewart W. Wilson; Introduction to the Special Issue: Learning Classifier Systems. Evol Comput 2003; 11 (3): iii–iv. doi: https://doi.org/10.1162/106365603322365270 Download citation file: Ris (Zotero) Reference Manager EasyBib Bookends Mendeley Papers EndNote RefWorks BibTex toolbar search Search Dropdown Menu toolbar search search input Search input auto suggest filter your search All ContentAll JournalsEvolutionary Computation Search Advanced Search This content is only available as a PDF. © 2003 Massachusetts Institute of Technology2003 Article PDF first page preview Close Modal You do not currently have access to this content.

Wilson's (1994) bit-register memory scheme was incorporated into the XCS classifier system and investigated in a series of non-Markov environments. Two extensions to the scheme were important in obtaining near-optimal performance in the harder environments. The first was an exploration strategy in which exploration of external actions was probabilistic as in Markov environments, but internal "actions" (register settings) were selected deterministically. The second was use of a register having more bit-positions than were strictly necessary to resolve environmental aliasing. The origins and effects of the two extensions are discussed.

In many classifier systems, the classifier strength parameter serves as a predictor of future payoff and as the classifier's fitness for the genetic algorithm. We investigate a classifier system, XCS, in which each classifier maintains a prediction of expected payoff, but the classifier's fitness is given by a measure of the prediction's accuracy. The system executes the genetic algorithm in niches defined by the match sets, instead of panmictically. These aspects of XCS result in its population tending to form a complete and accurate mapping X × A → P from inputs and actions to payoff predictions. Further, XCS tends to evolve classifiers that are maximally general, subject to an accuracy criterion. Besides introducing a new direction for classifier system research, these properties of XCS make it suitable for a wide range of reinforcement learning situations where generalization over states is desirable.

A basic classifier system, ZCS, is presented that keeps much of Holland's original framework but simplifies it to increase understandability and performance. ZCS's relation to Q-learning is brought out, and their performances compared in environments of two difficulty levels. Extensions to ZCS are proposed for temporary memory, better action selection, more efficient use of the genetic algorithm, and more general classifier representation.