Strength or Accuracy: Credit Assignment in Learning Classifier Systems (Distinguished Dissertations)

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Strength or Accuracy: Credit Assignment in Learning Classifier Systems

Description Table of Contents Product Details Click on the cover image above to read some pages of this book! Industry Reviews From the reviews: "This book is a monograph on learning classifier systems In Stock. Overgeneral rules are those which misclassify some of the inputs they match. Since actions do not contain wildcards the system cannot generalise over them.

If no rule matches the current input, XCS's covering mechanism is triggered. This mechanism takes the current input and with probability P for each bit flips it to a , and uses this as the condition for a new rule with a random classification. XCS may or may not use an initial population of random rules whose conditions are generated with P and equiprobable 0s and 1s. The covering mechanism is used regardless of whether an initial population is used, but, when P is not very close to 0, covering is triggered only sparingly and typically only at the outset of the experiment, even in the absence of an initial population.

The adaptive power of this approach lies in the XCS updates which estimate the prediction and fitness of rules, and weight classification votes on these two values. In section 3. We could attempt to improve XCS-NGA by restricting the generality of rules found to be overgeneral, or simply deleting them. However, our aim is not to propose a practical learning technique but rather to provide a baseline against which to evaluate other methods.

We note that in experimental results presented later we will quote a certain number of random rules having been used. In some experiments, some additional rules will have been generated by covering.

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In these cases, the same number of initial random rules will have been removed from the population in order to make room for the rules generated by covering. In most experiments covering does not occur, and when it does typically when the rule set is small it is not triggered many times.

The first k bits are used to encode an address into the remaining 2 k bits, and the value of the function is the value of the addressed bit. For example, the value of is 0 as the first two bits 10 represent the index 2 in base ten which is the third bit following the address.

Similarly, the value of is 1 as the 0th bit after the address is indexed.

A Grid Data Mining Architecture for Learning Classifier Systems

To use the 6 multiplexer as a test, on each time step we generate a random binary string of 6 digits which we present as input to the LCS. The LCS responds with either a 0 or 1, and receives a high reward if its output is that of the multiplexer function on the same string, and a low reward 0 otherwise. Specifically, on each time step we alternate between explore and exploit modes.

In the former we select an action at random from among those advocated by the set of matching rules. In the latter we select the action most strongly advocated by the matching rules. We record statistics only on those time steps in which we exploit exploit trials.

ISBN 13: 9781447110583

Wilson defines a measure of performance which he refers to simply as "performance" [Wilson95a]. Performance is defined as a moving average of the proportion of the last n trials in which the system has responded with the correct action, where n is customarily That is, on each time step, we determine the proportion of the last n time steps on which the LCS has taken the correct action. The performance curve is scaled so that when the system has acted correctly on all of the last 50 time steps it reaches the top of the figure, and when it has acted incorrectly on all these time steps it reaches the bottom of the figure.

In addition to performance, on each exploit trial we monitor the number of macroclassifiers in the population. These are rules with a numerosity parameter indicating the number of identical virtual rules represented by the macroclassifier. The macroclassifier curves gives us an indication of the diversity in the rule population and the extent to which it has found and converged on useful general rules and hence a compact representation of the solution.

When an initial population is used the macroclassifier curve starts a little below the specified population size limit since a few duplicate rules are likely to have been generated. In the figures shown later, the number of macroclassifiers is divided by in order to display it simultaneously with other curves. GA subsumption was used but not action set subsumption. The original accuracy calculation was used [Wilson95a]. Initial random populations were used except as noted. Parameter settings for the 11 multiplexer differed only in having a population size of and hash probability of 0.

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Curves are averages of runs. The upper two curves show performance and the lower two show the population size in macroclassifiers divided by Although initial rules were generated for each system, both population size curves start somewhat below this as the curves show macroclassifiers, and some duplicate rules were generated. Curves are an average of 50 runs. The upper two curves show performance and the lower two show the population size in macroclassifiers.

Suppose we have a space of data points to be categorised. XCS uses a generate-and-test approach to classification, which entails two problems: i rule discovery and ii credit assignment.


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Specifically, XCS addresses problem i using a GA to generate fitter rules regions in the data space , each with an associated class label. Problem ii is that of evaluating rule fitness such that more general rules and rules with higher classification accuracy are fitter. Essentially, rules must be found which capture many positive data points and few negative ones or vice versa. XCS classifies data points by a vote among the rules which match it, with each vote weighted both by the rule's fitness.

In this way, a point matched by a low-accuracy rule and a high-accuracy rule is given the classification of the high-accuracy rule.


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In XCS, the rules region shapes and sizes are adapted by the genetic algorithm. Of the randomly generated rules, those with low classification accuracy are assigned low weights and have less influence in the classification vote than higher accuracy rules. Roughly speaking, XCS-NGA's approach is to generate many random rules and ignore those which happen to have low accuracy. The number of random rules needed for high classification accuracy on small multiplexers is low because there are relatively few data points and clustering them into regions of the same class is easy using our chosen language.

The difficulty of the rule discovery problem depends on the Kolmogorov complexity In simple terms, the shortest possible representation in a given formalism [Li97a]. There is considerable variability in the Kolmogorov complexity of functions of the same length and representation. For example, with the language we have used the 6-bit parity functions are much more complex than the 6 multiplexer, which in turn is considerably more complex than 6-bit constant functions.

Elsewhere, we have demonstrated a strong correlation between the size of the minimal representation of these functions and their difficulty for XCS [Kovacs01c]. One consequence is that even successful solution by XCS of a large multiplexer, such as the bit multiplexer [Butza], does not mean that XCS can solve all bit functions with comparable effort; quite the opposite. We hypothesise that the difficulty of a function for XCS-NGA will also correlate with the minimal number of rules needed to represent the function in a particular language. For example, CMAC function approximators [Albus75a] adapt the weight of each region in each of multiple partitions of the input space.

Partitions may be regular or generated at random, and XCS-NGA differs essentially only in the details of how regions are formed. XCS-NGA is also very similar to the Weighted-Majority algorithm [Mitchell97a], which enumerates all possible concepts and weights them according to their consistency with the training data. It is not clear why XCS-NGA initially outperform XCS, but it may be that XCS is deleting overgeneral rules which have some value; overgenerals can advocate the correct action for the great majority of inputs they match.

In XCS, however, low accuracy results in low fitness and greater likelihood of deletion under the genetic algorithm, and once deleted rules have no effect. Further study of this phenomenon is warranted, and perhaps improved performance in XCS can be obtained by allowing it to retain overgeneral rules when no accurate rule matches an input, or by delaying the application of the GA to the initial population until it has been better evaluated.

Although we have shown that good performance on the 6 multiplexer with rules does not demonstrate effective genetic search in a classifier system, we do not claim that the 6 multiplexer is without uses. For example, in section 2. Keine Kommentare vorhanden Jetzt bewerten. Kommentar verfassen. Produkt empfehlen. Inreinforcement learning tasks they simultaneously address the two major problems of Mehr zum Inhalt Video Inhaltsverzeichnis Rezension.

Produktbeschreibung Inhaltsverzeichnis Video Biblio. Inreinforcement learning tasks they simultaneously address the two major problems of learning a policy and generalising over it and re lated objects, such as value functions. Despite over 20 years of research, however, classifier systems have met with mixed success, for reasons which were often unclear. Finally, in Stewart Wilson claimed a long-awaited breakthrough with his XCS system, which differs from earlier classifier sys tems in a number of respects, the most significant of which is the way in which it calculates the value of rules for use by the rule generation system.

Specifically, XCS like most classifiersystems employs a genetic algorithm for rule generation, and the way in whichit calculates rule fitness differsfrom earlier systems.