Learning classifier system

Learning classifier systems, or LCS, are a paradigm of rule-based machine learning methods that combine a discovery component with a learning component. Learning classifier systems seek to identify a set of context-dependent rules that collectively store and apply knowledge in a piecewise manner in order to make predictions. This approach allows complex solution spaces to be broken up into smaller, simpler parts for the reinforcement learning that is inside artificial intelligence research.
The founding concepts behind learning classifier systems came from attempts to model complex adaptive systems, using rule-based agents to form an artificial cognitive system.

Methodology

The architecture and components of a given learning classifier system can be quite variable. It is useful to think of an LCS as a machine consisting of several interacting components. Components may be added or removed, or existing components modified/exchanged to suit the demands of a given problem domain or to make the algorithm flexible enough to function in many different problem domains. As a result, the LCS paradigm can be flexibly applied to many problem domains that call for machine learning. The major divisions among LCS implementations are as follows: Michigan-style architecture vs. Pittsburgh-style architecture, reinforcement learning vs. supervised learning, incremental learning vs. batch learning, online learning vs. offline learning, strength-based fitness vs. accuracy-based fitness, and complete action mapping vs best action mapping. These divisions are not necessarily mutually exclusive. For example, XCS, the best known and best studied LCS algorithm, is Michigan-style, was designed for reinforcement learning but can also perform supervised learning, applies incremental learning that can be either online or offline, applies accuracy-based fitness, and seeks to generate a complete action mapping.

Elements of a generic LCS algorithm

Keeping in mind that LCS is a paradigm for genetic-based machine learning rather than a specific method, the following outlines key elements of a generic, modern LCS algorithm. For simplicity let us focus on Michigan-style architecture with supervised learning. See the illustrations on the right laying out the sequential steps involved in this type of generic LCS.

Environment

The environment is the source of data upon which an LCS learns. It can be an offline, finite training dataset, or an online sequential stream of live training instances. Each training instance is assumed to include some number of features, and a single endpoint of interest. Part of LCS learning can involve feature selection, therefore not all of the features in the training data need to be informative. The set of feature values of an instance is commonly referred to as the state. For simplicity let's assume an example problem domain with Boolean/binary features and a Boolean/binary class. For Michigan-style systems, one instance from the environment is trained on each learning cycle. Pittsburgh-style systems perform batch learning, where rule sets are evaluated in each iteration over much or all of the training data.

Rule/classifier/population

A rule is a context dependent relationship between state values and some prediction. Rules typically take the form of an expression,. A critical concept in LCS and rule-based machine learning alike, is that an individual rule is not in itself a model, since the rule is only applicable when its condition is satisfied. Think of a rule as a "local-model" of the solution space.
Rules can be represented in many different ways to handle different data types. Given binary data LCS traditionally applies a ternary rule representation. The 'don't care' symbol serves as a wild card within a rule's condition allowing rules, and the system as a whole to generalize relationships between features and the target endpoint to be predicted. Consider the following rule . This rule can be interpreted as: IF the second feature = 1 AND the sixth feature = 0 THEN the class prediction = 1. We would say that the second and sixth features were specified in this rule, while the others were generalized. This rule, and the corresponding prediction are only applicable to an instance when the condition of the rule is satisfied by the instance. This is more commonly referred to as matching. In Michigan-style LCS, each rule has its own fitness, as well as a number of other rule-parameters associated with it that can describe the number of copies of that rule that exist, the age of the rule, its accuracy, or the accuracy of its reward predictions, and other descriptive or experiential statistics. A rule along with its parameters is often referred to as a classifier. In Michigan-style systems, classifiers are contained within a population that has a user defined maximum number of classifiers. Unlike most stochastic search algorithms, LCS populations start out empty. Classifiers will instead be initially introduced to the population with a covering mechanism.
In any LCS, the trained model is a set of rules/classifiers, rather than any single rule/classifier. In Michigan-style LCS, the entire trained classifier population forms the prediction model.

Matching

One of the most critical and often time-consuming elements of an LCS is the matching process. The first step in an LCS learning cycle takes a single training instance from the environment and passes it to where matching takes place. In step two, every rule in is now compared to the training instance to see which rules match. In step three, any matching rules are moved to a match set . A rule matches a training instance if all feature values specified in the rule condition are equivalent to the corresponding feature value in the training instance. For example, assuming the training instance is, these rules would match:,,, but these rules would not,,. Notice that in matching, the endpoint/action specified by the rule is not taken into consideration. As a result, the match set may contain classifiers that propose conflicting actions. In the fourth step, since we are performing supervised learning, is divided into a correct set and an incorrect set . A matching rule goes into the correct set if it proposes the correct action, otherwise it goes into . In reinforcement learning LCS, an action set would be formed here instead, since the correct action is not known.

Covering

At this point in the learning cycle, if no classifiers made it into either or , the covering mechanism is applied. Covering is a form of online smart population initialization. Covering randomly generates a rule that matches the current training instance, covering might generate any of the following rules: ,,. Covering not only ensures that each learning cycle there is at least one correct, matching rule in , but that any rule initialized into the population will match at least one training instance. This prevents LCS from exploring the search space of rules that do not match any training instances.

Parameter updates/credit assignment/learning

In the sixth step, the rule parameters of any rule in are updated to reflect the new experience gained from the current training instance. Depending on the LCS algorithm, a number of updates can take place at this step. For supervised learning, we can simply update the accuracy/error of a rule. Rule accuracy/error is different than model accuracy/error, since it is not calculated over the entire training data, but only over all instances that it matched. Rule accuracy is calculated by dividing the number of times the rule was in a correct set by the number of times it was in a match set . Rule accuracy can be thought of as a 'local accuracy'. Rule fitness is also updated here, and is commonly calculated as a function of rule accuracy. The concept of fitness is taken directly from classic genetic algorithms. Be aware that there are many variations on how LCS updates parameters in order to perform credit assignment and learning.

Subsumption

In the seventh step, a subsumption mechanism is typically applied. Subsumption is an explicit generalization mechanism that merges classifiers that cover redundant parts of the problem space. The subsuming classifier effectively absorbs the subsumed classifier. This can only happen when the subsuming classifier is more general, just as accurate, and covers all of the problem space of the classifier it subsumes.

Rule discovery/genetic algorithm

In the eighth step, LCS adopts a highly elitist genetic algorithm which will select two parent classifiers based on fitness. Crossover and mutation operators are now applied to generate two new offspring rules. At this point, both the parent and offspring rules are returned to . The LCS genetic algorithm is highly elitist since each learning iteration, the vast majority of the population is preserved. Rule discovery may alternatively be performed by some other method, such as an estimation of distribution algorithm, but a GA is by far the most common approach. Evolutionary algorithms like the GA employ a stochastic search, which makes LCS a stochastic algorithm. LCS seeks to cleverly explore the search space, but does not perform an exhaustive search of rule combinations, and is not guaranteed to converge on an optimal solution.

Deletion

The last step in a generic LCS learning cycle is to maintain the maximum population size. The deletion mechanism will select classifiers for deletion. The probability of a classifier being selected for deletion is inversely proportional to its fitness. When a classifier is selected for deletion, its numerosity parameter is reduced by one. When the numerosity of a classifier is reduced to zero, it is removed entirely from the population.

Training

LCS will cycle through these steps repeatedly for some user defined number of training iterations, or until some user defined termination criteria have been met. For online learning, LCS will obtain a completely new training instance each iteration from the environment. For offline learning, LCS will iterate through a finite training dataset. Once it reaches the last instance in the dataset, it will go back to the first instance and cycle through the dataset again.