Investigating the Impact of Independent Rule Fitnesses in a Learning Classifier System

Achieving at least some level of explainability requires complex analyses for many machine learning systems, such as common black-box models. We recently proposed a new rule-based learning system, SupRB, to construct compact, interpretable and transparent models by utilizing separate optimizers for the model selection tasks concerning rule discovery and rule set composition.This allows users to specifically tailor their model structure to fulfil use-case specific explainability requirements. From an optimization perspective, this allows us to define clearer goals and we find that -- in contrast to many state of the art systems -- this allows us to keep rule fitnesses independent. In this paper we investigate this system's performance thoroughly on a set of regression problems and compare it against XCSF, a prominent rule-based learning system. We find the overall results of SupRB's evaluation comparable to XCSF's while allowing easier control of model structure and showing a substantially smaller sensitivity to random seeds and data splits. This increased control can aid in subsequently providing explanations for both training and final structure of the model.Comment: arXiv admin note: substantial text overlap with arXiv:2202.0167

XCS Classifier System with Experience Replay

XCS constitutes the most deeply investigated classifier system today. It bears strong potentials and comes with inherent capabilities for mastering a variety of different learning tasks. Besides outstanding successes in various classification and regression tasks, XCS also proved very effective in certain multi-step environments from the domain of reinforcement learning. Especially in the latter domain, recent advances have been mainly driven by algorithms which model their policies based on deep neural networks -- among which the Deep-Q-Network (DQN) is a prominent representative. Experience Replay (ER) constitutes one of the crucial factors for the DQN's successes, since it facilitates stabilized training of the neural network-based Q-function approximators. Surprisingly, XCS barely takes advantage of similar mechanisms that leverage stored raw experiences encountered so far. To bridge this gap, this paper investigates the benefits of extending XCS with ER. On the one hand, we demonstrate that for single-step tasks ER bears massive potential for improvements in terms of sample efficiency. On the shady side, however, we reveal that the use of ER might further aggravate well-studied issues not yet solved for XCS when applied to sequential decision problems demanding for long-action-chains

Absumption and subsumption based learning classifier systems

Learning Classifier Systems (LCSs) are a group of rule-based evolutionary computation techniques, which have been frequently applied to data-mining tasks. Evidence shows that LCSs can produce models containing human-discernible patterns. But, traditional LCSs cannot efficiently discover consistent, general rules - especially in domains that have unbalanced class distribution. The reason is that traditional search methods, e.g. crossover, mutation, and roulette wheel deletion, rely on stochasticity to find and keep optimum rules. Recently, absumption has been introduced to deterministically remove over-general rules, which is complementary to subsumption that deterministically removes over-specific rules. It is hypothesized that utilizing just assumption &amp; subsumption transforms the search process from stochastic to deterministic, which benefits LCSs in evolving interpretable models and removing the need to tune search parameters to the problem. Interrogatable artificial Boolean domains with varying numbers of attributes are considered as benchmarks. The new LCS, termed Absumption Subsumption Classifier System (ASCS), successfully produces interpretable models for all the complex domains tested, whereas the non-optimal rules in existing techniques obscure the patterns. ACSC's ability to handle complex search spaces is observed, e.g. for the 14-bits Majority-On problem the required 6435 different cooperating rules were discovered enabling correct pattern visualization.</p

Absumption to complement subsumption in learning classifier systems

Learning Classifier Systems (LCSs), a 40-year-old technique, evolve interrogatable production rules. XCSs are the most popular reinforcement learning based LCSs. It is well established that the subsumption method in XCSs removes overly detailed rules. However, the technique still suffers from overly general rules that reduce accuracy and clarity in the discovered patterns. This adverse impact is especially true for domains that are containing accurate solutions that overlap, i.e. one data instance is covered by two plausible, but competing rules. A novel method, termed absumption, is introduced to counter over-general rules. Complex Boolean problems that contain epistasis, heterogeneity and overlap are used to test the absumption method. Results show that absumption successfully improves the training performance of XCSs by counteracting over-general rules. Moreover, absumption enables the rule-set to be compacted, such that underlying patterns can be precisely visualized successfully. Additionally, the equations for the optimal size of solutions for a problem domain can now be determined.</p

Absumption and Subsumption based Learning Classifier System for Real-World Continuous-based Problems

Learning Classifier Systems (LCSs), a series of rules-based evolutionary computation techniques, which have solved a wide range of discrete-feature-based applications over their 40 years of history. Yet, adapting LCSs to complicated continuous-feature-based domains is still an unsolved challenge. This paper proposes new LCS methods specialized for continuous problems. Concretely, phenotype-orientated Absumption, Subsumption, and Mutation are proposed and employed to form and revise rules directly in a single iteration according to the target problems’ inherent data distribution, allowing rules to be released from the burden of directly carrying the information of previous instances. Furthermore, a novel representation format supporting fine-grained generalization degree modification is also proposed. Experiments demonstrate for the first time that LCSs are promising techniques in efficiently producing models with satisfactory prediction performance for complicated continuous problems.</p

Learning Classifier Systems for Understanding Patterns in Data

In the field of data-mining, symbolic techniques have produced optimal solutions, which are expected to contain informative patterns. Visualizing these patterns can improve the understanding of the ground truth of the explored domain. However, up to now, the symbolic algorithms struggle to produce optimal solutions for domains that have an overlapping distribution of feature patterns. Furthermore, the majority of problems have an overlapping distribution. Thus, novel techniques are needed to improve symbolic techniques’ capacity to address overlapping domains, so that it is practicable to achieve the visualization of the underlying patterns. Michigan-style Learning Classifier Systems (LCSs) are rule-based symbolic learning systems that utilize evolutionary computation to construct a population of rules to capture patterns and knowledge of the explored domains. LCSs have been applied to many data-mining tasks and have achieved good performance. Recently, employing visualization methods to improve the understanding level of models has become more and more popular in the data-mining community. In the LCSs field, visualization techniques orientated to explore feature patterns have not been developed. Investigating LCSs’ models is commonly based on reading rules or viewing their distribution. However, LCSs’ models may contain hundreds or even thousands of unduplicated rules, which makes the identification of patterns challenging. Previously, Butz defined LCSs’ optimal solutions as [O] sets, which are expected to utilize a minimal number of non-overlapping rules to present an explored domain completely and correctly. In the last two decades, rule compaction algorithms have been designed to search for [O]s by compacting LCSs’ models, where rules that violate [O]’s definition are considered redundant rules. However, in many problems, an ideal [O] does not exist. Even if such a ruleset exists, redundant rules are often discovered in the compacted models. Furthermore, compaction often results in a decreased prediction performance. The LCSs community used to believe the reduced performance is an unavoidable and acceptable price for producing a compacted model. It is observed that across multiple LCS produced populations for the same problem, the irrelevant/redundant rules are varied, but useful/accurate rules are consistent. According to this observation, this thesis collects the common accurate rules and finds that for an arbitrary clean dataset, the common rules can form a determinate and unique solution, i.e. the proposed natural solution. A natural solution is composed of all consistent and unsubsumable rules under the global search space. A natural solution can correctly and completely represent the explored clean datasets. Furthermore, searching for natural solutions can produce concise correct solutions without reducing performance. To visualize the knowledge in the solutions, three visualization methods are developed, i.e. Feature Important Map (FIM), Action-based Feature Importance Map (AFIM), and Action-based Average value Map (AFVM). FIM can trace how LCSs form patterns during the training process. Besides, AFIM and AFVM precisely present patterns in LCSs’ optimal solution respectively regarding attribute importance and specified attribute’s value’s importance. For the sake of efficiently producing natural solutions, a new type of compaction algorithm is introduced, termed Razor Cluster Razor (RCR). RCR is the first algorithm that considers Pittsburgh-style LCSs’ conceptions to Michigan-style LCSs’ compaction algorithms, i.e. compacting is based on multiple models. RCR was first designed for Boolean domains, then RCR has been extended to adapt to real-value LCSs’ models. The conducted experiments demonstrated that natural solutions are producible for both Boolean domains and real domains. The experiments regarding producing natural solutions lead this thesis to discover that LCSs have an over-general issue when addressing domains that have an overlapping distribution, i.e. optimal rules’ encodings naturally share overlapped niches. The over-general issue causes LCSs to fail in maintaining the prediction performance, i.e. due to the optimal rules and over-general rules being repeatedly introduced and removed, training performance can never achieve 100% accuracy. This newly discovered issue inspires the development of the Absumption method as a complement to the existing Subsumption method, which continuously seeks to produce optimal rules by correcting over-general rules. Absumption not only improves LCSs’ prediction performance in overlapping domains but also enables LCSs to employ hundreds of cooperative rules to precisely represent an explored domain. The success of Absumption demonstrates LCSs’ capacity in addressing overlapping domains. However, introducing Absumption to LCSs does increase the cost of computer resources for training, which results in a need for more efficient exploration. Furthermore, LCSs employed search techniques tend to evolve maximally generalized rules, rather than produce rules that do not overlap with the existing rules in the population. Thus, [O]s do not fit LCSs’ fundamental search techniques. As a result, LCSs’ accurate models often do not contain an optimal solution, which results in the LCSs produced models being poorly interpretable. This hampers LCSs from being a good data-mining technique. In this thesis, the Absumption and Subsumption based Learning Classifier System (ASCS) is developed. ASCSs consider natural solution as the search objective and promote the Absumption mechanism and Subsumption mechanism as the primary search strategies. Thus, it is possible to remove the traditional evolutionary search algorithms, i.e. crossover, mutation, roulette wheel deletion, and competition selection. Experiments demonstrated that ASCSs can use thousands of cooperative rules to represent an explored domain and enable easy pattern visualization that was previously not possible.</p