Value function approximation has demonstrated phenomenal empirical success in reinforcement learning (RL). Nevertheless, despite a handful of recent progress on developing theory for RL with linear function approximation, the understanding of general function approximation schemes largely remains missing. In this paper, we establish a provably efficient RL algorithm with general value function approximation. We show that if the value functions admit an approximation with a function class $\mathcal{F}$, our algorithm achieves a regret bound of $\widetilde{O}(\mathrm{poly}(dH)\sqrt{T})$ where $d$ is a complexity measure of $\mathcal{F}$ that depends on the eluder dimension [Russo and Van Roy, 2013] and log-covering numbers, $H$ is the planning horizon, and $T$ is the number interactions with the environment. Our theory generalizes recent progress on RL with linear value function approximation and does not make explicit assumptions on the model of the environment. Moreover, our algorithm is model-free and provides a framework to justify the effectiveness of algorithms used in practice.

Reward-free reinforcement learning (RL) is a framework which is suitable for both the batch RL setting and the setting where there are many reward functions of interest. During the exploration phase, an agent collects samples without using a pre-specified reward function. After the exploration phase, a reward function is given, and the agent uses samples collected during the exploration phase to compute a near-optimal policy. Jin et al. [2020] showed that in the tabular setting, the agent only needs to collect polynomial number of samples (in terms of the number states, the number of actions, and the planning horizon) for reward-free RL. However, in practice, the number of states and actions can be large, and thus function approximation schemes are required for generalization. In this work, we give both positive and negative results for reward-free RL with linear function approximation. We give an algorithm for reward-free RL in the linear Markov decision process setting where both the transition and the reward admit linear representations. The sample complexity of our algorithm is polynomial in the feature dimension and the planning horizon, and is completely independent of the number of states and actions. We further give an exponential lower bound for reward-free RL in the setting where only the optimal $Q$-function admits a linear representation. Our results imply several interesting exponential separations on the sample complexity of reward-free RL.

Neural Computing & Applications is an international journal which publishes original research and other information in the field of practical applications of neural computing and related techniques such as genetic algorithms, fuzzy logic and neuro-fuzzy systems. Featured contributions fall into several categories: Original Articles, Review Articles, Book Reviews, and Announcements. The Original Articles will be high-quality contributions, representing new and significant research, developments or applications of practical use and value. They will be reviewed by at least two referees. For all queries relating to papers after submission, please contact the Journal Editorial Office via "contact us" at Editorial Manager.

The article considers the problem of the optimal control of a wind power plant based on fuzzy control and automation of generating the fuzzy rule base. Fuzzy rules by experts do not always provide a maximum power output of the wind plant and fuzzy rule bases require an adjustment in the case of changing the parameters of the wind power plant or the environment. This research proposes the method for optimizing the fuzzy rules base compiled by various experts. The method is based on balancing weights of fuzzy rules into the base by the Particle Swarm Optimization algorithm. The experiment has shown that the proposed method allows forming the fuzzy rule base as an exemplary optimal base from a non-optimized set of fuzzy rules. The optimal fuzzy rule base has been taken under consideration for the concrete control loop of wind power plant and the concrete fuzzy model of the wind.

Combining symbolic and neural approaches has gained considerable attention in the AI community, as it is often argued that the strengths and weaknesses of these approaches are complementary. One such trend in the literature are weakly supervised learning techniques that employ operators from fuzzy logics. In particular, they use prior background knowledge described in such logics to help the training of a neural network from unlabeled and noisy data. By interpreting logical symbols using neural networks (or grounding them), this background knowledge can be added to regular loss functions, hence making reasoning a part of learning. In this paper, we investigate how implications from the fuzzy logic literature behave in a differentiable setting. In such a setting, we analyze the differences between the formal properties of these fuzzy implications. It turns out that various fuzzy implications, including some of the most well-known, are highly unsuitable for use in a differentiable learning setting. A further finding shows a strong imbalance between gradients driven by the antecedent and the consequent of the implication. Furthermore, we introduce a new family of fuzzy implications (called sigmoidal implications) to tackle this phenomenon. Finally, we empirically show that it is possible to use Differentiable Fuzzy Logics for semi-supervised learning, and show that sigmoidal implications outperform other choices of fuzzy implications.

This has led to the development of a plethora of domain-dependent and context-specific methods for dealing with the interpretation of machine learning (ML) models and the formation of explanations for humans. Unfortunately, this trend is far from being over, with an abundance of knowledge in the field which is scattered and needs organisation. The goal of this article is to systematically review research works in the field of XAI and to try to define some boundaries in the field. From several hundreds of research articles focused on the concept of explainability, about 350 have been considered for review by using the following search methodology. In a first phase, Google Scholar was queried to find papers related to "explainable artificial intelligence", "explainable machine learning" and "interpretable machine learning". Subsequently, the bibliographic section of these articles was thoroughly examined to retrieve further relevant scientific studies. The first noticeable thing, as shown in figure 2 (a), is the distribution of the publication dates of selected research articles: sporadic in the 70s and 80s, receiving preliminary attention in the 90s, showing raising interest in 2000 and becoming a recognised body of knowledge after 2010. The first research concerned the development of an explanation-based system and its integration in a computer program designed to help doctors make diagnoses [3]. Some of the more recent papers focus on work devoted to the clustering of methods for explainability, motivating the need for organising the XAI literature [4, 5, 6].

Drought is a natural creeping threat with numerous damaging effects in various aspects of human life. Accurate drought prediction is a promising step in helping policy makers to set drought risk management strategies. To fulfill this purpose, choosing appropriate models plays an important role in predicting approach. In this study, different models of Artificial Neural Network (ANN) are employed to predict short and long-term of droughts by using Standardized Precipitation Index (SPI) at different time scales, including 3, 6, 12, 24 and 48 months in Tabriz city, Iran. To this end, different combination of calculated SPI and time series of various hydro-meteorological variables, such as precipitation, wind velocity, relative humidity and sunshine hours for years 1992 to 2010 are used to train the ANN models. In order to compare the models performances, some well-known measures, namely RMSE, Mean Absolute Error (MAE) and Correlation Coefficient (CC) are utilized in the present study. The results illustrate that the application of all hydro-meteorological variables significantly improves the prediction of SPI at different time scales.

This paper proposes a simple yet powerful ensemble classifier, called Random Hyperboxes, constructed from individual hyperbox-based classifiers trained on the random subsets of sample and feature spaces of the training set. We also show a generalization error bound of the proposed classifier based on the strength of the individual hyperbox-based classifiers as well as the correlation among them. The effectiveness of the proposed classifier is analyzed using a carefully selected illustrative example and compared empirically with other popular single and ensemble classifiers via 20 datasets using statistical testing methods. The experimental results confirmed that our proposed method outperformed other fuzzy min-max neural networks, popular learning algorithms, and is competitive with other ensemble methods. Finally, we identify the existing issues related to the generalization error bounds of the real datasets and inform the potential research directions.

Recommendation system or also known as a recommender system is a tool to help the user in providing a suggestion of a specific dilemma. Thus, recently, the interest in developing a recommendation system in many fields has increased. Fuzzy Logic system (FLSs) is one of the approaches that can be used to model the recommendation systems as it can deal with uncertainty and imprecise information. However, one of the fundamental issues in FLS is the problem of the curse of dimensionality. That is, the number of rules in FLSs is increasing exponentially with the number of input variables. One effective way to overcome this problem is by using Hierarchical Fuzzy System (HFSs). This paper aims to explore the use of HFSs for Recommendation system. Specifically, we are interested in exploring and comparing the HFS and FLS for the Career path recommendation system (CPRS) based on four key criteria, namely topology, the number of rules, the rules structures and interpretability. The findings suggested that the HFS has advantages over FLS towards improving the interpretability models, in the context of a recommendation system example. This study contributes to providing an insight into the development of interpretable HFSs in the Recommendation systems.

In this paper, based on a fuzzy entropy feature selection framework, different methods have been implemented and compared to improve the key components of the framework. Those methods include the combinations of three ideal vector calculations, three maximal similarity classifiers and three fuzzy entropy functions. Different feature removal orders based on the fuzzy entropy values were also compared. The proposed method was evaluated on three publicly available biomedical datasets. From the experiments, we concluded the optimized combination of the ideal vector, similarity classifier and fuzzy entropy function for feature selection. The optimized framework was also compared with other six classical filter-based feature selection methods. The proposed method was ranked as one of the top performers together with the Correlation and ReliefF methods. More importantly, the proposed method achieved the most stable performance for all three datasets when the features being gradually removed. This indicates a better feature ranking performance than the other compared methods.