Multi-agent reinforcement learning (MARL) has achieved tremendous practical success across a wide range of machine learning tasks, including large-scale strategy games such as GO (Silver et al., 2016), TexasHold'em poker (Brown and Sandholm, 2019), real-time video games such as Starcraft (Vinyals et al., 2019), and autonomous driving (Shalev-Shwartz et al., 2016). Among these models used in MARL, two-player zero-sum Markov games (MG) (Shapley, 1953; Littman, 1994) is probably one of the most widely studied models and can be regarded as a generalization of the Markov Decision Processes (MDP) (Puterman, 2014). In two-player Markov games, the two players share states, play actions simultaneously and independently, and observe the same reward. One player (i.e., max-player) aims to maximize the return while the other (i.e., min-player) aims to minimize it. A special case of general Markov games (i.e., simultaneous-move games) is turn-based games, where only one player can take action in each step, i.e., the max and min players take turns to play the game. The players aim to find the Nash equilibrium for this game.

We study reinforcement learning in an infinite-horizon average-reward setting with linear function approximation, where the transition probability function of the underlying Markov Decision Process (MDP) admits a linear form over a feature mapping of the current state, action, and next state. We propose a new algorithm UCRL2-VTR, which can be seen as an extension of the UCRL2 algorithm with linear function approximation. We show that UCRL2-VTR with Bernstein-type bonus can achieve a regret of $\tilde{O}(d\sqrt{DT})$, where $d$ is the dimension of the feature mapping, $T$ is the horizon, and $\sqrt{D}$ is the diameter of the MDP. We also prove a matching lower bound $\tilde{\Omega}(d\sqrt{DT})$, which suggests that the proposed UCRL2-VTR is minimax optimal up to logarithmic factors. To the best of our knowledge, our algorithm is the first nearly minimax optimal RL algorithm with function approximation in the infinite-horizon average-reward setting.

Takagi-Sugeno-Kang (TSK) fuzzy system with Gaussian membership functions (MFs) is one of the most widely used fuzzy systems in machine learning. However, it usually has difficulty handling high-dimensional datasets. This paper explores why TSK fuzzy systems with Gaussian MFs may fail on high-dimensional inputs. After transforming defuzzification to an equivalent form of softmax function, we find that the poor performance is due to the saturation of softmax. We show that two defuzzification operations, LogTSK and HTSK, the latter of which is first proposed in this paper, can avoid the saturation. Experimental results on datasets with various dimensionalities validated our analysis and demonstrated the effectiveness of LogTSK and HTSK.

Quantum mass function has been applied in lots of fields because of its efficiency and validity of managing uncertainties in the form of quantum which can be regarded as an extension of classical Dempster-Shafer (D-S) evidence theory. However, how to handle uncertainties in the form of quantum is still an open issue. In this paper, a new method is proposed to dispose uncertain quantum information, which is called two-dimensional quantum mass function (TDQMF). A TDQMF is consist of two elements, TQ = (Qoriginal, Qindicative), both of the Qs are quantum mass functions, in which the Qindicative is an indicator of the reliability on Qoriginal. More flexibility and effectiveness are offered in handling uncertainty in the field of quantum by the proposed method compared with primary quantum mass function. Besides, some numerical examples are provided and some practical applications are given to verify its correctness and validity

The pythagorean fuzzy set (PFS) which is developed based on intuitionistic fuzzy set, is more efficient in elaborating and disposing uncertainties in indeterminate situations, which is a very reason of that PFS is applied in various kinds of fields. How to measure the distance between two pythagorean fuzzy sets is still an open issue. Mnay kinds of methods have been proposed to present the of the question in former reaserches. However, not all of existing methods can accurately manifest differences among pythagorean fuzzy sets and satisfy the property of similarity. And some other kinds of methods neglect the relationship among three variables of pythagorean fuzzy set. To addrees the proplem, a new method of measuring distance is proposed which meets the requirements of axiom of distance measurement and is able to indicate the degree of distinction of PFSs well. Then some numerical examples are offered to to verify that the method of measuring distances can avoid the situation that some counter? intuitive and irrational results are produced and is more effective, reasonable and advanced than other similar methods. Besides, the proposed method of measuring distances between PFSs is applied in a real environment of application which is the medical diagnosis and is compared with other previous methods to demonstrate its superiority and efficiency. And the feasibility of the proposed method in handling uncertainties in practice is also proved at the same time.

Data mining techniques can be used to discover useful patterns by exploring and analyzing data and it's feasible to synergitically combine machine learning tools to discover fuzzy classification rules.In this paper, an adaptive Neuro fuzzy network with TSK fuzzy type and an improved quantum subtractive clustering has been developed. Quantum clustering (QC) is an intuition from quantum mechanics which uses Schrodinger potential and time-consuming gradient descent method. The principle advantage and shortcoming of QC is analyzed and based on its shortcomings, an improved algorithm through a subtractive clustering method is proposed. Cluster centers represent a general model with essential characteristics of data which can be use as premise part of fuzzy rules.The experimental results revealed that proposed Anfis based on quantum subtractive clustering yielded good approximation and generalization capabilities and impressive decrease in the number of fuzzy rules and network output accuracy in comparison with traditional methods.

In this paper we propose an extension of the notion of deviation-based aggregation function tailored to aggregate multidimensional data. Our objective is both to improve the results obtained by other methods that try to select the best aggregation function for a particular set of data, such as penalty functions, and to reduce the temporal complexity required by such approaches. We discuss how this notion can be defined and present three illustrative examples of the applicability of our new proposal in areas where temporal constraints can be strict, such as image processing, deep learning and decision making, obtaining favourable results in the process.

Attribute reduction is one of the most important research topics in the theory of rough sets, and many rough sets-based attribute reduction methods have thus been presented. However, most of them are specifically designed for dealing with either labeled data or unlabeled data, while many real-world applications come in the form of partial supervision. In this paper, we propose a rough sets-based semi-supervised attribute reduction method for partially labeled data. Particularly, with the aid of prior class distribution information about data, we first develop a simple yet effective strategy to produce the proxy labels for unlabeled data. Then the concept of information granularity is integrated into the information-theoretic measure, based on which, a novel granular conditional entropy measure is proposed, and its monotonicity is proved in theory. Furthermore, a fast heuristic algorithm is provided to generate the optimal reduct of partially labeled data, which could accelerate the process of attribute reduction by removing irrelevant examples and excluding redundant attributes simultaneously. Extensive experiments conducted on UCI data sets demonstrate that the proposed semi-supervised attribute reduction method is promising and even compares favourably with the supervised methods on labeled data and unlabeled data with true labels in terms of classification performance.

Brain Computer Interface technologies are popular methods of communication between the human brain and external devices. One of the most popular approaches to BCI is Motor Imagery. In BCI applications, the ElectroEncephaloGraphy is a very popular measurement for brain dynamics because of its non-invasive nature. Although there is a high interest in the BCI topic, the performance of existing systems is still far from ideal, due to the difficulty of performing pattern recognition tasks in EEG signals. BCI systems are composed of a wide range of components that perform signal pre-processing, feature extraction and decision making. In this paper, we define a BCI Framework, named Enhanced Fusion Framework, where we propose three different ideas to improve the existing MI-based BCI frameworks. Firstly, we include aan additional pre-processing step of the signal: a differentiation of the EEG signal that makes it time-invariant. Secondly, we add an additional frequency band as feature for the system and we show its effect on the performance of the system. Finally, we make a profound study of how to make the final decision in the system. We propose the usage of both up to six types of different classifiers and a wide range of aggregation functions (including classical aggregations, Choquet and Sugeno integrals and their extensions and overlap functions) to fuse the information given by the considered classifiers. We have tested this new system on a dataset of 20 volunteers performing motor imagery-based brain-computer interface experiments. On this dataset, the new system achieved a 88.80% of accuracy. We also propose an optimized version of our system that is able to obtain up to 90,76%. Furthermore, we find that the pair Choquet/Sugeno integrals and overlap functions are the ones providing the best results.

Theoretical and abstract approaches to information have made great advances, but human information processing is still unmatched in many areas, including information management, representation and understanding. Neurocognitive informatics is a new, emerging field that should help to improve the matching of artificial and natural systems, and inspire better computational algorithms to solve problems that are still beyond the reach of machines. In this position paper examples of neurocognitive inspirations and promising directions in this area are given.