We study robust reinforcement learning (RL) with the goal of determining a well-performing policy that is robust against model mismatch between the training simulator and the testing environment. Previous policy-based robust RL algorithms mainly focus on the tabular setting under uncertainty sets that facilitate robust policy evaluation, but are no longer tractable when the number of states scales up. To this end, we propose two novel uncertainty set formulations, one based on double sampling and the other on an integral probability metric. Both make large-scale robust RL tractable even when one only has access to a simulator. We propose a robust natural actor-critic (RNAC) approach that incorporates the new uncertainty sets and employs function approximation. We provide finite-time convergence guarantees for the proposed RNAC algorithm to the optimal robust policy within the function approximation error. Finally, we demonstrate the robust performance of the policy learned by our proposed RNAC approach in multiple MuJoCo environments and a real-world TurtleBot navigation task.

We consider two-player zero-sum stochastic games and propose a two-timescale $Q$-learning algorithm with function approximation that is payoff-based, convergent, rational, and symmetric between the two players. In two-timescale $Q$-learning, the fast-timescale iterates are updated in spirit to the stochastic gradient descent and the slow-timescale iterates (which we use to compute the policies) are updated by taking a convex combination between its previous iterate and the latest fast-timescale iterate. Introducing the slow timescale as well as its update equation marks as our main algorithmic novelty. In the special case of linear function approximation, we establish, to the best of our knowledge, the first last-iterate finite-sample bound for payoff-based independent learning dynamics of these types. The result implies a polynomial sample complexity to find a Nash equilibrium in such stochastic games. To establish the results, we model our proposed algorithm as a two-timescale stochastic approximation and derive the finite-sample bound through a Lyapunov-based approach. The key novelty lies in constructing a valid Lyapunov function to capture the evolution of the slow-timescale iterates. Specifically, through a change of variable, we show that the update equation of the slow-timescale iterates resembles the classical smoothed best-response dynamics, where the regularized Nash gap serves as a valid Lyapunov function. This insight enables us to construct a valid Lyapunov function via a generalized variant of the Moreau envelope of the regularized Nash gap. The construction of our Lyapunov function might be of broad independent interest in studying the behavior of stochastic approximation algorithms.

To tackle long planning horizon problems in reinforcement learning with general function approximation, we propose the first algorithm, termed as UCRL-WVTR, that achieves both \emph{horizon-free} and \emph{instance-dependent}, since it eliminates the polynomial dependency on the planning horizon. The derived regret bound is deemed \emph{sharp}, as it matches the minimax lower bound when specialized to linear mixture MDPs up to logarithmic factors. Furthermore, UCRL-WVTR is \emph{computationally efficient} with access to a regression oracle. The achievement of such a horizon-free, instance-dependent, and sharp regret bound hinges upon (i) novel algorithm designs: weighted value-targeted regression and a high-order moment estimator in the context of general function approximation; and (ii) fine-grained analyses: a novel concentration bound of weighted non-linear least squares and a refined analysis which leads to the tight instance-dependent bound. We also conduct comprehensive experiments to corroborate our theoretical findings.

Hesitant fuzzy sets are widely used in the instances of uncertainty and hesitation. The inclusion relationship is an important and foundational definition for sets. Hesitant fuzzy set, as a kind of set, needs explicit definition of inclusion relationship. Base on the hesitant fuzzy membership degree of discrete form, several kinds of inclusion relationships for hesitant fuzzy sets are proposed. And then some foundational propositions of hesitant fuzzy sets and the families of hesitant fuzzy sets are presented. Finally, some foundational propositions of hesitant fuzzy information systems with respect to parameter reductions are put forward, and an example and an algorithm are given to illustrate the processes of parameter reductions.

In the context of autonomous driving, pedestrian crossing prediction is a key component for improving road safety. Presently, the focus of these predictions extends beyond achieving trustworthy results; it is shifting towards the explainability and interpretability of these predictions. This research introduces a novel neuro-symbolic approach that combines deep learning and fuzzy logic for an explainable and interpretable pedestrian crossing prediction. We have developed an explainable predictor (ExPedCross), which utilizes a set of explainable features and employs a fuzzy inference system to predict whether the pedestrian will cross or not. Our approach was evaluated on both the PIE and JAAD datasets. The results offer experimental insights into achieving explainability and interpretability in the pedestrian crossing prediction task. Furthermore, the testing results yield a set of guidelines and recommendations regarding the process of dataset selection, feature selection, and explainability.

Risk-sensitive reinforcement learning (RL) aims to optimize policies that balance the expected reward and risk. In this paper, we present a novel risk-sensitive RL framework that employs an Iterated Conditional Value-at-Risk (CVaR) objective under both linear and general function approximations, enriched by human feedback. These new formulations provide a principled way to guarantee safety in each decision making step throughout the control process. Moreover, integrating human feedback into risk-sensitive RL framework bridges the gap between algorithmic decision-making and human participation, allowing us to also guarantee safety for human-in-the-loop systems. We propose provably sample-efficient algorithms for this Iterated CVaR RL and provide rigorous theoretical analysis. Furthermore, we establish a matching lower bound to corroborate the optimality of our algorithms in a linear context.

The software for clustering students according to their educational achievements using fuzzy logic was developed in Python using the Google Colab cloud service. In the process of analyzing educational data, the problems of Data Mining are solved, since only some characteristics of the educational process are obtained from a large sample of data. Data clustering was performed using the classic K-Means method, which is characterized by simplicity and high speed. Cluster analysis was performed in the space of two features using the machine learning library scikit-learn (Python). The obtained clusters are described by fuzzy triangular membership functions, which allowed to correctly determine the membership of each student to a certain cluster. Creation of fuzzy membership functions is done using the scikit-fuzzy library. The development of fuzzy functions of objects belonging to clusters is also useful for educational purposes, as it allows a better understanding of the principles of using fuzzy logic. As a result of processing test educational data using the developed software, correct results were obtained. It is shown that the use of fuzzy membership functions makes it possible to correctly determine the belonging of students to certain clusters, even if such clusters are not clearly separated. Due to this, it is possible to more accurately determine the recommended level of difficulty of tasks for each student, depending on his previous evaluations.

In real-world tasks, there is usually a large amount of unlabeled data and labeled data. The task of combining the two to learn is known as semi-supervised learning. Experts can use logical rules to label unlabeled data, but this operation is costly. The combination of perception and reasoning has a good effect in processing such semi-supervised tasks with domain knowledge. However, acquiring domain knowledge and the correction, reduction and generation of rules remain complex problems to be solved. Rough set theory is an important method for solving knowledge processing in information systems. In this paper, we propose a rule general abductive learning by rough set (RS-ABL). By transforming the target concept and sub-concepts of rules into information tables, rough set theory is used to solve the acquisition of domain knowledge and the correction, reduction and generation of rules at a lower cost. This framework can also generate more extensive negative rules to enhance the breadth of the knowledge base. Compared with the traditional semi-supervised learning method, RS-ABL has higher accuracy in dealing with semi-supervised tasks.

Art objects can evoke certain emotions. Color is a fundamental element of visual art and plays a significant role in how art is perceived. This paper introduces a novel approach to classifying emotions in art using Fuzzy Sets. We employ a fuzzy approach because it aligns well with human judgments' imprecise and subjective nature. Extensive fuzzy colors (n=120) and a broad emotional spectrum (n=10) allow for a more human-consistent and context-aware exploration of emotions inherent in paintings. First, we introduce the fuzzy color representation model. Then, at the fuzzification stage, we process the Wiki Art Dataset of paintings tagged with emotions, extracting fuzzy dominant colors linked to specific emotions. This results in fuzzy color distributions for ten emotions. Finally, we convert them back to a crisp domain, obtaining a knowledge base of color-emotion associations in primary colors. Our findings reveal strong associations between specific emotions and colors; for instance, gratitude strongly correlates with green, brown, and orange. Other noteworthy associations include brown and anger, orange with shame, yellow with happiness, and gray with fear. Using these associations and Jaccard similarity, we can find the emotions in the arbitrary untagged image. We conducted a 2AFC experiment involving human subjects to evaluate the proposed method. The average hit rate of 0.77 indicates a significant correlation between the method's predictions and human perception. The proposed method is simple to adapt to art painting retrieval systems. The study contributes to the theoretical understanding of color-emotion associations in art, offering valuable insights for various practical applications besides art, like marketing, design, and psychology.

Online active learning is a paradigm in machine learning that aims to select the most informative data points to label from a data stream. The problem of minimizing the cost associated with collecting labeled observations has gained a lot of attention in recent years, particularly in real-world applications where data is only available in an unlabeled form. Annotating each observation can be time-consuming and costly, making it difficult to obtain large amounts of labeled data. To overcome this issue, many active learning strategies have been proposed in the last decades, aiming to select the most informative observations for labeling in order to improve the performance of machine learning models. These approaches can be broadly divided into two categories: static pool-based and stream-based active learning. Pool-based active learning involves selecting a subset of observations from a closed pool of unlabeled data, and it has been the focus of many surveys and literature reviews. However, the growing availability of data streams has led to an increase in the number of approaches that focus on online active learning, which involves continuously selecting and labeling observations as they arrive in a stream. This work aims to provide an overview of the most recently proposed approaches for selecting the most informative observations from data streams in real time. We review the various techniques that have been proposed and discuss their strengths and limitations, as well as the challenges and opportunities that exist in this area of research.