During the exploration phase, an agent collects samples without using a pre-specified reward function.

Real-world reinforcement learning (RL) applications often come with possibly infinite state and action space, and in such a situation classical RL algorithms developed in the tabular setting are not applicable anymore. A popular approach to overcoming this issue is by applying function approximation techniques to the underlying structures of the Markov decision processes (MDPs).

Consequently, the state of the environment changes according to the transition function of the underlying MDP, as a function of the previous state and the action taken by the learner.

In reinforcement learning (RL), an agent interacts with a stochastic environment in order to maximize the total reward [Sutton and Barto, 2018].

We consider learning Nash equilibria in two-player zero-sum Markov Games with nonlinear function approximation, where the action-value function is approximated by a function in a Reproducing Kernel Hilbert Space (RKHS). The key challenge is how to do exploration in the high-dimensional function space. We propose a novel online learning algorithm to find a Nash equilibrium by minimizing the duality gap. At the core of our algorithms are upper and lower confidence bounds that are derived based on the principle of optimism in the face of uncertainty. We prove that our algorithm is able to attain an O(\sqrt{T}) regret with polynomial computational complexity, under very mild assumptions on the reward function and the underlying dynamic of the Markov Games.

We introduce a modular prompting framework that supports safer and more adaptive use of large language models (LLMs) across dynamic, user-centered tasks. Grounded in human learning theory, particularly the Zone of Proximal Development (ZPD), our method combines a natural language boundary prompt with a control schema encoded with fuzzy scaffolding logic and adaptation rules. This architecture enables LLMs to modulate behavior in response to user state without requiring fine-tuning or external orchestration. In a simulated intelligent tutoring setting, the framework improves scaffolding quality, adaptivity, and instructional alignment across multiple models, outperforming standard prompting baselines. Evaluation is conducted using rubric-based LLM graders at scale. While initially developed for education, the framework has shown promise in other interaction-heavy domains, such as procedural content generation for games. Designed for safe deployment, it provides a reusable methodology for structuring interpretable, goal-aligned LLM behavior in uncertain or evolving contexts.

Abstract: This research proposes a robust adaptive fuzzy sliding mode control (AFSMC) approach to enhance the trajectory tracking performance of cylindrical robotic manipulators, extensively utilized in applications such as CNC and 3D printing. The proposed approach integrates fuzzy logic with sliding mode control (SMC) to bolster adaptability and robustness, with fuzzy logic approximating the uncertain dynamics of the system, while SMC ensures strong performance. Simulation results in MATLAB/Simulink demonstrate that AFSMC significantly improves trajectory tracking accuracy, stability, and disturbance rejection compared to traditional methods. This research underscores the effectiveness of AFSMC in controlling robotic manipulators, contributing to enhanced precision in industrial robotic applications. Keywords: Adaptive Fuzzy Sliding Mode Control (AFSMC), Sliding Mode Control (SMC), Fuzzy Logic, Robotic Manipulators, Cylindrical Manipulator 1. INTRODUCTION Cylindrical robotic manipulators, combining a prismatic and a revolute joint, are extensively utilized in applications such as CNC machining, 3D printing, and assembly tasks.

Unsupervised classification is a fundamental machine learning problem. Real-world data often contain imperfections, characterized by uncertainty and imprecision, which are not well handled by traditional methods. Evidential clustering, based on Dempster-Shafer theory, addresses these challenges. This paper explores the underexplored problem of explaining evidential clustering results, which is crucial for high-stakes domains such as healthcare. Our analysis shows that, in the general case, representativity is a necessary and sufficient condition for decision trees to serve as abductive explainers. Building on the concept of representativity, we generalize this idea to accommodate partial labeling through utility functions. These functions enable the representation of "tolerable" mistakes, leading to the definition of evidential mistakeness as explanation cost and the construction of explainers tailored to evidential classifiers. Finally, we propose the Iterative Evidential Mistake Minimization (IEMM) algorithm, which provides interpretable and cautious decision tree explanations for evidential clustering functions. We validate the proposed algorithm on synthetic and real-world data. Taking into account the decision-maker's preferences, we were able to provide an explanation that was satisfactory up to 93% of the time.

The Polymorphic Combinatorial Framework (PCF) leverages Large Language Models (LLMs) and mathematical frameworks to guide the meta-prompt enabled design of solution spaces and adaptive AI agents for complex, dynamic environments. Unlike static agent architectures, PCF enables real-time parameter reconfiguration through mathematically-grounded combinatorial spaces, allowing agents to adapt their core behavioral traits dynamically. Grounded in combinatorial logic, topos theory, and rough fuzzy set theory, PCF defines a multidimensional SPARK parameter space (Skills, Personalities, Approaches, Resources, Knowledge) to capture agent behaviors. This paper demonstrates how LLMs can parameterize complex spaces and estimate likely parameter values/variabilities. Using PCF, we parameterized mock café domains (five levels of complexity), estimated variables/variabilities, and conducted over 1.25 million Monte Carlo simulations. The results revealed trends in agent adaptability and performance across the five complexity tiers, with diminishing returns at higher complexity levels highlighting thresholds for scalable designs. PCF enables the generation of optimized agent configurations for specific scenarios while maintaining logical consistency. This framework supports scalable, dynamic, explainable, and ethical AI applications in domains like customer service, healthcare, robotics, and collaborative systems, paving the way for adaptable and cooperative next-generation polymorphic agents.

The emergence of Symbiotic AI (SAI) introduces new challenges to ethical decision-making as it deepens human-AI collaboration. As symbiosis grows, AI systems pose greater ethical risks, including harm to human rights and trust. Ethical Risk Assessment (ERA) thus becomes crucial for guiding decisions that minimize such risks. However, ERA is hindered by uncertainty, vagueness, and incomplete information, and morality itself is context-dependent and imprecise. This motivates the need for a flexible, transparent, yet robust framework for ERA. Our work supports ethical decision-making by quantitatively assessing and prioritizing multiple ethical risks so that artificial agents can select actions aligned with human values and acceptable risk levels. We introduce ff4ERA, a fuzzy framework that integrates Fuzzy Logic, the Fuzzy Analytic Hierarchy Process (FAHP), and Certainty Factors (CF) to quantify ethical risks via an Ethical Risk Score (ERS) for each risk type. The final ERS combines the FAHP-derived weight, propagated CF, and risk level. The framework offers a robust mathematical approach for collaborative ERA modeling and systematic, step-by-step analysis. A case study confirms that ff4ERA yields context-sensitive, ethically meaningful risk scores reflecting both expert input and sensor-based evidence. Risk scores vary consistently with relevant factors while remaining robust to unrelated inputs. Local sensitivity analysis shows predictable, mostly monotonic behavior across perturbations, and global Sobol analysis highlights the dominant influence of expert-defined weights and certainty factors, validating the model design. Overall, the results demonstrate ff4ERA ability to produce interpretable, traceable, and risk-aware ethical assessments, enabling what-if analyses and guiding designers in calibrating membership functions and expert judgments for reliable ethical decision support.