The current paper studies the problem of agnostic Q -learning with function approximation in deterministic systems where the optimal Q -function is approximable by a function in the class \mathcal{F} with approximation error \delta \ge 0 . We propose a novel recursion-based algorithm and show that if \delta O\left(\rho/\sqrt{\dim_E}\right), then one can find the optimal policy using O(\dim_E) trajectories, where \rho is the gap between the optimal Q -value of the best actions and that of the second-best actions and \dim_E is the Eluder dimension of \mathcal{F} . Our result has two implications: \begin{enumerate} \item In conjunction with the lower bound in [Du et al., 2020], our upper bound suggests that the condition \delta \widetilde{\Theta}\left(\rho/\sqrt{\dim_E}\right) is necessary and sufficient for algorithms with polynomial sample complexity. We further extend our algorithm to the stochastic reward setting and obtain similar results.

Random fuzzy variables join the modeling of the impreciseness (due to their ``fuzzy part'') and randomness. Statistical samples of such objects are widely used, and their direct, numerically effective generation is therefore necessary. Usually, these samples consist of triangular or trapezoidal fuzzy numbers. In this paper, we describe theoretical results and simulation algorithms for another family of fuzzy numbers -- LR fuzzy numbers with interval-valued cores. Starting from a simulation perspective on the piecewise linear LR fuzzy numbers with the interval-valued cores, their limiting behavior is then considered. This leads us to the numerically efficient algorithm for simulating a sample consisting of such fuzzy values.

We provide a theoretical framework for analyzing basis function construction for linear value function approximation in Markov Decision Processes (MDPs). We show that important existing methods, such as Krylov bases and Bellman-error-based methods are a special case of the general framework we develop. We provide a general algorithmic framework for computing basis function refinements which "respect" the dynamics of the environment, and we derive approximation error bounds that apply for any algorithm respecting this general framework. We also show how, using ideas related to bisimulation metrics, one can translate basis refinement into a process of finding "prototypes" that are diverse enough to represent the given MDP.

This paper introduces a novel tree-based model, Learning Hyperplane Tree (LHT), which outperforms state-of-the-art (SOTA) tree models for classification tasks on several public datasets. The structure of LHT is simple and efficient: it partitions the data using several hyperplanes to progressively distinguish between target and non-target class samples. Although the separation is not perfect at each stage, LHT effectively improves the distinction through successive partitions. During testing, a sample is classified by evaluating the hyperplanes defined in the branching blocks and traversing down the tree until it reaches the corresponding leaf block. The class of the test sample is then determined using the piecewise linear membership function defined in the leaf blocks, which is derived through least-squares fitting and fuzzy logic. LHT is highly transparent and interpretable--at each branching block, the contribution of each feature to the classification can be clearly observed.

This article discusses the integration of the Artificial Bee Colony (ABC) algorithm with two supervised learning methods, namely Artificial Neural Networks (ANNs) and Adaptive Network-based Fuzzy Inference System (ANFIS), for feature selection from Near-Infrared (NIR) spectra for predicting the molecular weight of medical-grade Polylactic Acid (PLA). During extrusion processing of PLA, in-line NIR spectra were captured along with extrusion process and machine setting data. With a dataset comprising 63 observations and 512 input features, appropriate machine learning tools are essential for interpreting data and selecting features to improve prediction accuracy. Initially, the ABC optimization algorithm is coupled with ANN/ANFIS to forecast PLA molecular weight. The objective functions of the ABC algorithm are to minimize the root mean square error (RMSE) between experimental and predicted PLA molecular weights while also minimizing the number of input features. Results indicate that employing ABC-ANFIS yields the lowest RMSE of 282 Da and identifies four significant parameters (NIR wavenumbers 6158 cm-1, 6310 cm-1, 6349 cm-1, and melt temperature) for prediction. These findings demonstrate the effectiveness of using the ABC algorithm with ANFIS for selecting a minimal set of features to predict PLA molecular weight with high accuracy during processing

In-context learning, which allows large language models to perform diverse tasks with a few demonstrations, is found to have imbalanced per-class prediction accuracy on multi-class text classification. Although notable output correction methods have been developed to tackle the issue and simultaneously improve downstream prediction accuracy, they may fail to answer the core interpretability challenges: why and which certain classes need corrections, and more importantly, a tailored correction for per-sample, per-class's probability. To address such interpretability gaps, we first find that the imbalance arises from certain classes consistently receiving high ICL output probabilities, whereas others receiving lower or mixed ranges, so the former is more frequently chosen, resulting in higher accuracy; more crucially, we find that these ranges have significantly varying degrees of influence on the accuracy bias, highlighting the need for precise, interpretable probability corrections by range. Motivated by this, we propose FuRud, a Fuzzy Rule Optimization based Debiasing method, that (1) detects which classes need corrections, and (2) for each correction-needed class, detects its probability ranges and applies asymmetric amplifications or reductions to correct them interpretably. Notably, across seven benchmark datasets, FuRud reduces the pairwise class accuracy bias (COBias) by more than half (56%), while achieving a relative increase of 21% in accuracy, outperforming state-of-the-art debiasing methods. Moreover, FuRud can optimize downstream tasks with as few as 10 optimization examples. Furthermore, FuRud can work for prompt formats that lead to highly skewed predictions. For example, FuRud greatly improves ICL outputs which use letter options, with 44% relative accuracy increase and 54% relative COBias reduction.

The fuzzy job shop scheduling problem (FJSSP) emerges as an innovative extension to the job shop scheduling problem (JSSP), incorporating a layer of uncertainty that aligns the problem more closely with the complexities of real-world manufacturing environments. This improvement increases the computational complexity of deriving the solution while improving its applicability. In the domain of deterministic scheduling, neural combinatorial optimization (NCO) has recently demonstrated remarkable efficacy. However, its application to the realm of fuzzy scheduling has been relatively unexplored. This paper aims to bridge this gap by investigating the feasibility of employing neural networks to assimilate and process fuzzy information for the resolution of FJSSP, thereby leveraging the advancements in NCO to enhance fuzzy scheduling methodologies. To achieve this, we approach the FJSSP as a generative task and introduce an expectation-maximization algorithm-based autoregressive model (EMARM) to address it. During training, our model alternates between generating scheduling schemes from given instances (E-step) and adjusting the autoregressive model weights based on these generated schemes (M-step). This novel methodology effectively navigates around the substantial hurdle of obtaining ground-truth labels, which is a prevalent issue in NCO frameworks. In testing, the experimental results demonstrate the superior capability of EMARM in addressing the FJSSP, showcasing its effectiveness and potential for practical applications in fuzzy scheduling.

The performance of pavement under loading depends on the strength of the subgrade. However, experimental estimation of properties of pavement strengths such as California bearing ratio (CBR), unconfined compressive strength (UCS) and resistance value (R) are often tedious, time-consuming and costly, thereby inspiring a growing interest in machine learning based tools which are simple, cheap and fast alternatives. Thus, the potential application of two boosting techniques; categorical boosting (CatBoost) and extreme gradient boosting (XGBoost) and support vector regression (SVR), is similarly explored in this study for estimation of properties of subgrade soil modified with hydrated lime activated rice husk ash (HARSH). Using 121 experimental data samples of varying proportions of HARSH, plastic limit, liquid limit, plasticity index, clay activity, optimum moisture content, and maximum dry density as input for CBR, UCS and R estimation, four evaluation metrics namely coefficient of determination (R2), root mean squared error (RMSE), mean absolute error (MAE) and mean absolute percentage error (MAPE) are used to evaluate the models' performance. The results indicate that XGBoost outperformed CatBoost and SVR in estimating these properties, yielding R2 of 0.9994, 0.9995 and 0.9999 in estimating the CBR, UCS and R respectively. Also, SVR outperformed CatBoost in estimating the CBR and R with R2 of 0.9997 respectively. On the other hand, CatBoost outperformed SVR in estimating the UCS with R2 of 0.9994. Feature sensitivity analysis shows that the three machine learning techniques are unanimous that increasing HARSH proportion lead to values of the estimated properties respectively. A comparison with previous results also shows superiority of XGBoost in estimating subgrade properties.

Outlier detection refers to the identification of anomalous samples that deviate significantly from the distribution of normal data and has been extensively studied and used in a variety of practical tasks. However, most unsupervised outlier detection methods are carefully designed to detect specified outliers, while real-world data may be entangled with different types of outliers. In this study, we propose a fuzzy rough sets-based multi-scale outlier detection method to identify various types of outliers. Specifically, a novel fuzzy rough sets-based method that integrates relative fuzzy granule density is first introduced to improve the capability of detecting local outliers. Then, a multi-scale view generation method based on granular-ball computing is proposed to collaboratively identify group outliers at different levels of granularity. Moreover, reliable outliers and inliers determined by the three-way decision are used to train a weighted support vector machine to further improve the performance of outlier detection. The proposed method innovatively transforms unsupervised outlier detection into a semi-supervised classification problem and for the first time explores the fuzzy rough sets-based outlier detection from the perspective of multi-scale granular balls, allowing for high adaptability to different types of outliers. Extensive experiments carried out on both artificial and UCI datasets demonstrate that the proposed outlier detection method significantly outperforms the state-of-the-art methods, improving the results by at least 8.48% in terms of the Area Under the ROC Curve (AUROC) index. { The source codes are released at \url{https://github.com/Xiaofeng-Tan/MGBOD}. }

Traditionally, TD and FQI are viewed as differing in the number of updates toward the target value function: TD makes one update, FQI makes an infinite number, and Partial Fitted Q-Iteration (PFQI) performs a finite number, such as the use of a target network in Deep Q-Networks (DQN) in the OPE setting. This perspective, however, fails to capture the convergence connections between these algorithms and may lead to incorrect conclusions, for example, that the convergence of TD implies the convergence of FQI. In this paper, we focus on linear value function approximation and offer a new perspective, unifying TD, FQI, and PFQI as the same iterative method for solving the Least Squares Temporal Difference (LSTD) system, but using different preconditioners and matrix splitting schemes. TD uses a constant preconditioner, FQI employs a data-feature adaptive preconditioner, and PFQI transitions between the two. Then, we reveal that in the context of linear function approximation, increasing the number of updates under the same target value function essentially represents a transition from using a constant preconditioner to data-feature adaptive preconditioner. This unifying perspective also simplifies the analyses of the convergence conditions for these algorithms and clarifies many issues. Consequently, we fully characterize the convergence of each algorithm without assuming specific properties of the chosen features (e.g., linear independence). We also examine how common assumptions about feature representations affect convergence, and discover new conditions on features that are important for convergence. These convergence conditions allow us to establish the convergence connections between these algorithms and to address important questions.