Abstract--In recent years, deep reinforcement learning (DRL) has gained traction for solving the NP-hard traveling salesman problem (TSP). However, limited attention has been given to the close-enough TSP (CETSP), primarily due to the challenge introduced by its neighborhood-based visitation criterion, wherein a node is considered visited if the agent enters a compact neighborhood around it. In this work, we formulate a Markov decision process (MDP) for CETSP using a discretization scheme and propose a novel unified dual-decoder DRL (UD3RL) framework that separates decision-making into node selection and waypoint determination. Specifically, an adapted encoder is employed for effective feature extraction, followed by a node-decoder and a loc-decoder to handle the two sub-tasks, respectively. A k-nearest neighbors subgraph interaction strategy is further introduced to enhance spatial reasoning during location decoding. Furthermore, we customize the REINFORCE algorithm to train UD3RL as a unified model capable of generalizing across different problem sizes and varying neighborhood radius types (i.e., constant and random radii). Experimental results show that UD3RL outperforms conventional methods in both solution quality and runtime, while exhibiting strong generalization across problem scales, spatial distributions, and radius ranges, as well as robustness to dynamic environments. HE close-enough traveling salesman problem (CETSP) is a well-known variant of the classical traveling salesman problem (TSP) that preserves its NP-hard complexity [1].

First provide a summary of the paper, and then address the following criteria: Quality, clarity, originality and significance. The paper proposes a new approach for Mahalanobis metric learning for k-nearest neighbor (kNN) classification. The main difference from the existing work is in the way how k nearest neighbors are found. Instead of simply looking for the k nearest neighbors, the authors are searching for the closest k examples that also guarantee correct classification (the authors refer to it as the gerrymandering). They propose a greedy algorithm to find such a neighborhood.

First provide a summary of the paper, and then address the following criteria: Quality, clarity, originality and significance. The authors provide finite sample bounds on the excess risk of these classifiers. When taken to the limit these bounds reproduce the known consistency results for this class. However, they are superior in two ways: 1. They apply in the finite case 2. They apply to a broader set of metric spaces The presentation is very clear and the intuition is well described.

Consider an unweighted k-nearest neighbor graph on n points that have been sampled i.i.d.

Distance-based approaches to outlier detection are popular in data mining, as they do not require to model the underlying probability distribution, which is particularly challenging for high-dimensional data. We present an empirical comparison of various approaches to distance-based outlier detection across a large number of datasets. We report the surprising observation that a simple, sampling-based scheme outperforms state-of-the-art techniques in terms of both efficiency and effectiveness. To better understand this phenomenon, we provide a theoretical analysis why the sampling-based approach outperforms alternative methods based on k-nearest neighbor search.

All the existing multi-task local learning methods are defined on homogeneous neighborhood which consists of all data points from only one task. In this paper, different from existing methods, we propose local learning methods for multi-task classification and regression problems based on heterogeneous neighborhood which is defined on data points from all tasks. Specifically, we extend the k-nearest-neighbor classifier by formulating the decision function for each data point as a weighted voting among the neighbors from all tasks where the weights are task-specific. By defining a regularizer to enforce the task-specific weight matrix to approach a symmetric one, a regularized objective function is proposed and an efficient coordinate descent method is developed to solve it. For regression problems, we extend the kernel regression to multi-task setting in a similar way to the classification case. Experiments on some toy data and real-world datasets demonstrate the effectiveness of our proposed methods.

We formulate the problem of metric learning for k nearest neighbor classification as a large margin structured prediction problem, with a latent variable representing the choice of neighbors and the task loss directly corresponding to classification error. We describe an efficient algorithm for exact loss augmented inference,and a fast gradient descent algorithm for learning in this model. The objective drives the metric to establish neighborhood boundaries that benefit the true class labels for the training points. Our approach, reminiscent of gerrymandering (redrawing of political boundaries to provide advantage to certain parties), is more direct in its handling of optimizing classification accuracy than those previously proposed. In experiments on a variety of data sets our method is shown to achieve excellent results compared to current state of the art in metric learning.

We investigate the recovery dynamics of healthy cardiac activity after physical exertion using multimodal biosignals recorded with a polycardiograph. Multifractal features derived from the singularity spectrum capture the scale-invariant properties of cardiovascular regulation. Five supervised classification algorithms - Logistic Regression (LogReg), Suport Vector Machine with RBF kernel (SVM-RBF), k-Nearest Neighbors (kNN), Decision Tree (DT), and Random Forest (RF) - were evaluated to distinguish recovery states in a small, imbalanced dataset. Our results show that multifractal analysis, combined with multimodal sensing, yields reliable features for characterizing recovery and points toward nonlinear diagnostic methods for heart conditions.