Related papers: Breadth-First Search vs. Restarting Random Walks f…

These notes are devoted to fluctuations of one-dimensional random walks. We discuss various approaches to first-passage times and to the corresponding conditional distributions. After discussion of some classical methods, such as reflection…

We propose a novel algorithm for greedy forward feature selection for regularized least-squares (RLS) regression and classification, also known as the least-squares support vector machine or ridge regression. The algorithm, which we call…

Analytical results for the distribution of first hitting times of random walks on Erd\H{o}s-R\'enyi networks are presented. Starting from a random initial node, a random walker hops between adjacent nodes until it hits a node which it has…

Rapidly-exploring random trees (RRTs) are popular in motion planning because they find solutions efficiently to single-query problems. Optimal RRTs (RRT*s) extend RRTs to the problem of finding the optimal solution, but in doing so…

Random walks (RWs) are fundamental stochastic processes with applications across physics, computer science, and information processing. A recent extension, the laser chaos decision-maker, employs chaotic time series from semiconductor…

We study a discrete time self interacting random process on graphs, which we call Greedy Random Walk. The walker is located initially at some vertex. As time evolves, each vertex maintains the set of adjacent edges touching it that have not…

We study a one-dimensional random walk with memory. The behavior of the walker is modified with respect to the simple symmetric random walk (SSRW) only when he is at the maximum distance ever reached from his starting point (home). In this…

This note recapitulates an algorithmic observation for ordered Depth-First Search (DFS) in directed graphs that immediately leads to a parallel algorithm with linear speed-up for a range of processors for non-sparse graphs. The note extends…

Continuous-time quantum walks are natural tools for spatial search, where one searches for a marked vertex in a graph. Sometimes, the structure of the graph causes the walker to get trapped, such that the probability of finding the marked…

Hypergraphs are data structures capable of capturing supra-dyadic relations. We can use them to model binary relations, but also to model groups of entities, as well as the intersections between these groups or the contained subgroups. In…

The amount and variety of data is increasing drastically for several years. These data are often represented as networks, which are then explored with approaches arising from network theory. Recent years have witnessed the extension of…

Autonomous robot person-following (RPF) systems are crucial for personal assistance and security but suffer from target loss due to occlusions in dynamic, unknown environments. Current methods rely on pre-built maps and assume static…

Robots are increasingly deployed in dynamic and crowded environments, such as urban areas and shopping malls, where efficient and robust navigation is crucial. Traditional risk-based motion planning algorithms face challenges in such…

We consider the neighborhood tree induced by alternating the use of different neighborhood structures within a local search descent. We investigate the issue of designing a search strategy operating at the neighborhood tree level by…

The autonomous exploration of environments by multi-robot systems is a critical task with broad applications in rescue missions, exploration endeavors, and beyond. Current approaches often rely on either greedy frontier selection or…

In quadruped gait learning, policy search methods that scale high dimensional continuous action spaces are commonly used. In most approaches, it is necessary to introduce prior knowledge on the gaits to limit the highly non-convex search…

This paper examines the performance of spatial search where the Grover diffusion operator is replaced by continuous-time quantum walks on a class of interdependent networks. We prove that for a set of optimal quantum walk times and marked…

This paper considers the path planning problem for autonomous exploration of an unknown environment using multiple heterogeneous robots such as drones, wheeled, and legged robots, which have different capabilities to traverse complex…

Exploration is a difficult challenge in reinforcement learning and even recent state-of-the art curiosity-based methods rely on the simple epsilon-greedy strategy to generate novelty. We argue that pure random walks do not succeed to…

Model-based reinforcement learning algorithms with probabilistic dynamical models are amongst the most data-efficient learning methods. This is often attributed to their ability to distinguish between epistemic and aleatoric uncertainty.…