Related papers: Weaker Assumptions for the Short Path Optimization…
We revisit the problem of motion planning in the Gaussian belief space. Motivated by the fact that most existing sampling-based planners suffer from high computational costs due to the high-dimensional nature of the problem, we propose an…
We analyze the role played by entanglement in the dynamical evolution of Grover's search algorithm in the space of qubits. We show that the algorithm can be equivalently described as an iterative change of the entanglement between the…
We study worst-case guarantees on the expected return of fixed-dataset policy optimization algorithms. Our core contribution is a unified conceptual and mathematical framework for the study of algorithms in this regime. This analysis…
We consider a suboptimal solution path algorithm for the Support Vector Machine. The solution path algorithm is an effective tool for solving a sequence of a parametrized optimization problems in machine learning. The path of the solutions…
We consider optimal route planning when the objective function is a general nonlinear and non-monotonic function. Such an objective models user behavior more accurately, for example, when a user is risk-averse, or the utility function needs…
This paper focuses on automatic guided vehicle (AGV) trajectory planning in the presence of moving obstacles with known but complicated trajectories. In order to achieve good solution precision, optimality and unification, the concerned…
We propose a quantum algorithm, inspired by ADAPT-VQE, to variationally prepare the ground state of a quantum Hamiltonian, with the desirable property that if it fails to find the ground state, it still yields a physically meaningful…
Stochastic Shortest Path (SSP) MDPs is a problem class widely studied in AI, especially in probabilistic planning. They describe a wide range of scenarios but make the restrictive assumption that the goal is reachable from any state, i.e.,…
This paper presents the results of an experimental study of graph partitioning. We describe a new heuristic technique, path optimization, and its application to two variations of graph partitioning: the max_cut problem and the…
This short paper presents an efficient path following solution for ground vehicles tailored to game AI. Our focus is on adapting established techniques to design simple solutions with parameters that are easily tunable for an efficient…
Through the development of efficient algorithms, data structures and preprocessing techniques, real-world shortest path problems in street networks are now very fast to solve. But in reality, the exact travel times along each arc in the…
The Lookahead optimizer enhances deep learning models by employing a dual-weight update mechanism, which has been shown to improve the performance of underlying optimizers such as SGD. However, most theoretical studies focus on its…
Computing a shortest path between two nodes in an undirected unweighted graph is among the most basic algorithmic tasks. Breadth first search solves this problem in linear time, which is clearly also a lower bound in the worst case.…
We develop a toolbox for exact analysis of iterative algorithms on a class of high-dimensional nonconvex optimization problems with random data. While prior work has shown that low-dimensional statistics of (generalized) first-order methods…
We consider slow-fast systems of differential equations, in which both the slow and fast variables are perturbed by noise. When the deterministic system admits a uniformly asymptotically stable slow manifold, we show that the sample paths…
We consider gradient descent with `momentum', a widely used method for loss function minimization in machine learning. This method is often used with `Nesterov acceleration', meaning that the gradient is evaluated not at the current…
The purpose of this work is to introduce and characterize the Bounded Acceleration Shortest Path (BASP) problem, a generalization of the Shortest Path (SP) problem. This problem is associated to a graph: the nodes represent positions of a…
Shortest path algorithms have played a key role in the past century, paving the way for modern day GPS systems to find optimal routes along static systems in fractions of a second. One application of these algorithms includes optimizing the…
This paper considers stochastic weakly convex optimization without the standard Lipschitz continuity assumption. Based on new adaptive regularization (stepsize) strategies, we show that a wide class of stochastic algorithms, including the…
Numerous algorithms and parallelisations have been developed for short-range particle simulations; however, none are optimally performant for all scenarios. Such a concept led to the prior development of the particle simulation library…