Related papers: Methods to locate Saddle Points in Complex Landsca…
We analyze stochastic gradient descent for optimizing non-convex functions. In many cases for non-convex functions the goal is to find a reasonable local minimum, and the main concern is that gradient updates are trapped in saddle points.…
We analyze the semi-implicit scheme of high-index saddle dynamics, which provides a powerful numerical method for finding the any-index saddle points and constructing the solution landscape. Compared with the explicit schemes of saddle…
We introduce a saddle-point finder that can find the complex saddle points for any analytically continued action. We showcase our saddle-point finder by two examples in the EPRL spin foam model: the single vertex case and the case of…
Path finding is a well-studied problem in AI, which is often framed as graph search. Any-angle path finding is a technique that augments the initial graph with additional edges to build shorter paths to the goal. Indeed, optimal algorithms…
A path from s to t on a polyhedral terrain is descending if the height of a point p never increases while we move p along the path from s to t. No efficient algorithm is known to find a shortest descending path (SDP) from s to t in a…
This paper shows that a perturbed form of gradient descent converges to a second-order stationary point in a number iterations which depends only poly-logarithmically on dimension (i.e., it is almost "dimension-free"). The convergence rate…
In this paper we consider regression problems subject to arbitrary noise in the operator or design matrix. This characterization appropriately models many physical phenomena with uncertainty in the regressors. Although the problem has been…
Many methods in learning from demonstration assume that the demonstrator has knowledge of the full environment. However, in many scenarios, a demonstrator only sees part of the environment and they continuously replan as they gather…
Slow manifolds are important geometric structures in the state spaces of dynamical systems with multiple time scales. This paper introduces an algorithm for computing trajectories on slow manifolds that are normally hyperbolic with both…
Algorithms for computing local minima of smooth objective functions enjoy a mature theory as well as robust and efficient implementations. By comparison, the theory and practice of saddle search is destitute. In this paper we present…
We propose perturbed proximal algorithms that can provably escape strict saddles for nonsmooth weakly convex functions. The main results are based on a novel characterization of $\epsilon$-approximate local minimum for nonsmooth functions,…
A path from s to t on a polyhedral terrain is descending if the height of a point p never increases while we move p along the path from s to t. No efficient algorithm is known to find a shortest descending path (SDP) from s to t in a…
Real-time path planning in constrained environments remains a fundamental challenge for autonomous systems. Traditional classical planners, while effective under perfect perception assumptions, are often sensitive to real-world perception…
This work considers a Motion Planning Problem with Dynamic Obstacles (MPDO) in 2D that requires finding a minimum-arrival-time collision-free trajectory for a point robot between its start and goal locations amid dynamic obstacles moving…
In this paper we consider the problem of finding an evolution of a dynamical system that originates and terminates in given sets of states. However, if such an evolution exists then it is usually not unique. We investigate this problem and…
It is an old idea to use gradient flows or time-discretized variants thereof as methods for solving minimization problems. In some applications, for example in machine learning contexts, it is important to know that for generic initial…
Popular methods for identifying transition paths between energy minima, such as the nudged elastic band and string methods, typically do not incorporate potential energy curvature information, leading to slow relaxation to the minimum…
We consider convex-concave saddle-point problems where the objective functions may be split in many components, and extend recent stochastic variance reduction methods (such as SVRG or SAGA) to provide the first large-scale linearly…
Efficient and reliable identification and optimization of transition state structures is a longstanding challenge in computational chemistry. Popular chain-of-states methods require hundreds if not thousands of ab initio calculations to…
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.,…