相关论文: Higher Order Force Gradient Symplectic Algorithms

We study periodic orbits in the spatial rotating Kepler problem from a symplectic-topological perspective. Our first main result provides a complete classification of these orbits via a natural parametrization of the space of Kepler orbits,…

Shuffling gradient methods are widely used in modern machine learning tasks and include three popular implementations: Random Reshuffle (RR), Shuffle Once (SO), and Incremental Gradient (IG). Compared to the empirical success, the…

Recent work on high-resolution ordinary differential equations (HR-ODEs) captures fine nuances among different momentum-based optimization methods, leading to accurate theoretical insights. However, these HR-ODEs often appear disconnected,…

We show that the herding procedure of Welling (2009) takes exactly the form of a standard convex optimization algorithm--namely a conditional gradient algorithm minimizing a quadratic moment discrepancy. This link enables us to invoke…

This paper provides a theoretical and numerical comparison of classical first-order splitting methods for solving smooth convex optimization problems and cocoercive equations. From a theoretical point of view, we compare convergence rates…

We provide improved convergence rates for constrained convex-concave min-max problems and monotone variational inequalities with higher-order smoothness. In min-max settings where the $p^{th}$-order derivatives are Lipschitz continuous, we…

In this paper, we study the Lagrangian functions for a class of second-order differential systems arising from physics. For such systems, we present necessary and sufficient conditions for the existence of Lagrangian functions. Based on the…

Combinatorial optimization is frequently used in computer vision. For instance, in applications like semantic segmentation, human pose estimation and action recognition, programs are formulated for solving inference in Conditional Random…

Geometric properties can be leveraged to stabilize and speed reinforcement learning. Existing examples include encoding symmetry structure, geometry-aware data augmentation, and enforcing structural restrictions. In this paper, we take a…

We consider the problem of control in the setting of reinforcement learning (RL), where model information is not available. Policy gradient algorithms are a popular solution approach for this problem and are usually shown to converge to a…

We present in this paper two different classes of general $K$-splitting algorithms for solving finite-dimensional convex optimization problems. Under the assumption that the function being minimized has a Lipschitz continuous gradient, we…

Solving inverse problems, such as parameter estimation and optimal control, is a vital part of science. Many experiments repeatedly collect data and rely on machine learning algorithms to quickly infer solutions to the associated inverse…

We present a new symplectic integrator designed for collisional gravitational $N$-body problems which makes use of Kepler solvers. The integrator is also reversible and conserves 9 integrals of motion of the $N$-body problem to machine…

We propose a new concept of a relatively inexact stochastic subgradient and present novel first-order methods that can use such objects to approximately solve convex optimization problems in relative scale. An important example where…

We consider the problem of Cost-Aware Learning, where sampling different component functions of a finite-sum objective incurs different costs. The objective is to reach a target error while minimizing the total cost. First, we propose the…

One of the most attractive recent approaches to processing well-structured large-scale convex optimization problems is based on smooth convex-concave saddle point reformu-lation of the problem of interest and solving the resulting problem…

We investigate higher order symplectic integration strategies within Bayesian cosmic density field reconstruction methods. In particular, we study the fourth-order discretisation of Hamiltonian equations of motion (EoM). This is achieved by…

We propose two policy gradient algorithms for solving the problem of control in an off-policy reinforcement learning (RL) context. Both algorithms incorporate a smoothed functional (SF) based gradient estimation scheme. The first algorithm…

Local search heuristics for non-convex optimizations are popular in applied machine learning. However, in general it is hard to guarantee that such algorithms even converge to a local minimum, due to the existence of complicated saddle…

We investigate how sorting algorithms efficiently overcome the exponential size of the permutation space. Our main contribution is a new continuous-time formulation of sorting as a gradient flow on the permutohedron, yielding an independent…