相关论文: A Symplectic Analysis of Alternating Mirror Descen…

Based on the ideas of arXiv:1710.06612, we consider the problem of minimization of the Holder-continuous non-smooth functional $f$ with non-positive convex (generally, non-smooth) Lipschitz-continuous functional constraint. We propose some…

This work focuses on the setting of dynamic regret in the context of online learning with full information. In particular, we analyze regret bounds with respect to the temporal variability of the loss functions. By assuming that the…

We consider centralized and distributed mirror descent algorithms over a finite-dimensional Hilbert space, and prove that the problem variables converge to an optimizer of a possibly nonsmooth function when the step sizes are square…

We study convergence rates of Hamiltonian Monte Carlo (HMC) algorithms with leapfrog integration under mild conditions on stochastic gradient oracle for the target distribution (SGHMC). Our method extends standard HMC by allowing the use of…

The Metropolis-Hastings algorithm allows one to sample asymptotically from any probability distribution $\pi$. There has been recently much work devoted to the development of variants of the MH update which can handle scenarios where such…

Accelerated gradient methods have had significant impact in machine learning -- in particular the theoretical side of machine learning -- due to their ability to achieve oracle lower bounds. But their heuristic construction has hindered…

We present a new algorithm based on posterior sampling for learning in constrained Markov decision processes (CMDP) in the infinite-horizon undiscounted setting. The algorithm achieves near-optimal regret bounds while being advantageous…

Kinetic energy equipartition is a premise for many deterministic and stochastic molecular dynamics methods that aim at sampling a canonical ensemble. While this is expected for real systems, discretization errors introduced by the numerical…

Mirror Descent (MD) is a scalable first-order method widely used in large-scale optimization, with applications in image processing, policy optimization, and neural network training. This paper generalizes MD to optimization on Riemannian…

Optimization tasks are crucial in statistical machine learning. Recently, there has been great interest in leveraging tools from dynamical systems to derive accelerated and robust optimization methods via suitable discretizations of…

Non-smooth optimization models play a fundamental role in various disciplines, including engineering, science, management, and finance. However, classical algorithms for solving such models often struggle with convergence speed,…

In this note, we propose a symplectic algorithm for the stable manifolds of the Hamilton-Jacobi equations combined with an iterative procedure in [Sakamoto-van~der Schaft, IEEE Transactions on Automatic Control, 2008]. Our algorithm…

The paper focuses on the development of numerical methods for the compressible Euler equations. It is well-known that if the Mach number is small, the system becomes stiff and hence explicit schemes suffer from severe time-step…

Mirror descent (MD) is a powerful first-order optimization technique that subsumes several optimization algorithms including gradient descent (GD). In this work, we develop a semi-definite programming (SDP) framework to analyze the…

A new method is proposed for integrating the equations of motion of an elastic filament. In the standard finite-difference and finite-element formulations the continuum equations of motion are discretized in space and time, but it is then…

In this paper, we consider the online proximal mirror descent for solving the time-varying composite optimization problems. For various applications, the algorithm naturally involves the errors in the gradient and proximal operator. We…

In this paper, we propose, analyze, and test an efficient algorithm for computing ensemble average of incompressible magnetohydrodynamics (MHD) flows, where instances/members correspond to varying kinematic viscosity, magnetic diffusivity,…

We implement and investigate the numerical properties of a new family of integrators connecting both variants of the symplectic Euler schemes, and including an alternative to the classical symplectic mid-point scheme, with some additional…

We report on what seems to be an intriguing connection between variable integration time and partial velocity refreshment of Ideal Hamiltonian Monte Carlo samplers, both of which can be used for reducing the dissipative behavior of the…

An outstanding property of any Hamiltonian system is the symplecticity of its flow, namely, the continuous trajectory preserves volume in phase space. Given a symplectic but discrete trajectory generated by a transition matrix applied at a…