arXiv research

In this paper, we propose two discontinuous dynamical systems in continuous time with guaranteed prescribed finite-time local convergence to strict local minima of a given cost function. Our approach consists of exploiting a Lyapunov-based differential inequality for differential inclusions, which leads to finite-time …

We investigate finite-time decoupled convergence in nonlinear two-time-scale stochastic approximation.

The paper analyzes deep neural networks using control theory to set a time limit for their convergence.

In this paper, we consider multi-agent learning via online gradient descent in a class of games called $λ$-cocoercive games, a fairly broad class of games that admits many Nash equilibria and that properly includes unconstrained strongly monotone games. We characterize the finite-time last-iterate convergence rate for …

Study shows how a curve shortens to a half-circle under specific flow.

Improved convergence rates for Stein Variational Gradient Descent in finite-particle settings.

Paper shows no finite time singularities for smooth conformal heat flow of harmonic maps.

Paper analyzes convergence of dynamic policy gradient for MDPs, improving performance in finite-time problems.

First-order method solves stochastic bilevel optimization with linear constraints.

Study on convergence of Langevin dynamics for zero-sum games in probability distributions.

Paper analyzes finite-time convergence of double Q-learning.

Policy gradient methods achieve linear convergence in simple MDPs.

Cyclic coordinate descent identifies models in finite time and converges linearly.

This work analyzes actor-critic methods for faster convergence.

This work analyzes $Q$-learning with adaptive stepsizes for finite-time convergence.

Curve shortening flow converges to a point with entropy bound.

Theoretical justification for asymmetric actor-critic algorithms in reinforcement learning.

Local existence and uniqueness of Bakry-Émery Ricci flow solutions on finite graphs.

Paper analyzes convergence rates of two time-scale AC and NAC algorithms.

We show some results for the $L^2$ curvature flow linked by the theme of addressing collapsing phenomena. First we show long time existence and convergence of the flow for $SO(3)$-invariant initial data on $S^3$, as well as a long time existence and convergence statement for three-manifolds with initial $L^2$ norm of c…

The article explores Helfrich flow with spontaneous curvature, finding singularities and convergence behaviors.

Given any embedded Lagrangian on a four dimensional compact Calabi-Yau, we find another Lagrangian in the same Hamiltonian isotopy class which develops a finite time singularity under mean curvature flow. This contradicts a weaker version of the Thomas-Yau conjecture regarding long time existence and convergence of Lag…

Paper analyzes SVGD algorithm for non-asymptotic convergence.

Stochastic gradient descent (SGD) is almost ubiquitously used for training non-convex optimization tasks. Recently, a hypothesis proposed by Keskar et al. [2017] that large batch methods tend to converge to sharp minimizers has received increasing attention. We theoretically justify this hypothesis by providing new pro…

We study finite-time collapsing limits of the continuity method. When the continuity method starting from a rational initial Kähler metric on a projective manifold encounters a finite-time volume collapsing, this projective manifold admits a Fano fibration over a lower dimensional base. In this case, we prove the conti…

Improved TD learning with tail averaging and regularization achieves optimal convergence rates.

Paper analyzes convergence of decentralized algorithms with noise and bias.

We show that strictly convex surfaces expanding by the inverse Gauss curvature flow converge to infinity in finite time. After appropriate rescaling, they converge to spheres. We describe the algorithm to find our main test function.

The paper solves curvature problems on graphs using a special flow.

New scalable MARL framework for dynamic networked systems.

Q-learning with neural network function approximation (neural Q-learning for short) is among the most prevalent deep reinforcement learning algorithms. Despite its empirical success, the non-asymptotic convergence rate of neural Q-learning remains virtually unknown. In this paper, we present a finite-time analysis of a…

Constructing eigenfunctions for finite-time singularities in Lagrangian mean curvature flow

The Kähler-Ricci flow's singularities are analyzed with bounds and convergence results.

Study shows neural networks trained with GD converge to Gaussian processes with polynomial decay.

Improved convergence rates for MFLD in various gradient estimators.

In this paper, we study the convergence of Yang-Mills-Higgs fields defined on fiber bundles over Riemann surfaces where the fiber is a compact symplectic manifold and the conformal structure of the Riemann surface is allowed to vary. We show that away from the nodes, the YMH fields converges, up to gauge, to a smooth Y…

We overview some results on distributed learning with focus on a family of recently proposed algorithms known as non-Bayesian social learning. We consider different approaches to the distributed learning problem and its algorithmic solutions for the case of finitely many hypotheses. The original centralized problem is …

In this paper we present several curvature estimates and convergence results for solutions of the Ricci flow. The curvature estimates depend on smallness of certain local space-time integrals of the norm of the Riemann curvature tensor, while the convergence results require finiteness of space-time integrals of the nor…

In this work, convergence of evolving Finslerian metrics first in a general flow next under Finslerian Ricci flow is studied. More intuitively it is proved that a family of Finslerian metrics $g(t)$ which are solutions to the Finslerian Ricci flow converge in $C^{\infty}$ to a smooth limit Finslerian metric as $t$ ap…

Several results on existence and convergence of the Yang-Mills flow in dimension four are given. We show that a singularity modeled on an instanton cannot form within finite time. Given low initial self-dual energy, we then study convergence of the flow at infinite time. If an Uhlenbeck limit is anti-self-dual and has …

New analysis shows actor-critic method converges efficiently in practical settings.

A new sampler speeds up Bayesian mixture models.

Given a finite honest time, we first show that the associated Azéma optional supermartingale can be expressed as the drawdown and the relative drawdown of some local optional supermartingales with continuous running supremum. The relative drawdown representation then allows us to provide a characterisation of finite ho…

We use the momentum construction of Calabi to study the conical Kähler-Ricci flow on Hirzebruch surfaces with cone angle along the exceptional curve, and show that either the flow Gromov-Hausdorff converges to the Riemann sphere or a single point in finite time, or the flow contracts the cone divisor to a single point …

In this paper we show how to approximate a Heath-Jarrow-Morton dynamics for the forward prices in commodity markets with arbitrage-free models which have a finite dimensional state space. Moreover, we recover a closed form representation of the forward price dynamics in the approximation models and derive the rate of c…

Study shows Ricci flow's convergence and harmonic map heat flow's long-time existence.

Study extends convergence results to noncompact Ricci flows.

In this paper we prove that for a given Kähler-Ricci flow with uniformly bounded Ricci curvatures in an arbitrary dimension, for every sequence of times $t_i$ converging to infinity, there exists a subsequence such that $(M,g(t_i + t))\to (Y,\bar{g}(t))$ and the convergence is smooth outside a singular set (which is a …