arXiv research

New continuous-time optimization algorithms converge in finite time to local minima.

In this note, we first prove that the solution of mean curvature flow on a finite time interval $[0,T)$ can be extended over time $T$ if the space-time integration of the norm of the second fundamental form is finite. Secondly, we prove that the solution of certain mean curvature flow on a finite time interval $[0,T)$ …

Study finite time singularities in Ricci flow with bounded scalar curvature.

Uniform-in-time analysis for Stein Variational Gradient Descent across various metrics.

New method for pricing options in stochastic volatility models.

Finite time for Ricci flow on certain manifolds.

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

Finite-time blow-up in Yang-Mills flow for small energy initial connections.

Estimates for VPMCF show ancient MCF solutions and finite-time behavior.

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

Finite time for subsolutions on Riemannian manifolds proved.

Study on Ricci flows of awesome homogeneous spaces, proving finite extinction time.

We show that if on a compact Kahler threefold there is a solution of the Kahler-Ricci flow which encounters a finite time collapsing singularity, then the manifold admits a Fano fibration. Furthermore, if there is finite time extinction then the manifold is Fano and the initial class is a positive multiple of the first…

We consider the question of whether solutions of variants of Teichmüller harmonic map flow from surfaces $M$ to general targets can degenerate in finite time. For the original flow from closed surfaces of genus at least $2$, as well as the flow from cylinders, we prove that such a finite-time degeneration must occur in…

We give concentration bounds for martingales that are uniform over finite times and extend classical Hoeffding and Bernstein inequalities. We also demonstrate our concentration bounds to be optimal with a matching anti-concentration inequality, proved using the same method. Together these constitute a finite-time versi…

I analyse the frequentist regret of the famous Gittins index strategy for multi-armed bandits with Gaussian noise and a finite horizon. Remarkably it turns out that this approach leads to finite-time regret guarantees comparable to those available for the popular UCB algorithm. Along the way I derive finite-time bounds…

Finite singular times for symmetric network curvature flow.

It is known that a complete immersed minimal surface with finite total curvature in $\mathbb H^2\times\mathbb R$ is proper, has finite topology and each one of its ends is asymptotic to a geodesic polygon at infinity (Hauswirth and Rosenberg, 2006; Hauswirth, Nelli, Sa Earp and Toubiana, 2015). In this paper we prove t…

We show that the moment explosion time in the rough Heston model [El Euch, Rosenbaum 2016, arxiv:1609.02108] is finite if and only if it is finite for the classical Heston model. Upper and lower bounds for the explosion time are established, as well as an algorithm to compute the explosion time (under some restrictions…

Project infinite time series graphs to finite marginal models using number theory.

Study of deep neural networks using finite-time Lyapunov exponents.

Study on SA with heavy-tailed and LRD noise, establishing finite-time bounds.

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 investigate the integral conditions to extend the mean curvature flow in a Riemannian manifold. We prove that the mean curvature flow solution with finite total mean curvature on a finite time interval $[0,T)$ can be extended over time $T$. Moreover, we show that the condition is optimal in some sense.

Let $p$ be an odd prime. We construct a non-abelian extension $Γ$ of $S^1$ by $Z/p \times Z/p$, and prove that any finite subgroup of $Γ$ acts freely and smoothly on $S^{2p-1} \times S^{2p-1}$. In particular, for each odd prime $p$ we obtain free smooth actions of infinitely many non-metacyclic rank two $p$-groups on $…

In this note we study finite-time singularities in the Chern-Ricci flow. We show that finite-time singularities are characterized by the blow-up of the scalar curvature of the Chern connection.

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

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

Study optimal stopping problems with finite-time horizon and proves continuity and strict monotonicity of the boundary.

Paper analyzes finite-time performance of SA in RL with Markovian noise.

Study K-R flow on Hirzebruch surfaces, showing tangent flows are K-R flows with orbifold singularities.

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…

We construct a non-abelian extension $Γ$ of $S^1$ by $\cy 3 \times \cy 3$, and prove that $Γ$ acts freely and smoothly on $S^{5} \times S^{5}$. This gives new actions on $S^{5} \times S^{5}$ for an infinite family $\cP$ of finite 3-groups. We also show that any finite odd order subgroup of the exceptional Lie group $G_…

In this short paper, we show that Kähler-Ricci flows over closed manifolds would have scalar curvature blown-up for finite time singularity. Certain control of the blowing-up is achieved with some mild assumption.

Finite-time queue peaks in stochastic networks have logarithmic scaling after geometric thresholds.

Let $\mathbb{M}^{2}$ be a complete non compact orientable surface of non negative curvature. We prove in this paper some theorems involving parabolicity of minimal surfaces in $\mathbb{M}^{2}\times\mathbb{R}$. First, using a characterization of $δ$-parabolicity we prove that under additional conditions on $\mathbb{M}$,…

This work analyzes actor-critic methods for faster convergence.

I introduce and analyse an anytime version of the Optimally Confident UCB (OCUCB) algorithm designed for minimising the cumulative regret in finite-armed stochastic bandits with subgaussian noise. The new algorithm is simple, intuitive (in hindsight) and comes with the strongest finite-time regret guarantees for a hori…

Anisotropic curvature flow of networks shows unique solutions and behavior under finite time.

Paper analyzes convergence rates for multi-agent learning in games.

The paper analyzes finite-time singularities in Spin(7)-structure flows using Shi-type estimates.

Logarithmic regret achieved in continuous-time linear-quadratic reinforcement learning.

Simulated annealing is a popular method for approaching the solution of a global optimization problem. Existing results on its performance apply to discrete combinatorial optimization where the optimization variables can assume only a finite set of possible values. We introduce a new general formulation of simulated an…

Let H_g denote the closed 3-manifold obtained as the connected sum of g copies of S^2 times S^1, with free fundamental group of rank g. We prove that, for a finite group G acting on H_g which induces a faithful action on the fundamental group, there is an upper bound for the order of G which is quadratic in g, but that…

Enhances understanding of Kähler-Ricci flow singularities.

Compact curve solution emerges from non-compact curve.

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

Ricci flow singularities on compact Kähler surfaces are of Type I.