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 shows moment explosion time is finite for rough Heston model under certain conditions.

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

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

New method for pricing options in stochastic volatility models.

Finite-time degeneration of harmonic map flows on surfaces is proven under specific conditions.

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…

Study finite singularities in G2 structure flows using Shi-type estimates.

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…

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

The study characterizes honest times and extends semimartingale class for option pricing.

Study shows Whitney sphere collapses to a point in finite time.

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

New algorithms for risk-averse bandits minimize regret in finite time.

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

Finite extinction time for Hermitian curvature flow on homogeneous spaces.

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 $…

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.

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

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

This work achieves finite-time stabilization of uncertain LQ systems using random feedbacks.

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.

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.

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_…

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…

Finite-time bounds on error for linear stochastic approximation and TD learning.

The paper classifies hypersurfaces in a specific product space with finite curvature.

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

For finite networks, Bouchaud-Mézard model's steady state is lognormal and quasi-stationary.

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.

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…

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

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