arXiv research

New bounds derived for KG algorithm's performance in finite time.

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

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…

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

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

We consider the dynamics of a linear stochastic approximation algorithm driven by Markovian noise, and derive finite-time bounds on the moments of the error, i.e., deviation of the output of the algorithm from the equilibrium point of an associated ordinary differential equation (ODE). We obtain finite-time bounds on t…

We study two time-scale linear stochastic approximation algorithms, which can be used to model well-known reinforcement learning algorithms such as GTD, GTD2, and TDC. We present finite-time performance bounds for the case where the learning rate is fixed. The key idea in obtaining these bounds is to use a Lyapunov fun…

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

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

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

Algorithm estimates human decision-making in high-dimensional states with finite-time guarantees.

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…

The OLS estimator optimally identifies stable linear systems with a finite number of samples.

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

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

Paper analyzes NAC with neural networks for efficient policy optimization.

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.

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

RANDPOL uses randomized networks for efficient reinforcement learning in continuous state and action MDPs.

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

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.

Proposes a TS approach for Bayesian optimization with preferential feedback.

Novel algorithm reduces computational burden in IRL with finite-time guarantees.

This work analyzes actor-critic methods for faster convergence.

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

New algorithm for nonstationary multi-armed bandits with optimal performance.

Compact curve solution emerges from non-compact curve.

In this paper, a time substitution as used by Duru and Kleinert in their treatment of the hydrogen atom with path integrals is performed to price timer options under stochastic volatility models. We present general pricing formulas for both the perpetual timer call options and the finite time-horizon timer call options…

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

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

Paper analyzes Q-learning with neural networks, proving a fast convergence rate.

Finite-time extinction and smoothing effects in fractional fast diffusion on manifolds.

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

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…

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…

Study on improving the linear two-time-scale stochastic approximation method with a restarting scheme.

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

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

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

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

Paper analyzes finite-time guarantees for preference-based RL.

In this paper, we extend Lotay-Wei's Shi-type estimate from Laplacian flow to more general flows of G$_2$ structures including the modified Laplacian co-flow. Then we prove a version of $κ$-non-collapsing theorem. We will use both of them to study finite time singularities of general flows of G$_2$ structures.

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

Paper analyzes SVGD algorithm for non-asymptotic 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…

Researchers found a new type of singularity in surface evolution equations.