arXiv research

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

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

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…

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 …

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…

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

Meta-learning control algorithm with finite-time guarantees for unknown systems.

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

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

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…

We consider a discrete-time financial market model with finite time horizon and give conditions which guarantee the existence of an optimal strategy for the problem of maximizing expected terminal utility. Equivalent martingale measures are constructed using optimal strategies.

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

Stabilization of linear systems with unknown dynamics is a canonical problem in adaptive control. Since the lack of knowledge of system parameters can cause it to become destabilized, an adaptive stabilization procedure is needed prior to regulation. Therefore, the adaptive stabilization needs to be completed in finite…

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

Study verifies Joyce's conjectures for circle-invariant Lagrangian surfaces.

This work analyzes actor-critic methods for faster convergence.

In this paper, we study multi-armed bandit problems in explore-then-commit setting. In our proposed explore-then-commit setting, the goal is to identify the best arm after a pure experimentation (exploration) phase and exploit it once or for a given finite number of times. We identify that although the arm with the hig…

Temporal difference learning (TD) is a simple iterative algorithm used to estimate the value function corresponding to a given policy in a Markov decision process. Although TD is one of the most widely used algorithms in reinforcement learning, its theoretical analysis has proved challenging and few guarantees on its s…

Single-timescale analysis improves convergence in multi-sequence stochastic approximation.

The paper provides guarantees for feedback control with sensor errors.

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

We study an extension of the classic stochastic multi-armed bandit problem which involves multiple plays and Markovian rewards in the rested bandits setting. In order to tackle this problem we consider an adaptive allocation rule which at each stage combines the information from the sample means of all the arms, with t…

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

New framework for Bayesian inference using neural Schrödinger-Föllmer flows.

This paper investigates the problem of maximizing expected terminal utility in a (generically incomplete) discrete-time financial market model with finite time horizon. In contrast to the standard setting, a possibly non-concave utility function $U$ is considered, with domain of definition $\mathbb{R}$. Simple conditio…

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

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

This paper improves SGMs by using a predictor-corrector scheme to converge faster.

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…

The paper analyzes the InfoNCE loss under different temperature schedules using Langevin dynamics.

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 study local complexity measures for stochastic convex optimization problems, providing a local minimax theory analogous to that of Hájek and Le Cam for classical statistical problems. We give complementary optimality results, developing fully online methods that adaptively achieve optimal convergence guarantees. Our…

We consider the area preserving curve shortening flow with Neumann free boundary conditions outside of a convex domain or at a straight line. We give a criterion on initial curves that guarantees the appearance of a singularity in finite time. We prove that the singularity is of type II. Furthermore, if these initial c…

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…

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

Multi-armed bandits are a quintessential machine learning problem requiring the balancing of exploration and exploitation. While there has been progress in developing algorithms with strong theoretical guarantees, there has been less focus on practical near-optimal finite-time performance. In this paper, we propose an …

Last-iterate guarantees for learning in co-coercive games under noisy feedback.

Unified analysis of stochastic iterative algorithms using Lyapunov functions.

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

New algorithm learns Koopman operator online, with complexity control and convergence guarantees.

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

NSGLD improves SGLD for non-convex optimization problems.

Stochastic Gradient Langevin Dynamics (SGLD) is a popular variant of Stochastic Gradient Descent, where properly scaled isotropic Gaussian noise is added to an unbiased estimate of the gradient at each iteration. This modest change allows SGLD to escape local minima and suffices to guarantee asymptotic convergence to g…

This paper investigates stochastic and adversarial combinatorial multi-armed bandit problems. In the stochastic setting under semi-bandit feedback, we derive a problem-specific regret lower bound, and discuss its scaling with the dimension of the decision space. We propose ESCB, an algorithm that efficiently exploits t…

This paper provides guarantees for DFM models using KL divergence.

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 on fake stationary Volterra Heston model for non-stationary processes.

Leveraging on the convexity of the Lasso problem , screening rules help in accelerating solvers by discarding irrelevant variables, during the optimization process. However, because they provide better theoretical guarantees in identifying relevant variables, several non-convex regularizers for the Lasso have been prop…