arXiv research

Study on convergence of SDEs using entropy methods.

Unified analysis of stochastic iterative algorithms using Lyapunov functions.

The paper guarantees global stability for stochastic subgradient methods in nonsmooth nonconvex optimization.

Study on convergence rates of degenerate SDEs using Fisher information and generalized Bochner's formula.

Paper analyzes biased stochastic approximation with a novel multistep Lyapunov function.

Short note on soft-max and policy gradients in bandit problems using Lyapunov functions.

Paper analyzes SA for fixed-point equations with noise, establishing convergence rates.

Overview of non-stochastic-gradient SA algorithms in signal processing and ML.

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

Paper proves convergence of SA algorithm via martingale and converse Lyapunov methods.

The paper analyzes convergence of Langevin dynamics with time-dependent metrics.

Investigates optimal consumption and investment strategies with constraints in incomplete markets.

The paper refines optimization algorithms using Lyapunov functions and differential equations.

Study mini-batch SGD noise and its limits, proving complexity guarantees.

New analysis improves SGD for robust and quantile regression with sub-quadratic convergence.

In this paper, we consider the stochastic iterative counterpart of the value iteration scheme wherein only noisy and possibly biased approximations of the Bellman operator are available. We call this counterpart as the approximate value iteration (AVI) scheme. Neural networks are often used as function approximators, i…

This paper uses Gaussian Process and converse Lyapunov function to estimate power system ROA.

Operator calculus for population-based optimization provides a unified framework for analyzing convergence of various methods.

Lyapunov's second theorem is an essential tool for stability analysis of differential equations. The paper provides an analog theorem for incremental stability analysis by lifting the Lyapunov function to the tangent bundle. The Lyapunov function endows the state-space with a Finsler structure. Incremental stability is…

New algorithm reduces regret and constraint violation in constrained bandit problems.

The paper analyzes convergence of Riemannian SA schemes for stochastic optimization.

Unified framework for finite-sample RL algorithms using Lyapunov theory.

Functional portfolio generation, initiated by E.R. Fernholz almost twenty years ago, is a methodology for constructing trading strategies with controlled behavior. It is based on very weak and descriptive assumptions on the covariation structure of the underlying market model, and needs no estimation of model parameter…

Combines Lyapunov functions with controller synthesis for safe control policies.

SAGA algorithm improved for arbitrary sampling and minibatching.

New neural methods for stable control with provable guarantees.

Optimal algorithms for Riemannian optimization with reduced complexity.

Stabilizes complex systems using diffusion models trained on Lyapunov functions.

Improved reinforcement learning with adaptive learning rates.

Maximal concentration bounds for stochastic approximation with heavy-tailed noise.

Double Q-learning has the same mean-squared error as Q-learning under certain conditions.

Graphical models for covariance matrices improve structure learning.

Study the topology of stable vector fields and Lyapunov functions on R^n.

New insights into using momentum for non-convex optimization.

According to Pixton, there are Morse-Smale diffeomorphisms of the 3-sphere which have no energy function, that is a Lyapunov function whose critical points are all periodic points of the diffeomorphism. We introduce the concept of quasi-energy function for a Morse-Smale diffeomorphism as a Lyapunov function with the le…

We describe, in the general setting of closed cone fields, the set of causal functions which can be approximated by smooth Lyapunov. We derive several consequences on causality theory. Dans le contexte général des champs de cones fermés, on décrit l'ensemble des fonctions causales qui peuvent être approchées par des fo…

We prove diffeomorphisms of polygonal linkage moduli spaces to Euclidean spaces.

Study on bias of constant-step stochastic approximation with Markovian noise.

New method solves complex optimization problems with real-time learning.

New factorial power constants improve optimization convergence rates.

Develops a new theory for neural systems stability and width effects.

Lyapunov-based analysis shows polynomial sample complexity for WCMDPs and RBs.

New methods accelerate gradient descent for convex and strongly convex functions.

New RL policy for unbounded state space with stability guarantee.

The paper analyzes convergence rates for stochastic approximation and reinforcement learning.

We consider Lyapunov exponents for flat bundles over hyperbolic curves defined via parallel transport over the geodesic flow. We refine a lower bound obtained by Eskin, Kontsevich, Moeller and Zorich showing that the sum of the first k exponents is greater or equal than the sum of the degree of any rank k holomorphic s…

New approach to concentration inequalities for unbounded state space dynamical systems.

Fractionally integrated generalized autoregressive conditional heteroskedasticity (FIGARCH) arises in modeling of financial time series. FIGARCH is essentially governed by a system of nonlinear stochastic difference equations ${u_t}$ = ${z_t}$ $(1-\sum\limits_{j=1}^q β_j L^j)σ_{t}^2 = ω+(1-\sum\limits_{j=1}^q β_j L^j -…