arXiv research

Combines Lyapunov functions with controller synthesis for safe control policies.

New neural methods for stable control with provable guarantees.

Stabilizes complex systems using diffusion models trained on Lyapunov functions.

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

The paper uses temporal logic to guide safe reinforcement learning for complex tasks.

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

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

The paper proves Zimmer's conjecture for non-uniform lattices by controlling mass escape and Lyapunov exponents.

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

Stable deep models learn dynamical systems with formal stability guarantees.

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

Gradient flossing stabilizes RNN training by controlling Lyapunov exponents.

New RL policy for unbounded state space with stability guarantee.

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

Neural network outperforms traditional methods in chaotic dynamics classification.

In this paper, we propose a dynamical systems perspective of the Expectation-Maximization (EM) algorithm. More precisely, we can analyze the EM algorithm as a nonlinear state-space dynamical system. The EM algorithm is widely adopted for data clustering and density estimation in statistics, control systems, and machine…

Paper presents neural network controllers for offset-free setpoint tracking.

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…

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…

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

This paper analyzes and improves monotonic accelerated algorithms like M-NAG and M-FISTA.

DCRNN improves LSTM for chaotic dynamical system forecasting.

A new family of momentum coefficients improves the convergence rate of accelerated algorithms.

Study on convergence of SDEs using entropy methods.

Paper proves PI consensus algorithm converges exponentially under restricted secant inequality.

Improved TD learning with neural nets reduces sample complexity and overparameterization.

KCRL learns stable policies for nonlinear systems with formal guarantees.

Unified analysis of stochastic iterative algorithms using Lyapunov functions.

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

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

This work uses Lyapunov theory to improve the robustness of deep neural networks against adversarial attacks.

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.

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

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

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

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

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

Lyapunov 1-forms on orbifolds help understand flows on compact spaces.

In this paper, following J. Franks' work on Lyapunov graphs of nonsingular Smale flows on $S^3$, we study Lyapunov graphs of nonsingular Smale flows on $S^1 \times S^2$. More precisely, we determine necessary and sufficient conditions on an abstract Lyapunov graph to be associated with a nonsingular Smale flow on $S^1 …

Inference in hidden Markov model has been challenging in terms of scalability due to dependencies in the observation data. In this paper, we utilize the inherent memory decay in hidden Markov models, such that the forward and backward probabilities can be carried out with subsequences, enabling efficient inference over…

This paper presents a methodology and numerical algorithms for constructing accelerated gradient flows on the space of probability distributions. In particular, we extend the recent variational formulation of accelerated gradient methods in (wibisono, et. al. 2016) from vector valued variables to probability distributi…

In many real-world reinforcement learning (RL) problems, besides optimizing the main objective function, an agent must concurrently avoid violating a number of constraints. In particular, besides optimizing performance it is crucial to guarantee the safety of an agent during training as well as deployment (e.g. a robot…

We study the behaviour of a Hilbert geometry when going to infinity along a geodesic line. We prove that all the information is contained in the shape of the boundary at the endpoint of this geodesic line and have to introduce a regularity property of convex functions to make this link precise. The point of view is a d…

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

Optimizes control of noisy discrete systems without system matrix knowledge.