28 citations · 32 across the 16 of their papers we have counts for
8 papers · 1 filter
Autoencoding Dynamics: Topological Limitations and Capabilities
Matthew D. Kvalheim, Eduardo D. Sontag
Given a "data manifold" and "latent space" , an autoencoder is a pair of continuous maps consisting of an "encoder" $E\colon \mathbb{R}^n\t…
On the (almost) Global Exponential Convergence of the Overparameterized Policy Optimization for the LQR Problem
Moh Kamalul Wafi, Arthur Castello B. de Oliveira, Eduardo D. Sontag
In this work we study the convergence of gradient methods for nonconvex optimization problems -- specifically the effect of the problem formulation to the convergence behavior of t…
Small-Covariance Noise-to-State Stability of Stochastic Systems and Its Applications to Stochastic Gradient Dynamics
Leilei Cui, Zhong-Ping Jiang, Eduardo D. Sontag
This paper studies gradient dynamics subject to additive random noise, which may arise from sources such as stochastic gradient estimation, measurement noise, or stochastic samplin…
Some remarks on gradient dominance and LQR policy optimization
Eduardo D. Sontag
Solutions of optimization problems, including policy optimization in reinforcement learning, typically rely upon some variant of gradient descent. There has been much recent work i…
Perturbed Gradient Descent Algorithms are Small-Disturbance Input-to-State Stable
Leilei Cui, Zhong-Ping Jiang, Eduardo D. Sontag +1
This article investigates the robustness of gradient descent algorithms under perturbations. The concept of small-disturbance input-to-state stability (ISS) for discrete-time nonli…
Universal Formulas for Safe Control and Their Neural Network Approximations
Pol Mestres, Jorge Cortés, Eduardo D. Sontag
We study the problem of designing a controller that satisfies an arbitrary number of affine inequalities at every point in the state space. This is motivated by the fact that a var…