Search Results for author: Nicholas M. Boffi

Found 8 papers, 0 papers with code

Probability flow solution of the Fokker-Planck equation

no code implementations9 Jun 2022 Nicholas M. Boffi, Eric Vanden-Eijnden

The method of choice for integrating the time-dependent Fokker-Planck equation in high-dimension is to generate samples from the solution via integration of the associated stochastic differential equation.

Adversarially Robust Stability Certificates can be Sample-Efficient

no code implementations20 Dec 2021 Thomas T. C. K. Zhang, Stephen Tu, Nicholas M. Boffi, Jean-Jacques E. Slotine, Nikolai Matni

Motivated by bridging the simulation to reality gap in the context of safety-critical systems, we consider learning adversarially robust stability certificates for unknown nonlinear dynamical systems.

Nonparametric adaptive control and prediction: theory and randomized algorithms

no code implementations7 Jun 2021 Nicholas M. Boffi, Stephen Tu, Jean-Jacques E. Slotine

A key assumption in the theory of nonlinear adaptive control is that the uncertainty of the system can be expressed in the linear span of a set of known basis functions.

Regret Bounds for Adaptive Nonlinear Control

no code implementations26 Nov 2020 Nicholas M. Boffi, Stephen Tu, Jean-Jacques E. Slotine

We study the problem of adaptively controlling a known discrete-time nonlinear system subject to unmodeled disturbances.

Learning Stability Certificates from Data

no code implementations13 Aug 2020 Nicholas M. Boffi, Stephen Tu, Nikolai Matni, Jean-Jacques E. Slotine, Vikas Sindhwani

Many existing tools in nonlinear control theory for establishing stability or safety of a dynamical system can be distilled to the construction of a certificate function that guarantees a desired property.

The role of optimization geometry in single neuron learning

no code implementations15 Jun 2020 Nicholas M. Boffi, Stephen Tu, Jean-Jacques E. Slotine

Recent numerical experiments have demonstrated that the choice of optimization geometry used during training can impact generalization performance when learning expressive nonlinear model classes such as deep neural networks.

Implicit regularization and momentum algorithms in nonlinear adaptive control and prediction

no code implementations31 Dec 2019 Nicholas M. Boffi, Jean-Jacques E. Slotine

We show that the Euler Lagrange equations for the Bregman Lagrangian lead to natural gradient and mirror descent-like adaptation laws with momentum, and we recover their first-order analogues in the infinite friction limit.

A continuous-time analysis of distributed stochastic gradient

no code implementations28 Dec 2018 Nicholas M. Boffi, Jean-Jacques E. Slotine

We analyze the effect of synchronization on distributed stochastic gradient algorithms.

Distributed Optimization

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