4 papers
Distributed Gradient Flow: Nonsmoothness, Nonconvexity, and Saddle Point Evasion
Brian Swenson, Ryan Murray, H. Vincent Poor +1
The paper considers distributed gradient flow (DGF) for multi-agent nonconvex optimization. DGF is a continuous-time approximation of distributed gradient descent that is often eas…
Distributed Gradient Descent: Nonconvergence to Saddle Points and the Stable-Manifold Theorem
Brian Swenson, Ryan Murray, H. Vincent Poor +1
The paper studies a distributed gradient descent (DGD) process and considers the problem of showing that in nonconvex optimization problems, DGD typically converges to local minima…
A maximum principle argument for the uniform convergence of graph Laplacian regressors
Nicolas Garcia Trillos, Ryan Murray
This paper investigates the use of methods from partial differential equations and the Calculus of variations to study learning problems that are regularized using graph Laplacians…
A new analytical approach to consistency and overfitting in regularized empirical risk minimization
Nicolas Garcia Trillos, Ryan Murray
This work considers the problem of binary classification: given training data from a certain population, together with associated labels $y_1,\dots, y_n \in \left…