Distributed Gradient Tracking Methods with Finite Data Rates

Stabilization with Finite Data Rates

In this term project, we study the effects of finite communication rates in control problems. Traditionally, the communication channel between the plant and the controller is not modelled. This is because it is assumed that the outputs of the former (noisy or noiseless) are available completely and with infinite precision to the latter. In this work, we study systems where the link between the ...

Adaptive Finite Element Methods with convergence rates

Distributed Delayed Proximal Gradient Methods

We analyze distributed optimization algorithms where parts of data and variables are distributed over several machines and synchronization occurs asynchronously. We prove convergence for the general case of a nonconvex objective plus a convex and possibly nonsmooth penalty. We demonstrate two challenging applications, `1-regularized logistic regression and reconstruction ICA, and present experi...

A Distributed Stochastic Gradient Tracking Method

In this paper, we study the problem of distributed multi-agent optimization over a network, where each agent possesses a local cost function that is smooth and strongly convex. The global objective is to find a common solution that minimizes the average of all cost functions. Assuming agents only have access to unbiased estimates of the gradients of their local cost functions, we consider a dis...

Optimal Rates for Learning with Nyström Stochastic Gradient Methods

In the setting of nonparametric regression, we propose and study a combination of stochastic gradient methods with Nyström subsampling, allowing multiple passes over the data and mini-batches. Generalization error bounds for the studied algorithm are provided. Particularly, optimal learning rates are derived considering different possible choices of the step-size, the mini-batch size, the numbe...