To the best of our knowledge, the exact (exponential) rate of distributed MD has not been previously explored in the literature.
Inspired by this line of research, we study the distributed online linear quadratic regulator (LQR) problem for linear time-invariant (LTI) systems with unknown dynamics.
The global function is represented as a finite sum of smooth local functions, where each local function is associated with one agent and agents communicate with each other over an undirected connected graph.
We study the convergence properties of Riemannian gradient method for solving the consensus problem (for an undirected connected graph) over the Stiefel manifold.
Distributed optimization often requires finding the minimum of a global objective function written as a sum of local functions.
Recent advancement in online optimization and control has provided novel tools to study LQ problems that are robust to time-varying cost parameters.
This work addresses distributed optimization, where a network of agents wants to minimize a global strongly convex objective function.
The regret bound of dynamic online learning algorithms is often expressed in terms of the variation in the function sequence ($V_T$) and/or the path-length of the minimizer sequence after $T$ rounds.
Then, for any Hilbert space, we show that Optimal Recovery provides a formula which is user-friendly from an algorithmic point-of-view, as long as the hypothesis class is linear.
In this paper, we propose a distributed implementation of the stochastic subgradient method with a theoretical guarantee.
The idea of slicing divergences has been proven to be successful when comparing two probability measures in various machine learning applications including generative modeling, and consists in computing the expected value of a `base divergence' between one-dimensional random projections of the two measures.
Probability metrics have become an indispensable part of modern statistics and machine learning, and they play a quintessential role in various applications, including statistical hypothesis testing and generative modeling.
Often times large-scale finite-sum problems can be solved using efficient variants of Newton's method where the Hessian is approximated via sub-samples.
We subsequently leverage a particle stochastic gradient descent (SGD) method to solve the derived finite dimensional optimization problem.
We establish an out-of-sample error bound capturing the trade-off between the error in terms of explicit features (approximation error) and the error due to spectral properties of the best model in the Hilbert space associated to the combined kernel (spectral error).
The randomized-feature approach has been successfully employed in large-scale kernel approximation and supervised learning.
Such bias is measured by the cross validation procedure in practice where the data set is partitioned into a training set used for training and a validation set, which is not used in training and is left to measure the out-of-sample performance.
At each round, the budget is divided by a nonlinear function of remaining arms, and the arms are pulled correspondingly.
We formulate this problem as a distributed online optimization where agents communicate with each other to track the minimizer of the global loss.
Based on this result, we develop an algorithm that divides the budget according to a nonlinear function of remaining arms at each round.
In this paper, we address tracking of a time-varying parameter with unknown dynamics.
Recent literature on online learning has focused on developing adaptive algorithms that take advantage of a regularity of the sequence of observations, yet retain worst-case performance guarantees.
When the true state is globally identifiable, and the network is connected, we prove that agents eventually learn the true parameter using a randomized gossip scheme.