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Keith Rush

Publications and source records attributed to Keith Rush.

21 records · Page 2Linked to original sources
arXiv2021

Adaptive Federated Optimization

Federated learning is a distributed machine learning paradigm in which a large number of clients coordinate with a central server to learn a model without sharing their own training data. Standard federated optimization methods such as Federated Averaging (FedAvg) are often difficult to tune and exhibit unfavorable convergence behavior. In non-federated settings, adaptive optimization methods have had notable success in combating such issues. In this work, we propose federated versions of adaptive optimizers, including Adagrad, Adam, and Yogi, and analyze their convergence in the presence of heterogeneous data for general non-convex settings. Our results highlight the interplay between client heterogeneity and communication efficiency. We also perform extensive experiments on these methods and show that the use of adaptive optimizers can significantly improve the performance of federated learning.

cs.LG↗
arXiv2021

Fast Dimension Independent Private AdaGrad on Publicly Estimated Subspaces

We revisit the problem of empirical risk minimziation (ERM) with differential privacy. We show that noisy AdaGrad, given appropriate knowledge and conditions on the subspace from which gradients can be drawn, achieves a regret comparable to traditional AdaGrad plus a well-controlled term due to noise. We show a convergence rate of $O(\text{Tr}(G_T)/T)$, where $G_T$ captures the geometry of the gradient subspace. Since $\text{Tr}(G_T)=O(\sqrt{T})$ we can obtain faster rates for convex and Lipschitz functions, compared to the $O(1/\sqrt{T})$ rate achieved by known versions of noisy (stochastic) gradient descent with comparable noise variance. In particular, we show that if the gradients lie in a known constant rank subspace, and assuming algorithmic access to an envelope which bounds decaying sensitivity, one can achieve faster convergence to an excess empirical risk of $\tilde O(1/εn)$, where $ε$ is the privacy budget and $n$ the number of samples. Letting $p$ be the problem dimension, this result implies that, by running noisy Adagrad, we can bypass the DP-SGD bound $\tilde O(\sqrt{p}/εn)$ in $T=(εn)^{2/(1+2α)}$ iterations, where $α\geq 0$ is a parameter controlling gradient norm decay, instead of the rate achieved by SGD of $T=ε^2n^2$. Our results operate with general convex functions in both constrained and unconstrained minimization. Along the way, we do a perturbation analysis of noisy AdaGrad of independent interest. Our utility guarantee for the private ERM problem follows as a corollary to the regret guarantee of noisy AdaGrad.

cs.LG↗