Convergence of Gradient Descent with Linearly Correlated Noise and Applications to Differentially Private Learning

We study stochastic optimization with linearly correlated noise. Our study is motivated by recent methods for optimization with differential privacy (DP), such as DP-FTRL, which inject noise via matrix factorization mechanisms. We propose an optimization problem that distils key facets of these DP methods and that involves perturbing gradients by linearly correlated noise. We derive improved convergence rates for gradient descent in this framework for convex and non-convex loss functions. Our theoretical analysis is novel and might be of independent interest. We use these convergence rates to develop new, effective matrix factorizations for differentially private optimization, and highlight the benefits of these factorizations theoretically and empirically.

Federated Select: A Primitive for Communication- and Memory-Efficient Federated Learning

Federated learning (FL) is a framework for machine learning across heterogeneous client devices in a privacy-preserving fashion. To date, most FL algorithms learn a "global" server model across multiple rounds. At each round, the same server model is broadcast to all participating clients, updated locally, and then aggregated across clients. In this work, we propose a more general procedure in which clients "select" what values are sent to them. Notably, this allows clients to operate on smaller, data-dependent slices. In order to make this practical, we outline a primitive, federated select, which enables client-specific selection in realistic FL systems. We discuss how to use federated select for model training and show that it can lead to drastic reductions in communication and client memory usage, potentially enabling the training of models too large to fit on-device. We also discuss the implications of federated select on privacy and trust, which in turn affect possible system constraints and design. Finally, we discuss open questions concerning model architectures, privacy-preserving technologies, and practical FL systems.

Private Online Prefix Sums via Optimal Matrix Factorizations

Motivated by differentially-private (DP) training of machine learning models and other applications, we investigate the problem of computing prefix sums in the online (streaming) setting with DP. This problem has previously been addressed by special-purpose tree aggregation schemes with hand-crafted estimators. We show that these previous schemes can all be viewed as specific instances of a broad class of matrix-factorization-based DP mechanisms, and that in fact much better mechanisms exist in this class. In particular, we characterize optimal factorizations of linear queries under online constraints, deriving existence, uniqueness, and explicit expressions that allow us to efficiently compute optimal mechanisms, including for online prefix sums. These solutions improve over the existing state-of-the-art by a significant constant factor, and avoid some of the artifacts introduced by the use of the tree data structure.

Practical and Private (Deep) Learning without Sampling or Shuffling

We consider training models with differential privacy (DP) using mini-batch gradients. The existing state-of-the-art, Differentially Private Stochastic Gradient Descent (DP-SGD), requires privacy amplification by sampling or shuffling to obtain the best privacy/accuracy/computation trade-offs. Unfortunately, the precise requirements on exact sampling and shuffling can be hard to obtain in important practical scenarios, particularly federated learning (FL). We design and analyze a DP variant of Follow-The-Regularized-Leader (DP-FTRL) that compares favorably (both theoretically and empirically) to amplified DP-SGD, while allowing for much more flexible data access patterns. DP-FTRL does not use any form of privacy amplification.

Federated Learning with Autotuned Communication-Efficient Secure Aggregation

Federated Learning enables mobile devices to collaboratively learn a shared inference model while keeping all the training data on a user's device, decoupling the ability to do machine learning from the need to store the data in the cloud. Existing work on federated learning with limited communication demonstrates how random rotation can enable users' model updates to be quantized much more efficiently, reducing the communication cost between users and the server. Meanwhile, secure aggregation enables the server to learn an aggregate of at least a threshold number of device's model contributions without observing any individual device's contribution in unaggregated form. In this paper, we highlight some of the challenges of setting the parameters for secure aggregation to achieve communication efficiency, especially in the context of the aggressively quantized inputs enabled by random rotation. We then develop a recipe for auto-tuning communication-efficient secure aggregation, based on specific properties of random rotation and secure aggregation -- namely, the predictable distribution of vector entries post-rotation and the modular wrapping inherent in secure aggregation. We present both theoretical results and initial experiments.

Graph Oracle Models, Lower Bounds, and Gaps for Parallel Stochastic Optimization

We suggest a general oracle-based framework that captures different parallel stochastic optimization settings described by a dependency graph, and derive generic lower bounds in terms of this graph. We then use the framework and derive lower bounds for several specific parallel optimization settings, including delayed updates and parallel processing with intermittent communication. We highlight gaps between lower and upper bounds on the oracle complexity, and cases where the "natural" algorithms are not known to be optimal.

Federated Optimization:Distributed Optimization Beyond the Datacenter

We introduce a new and increasingly relevant setting for distributed optimization in machine learning, where the data defining the optimization are distributed (unevenly) over an extremely large number of \nodes, but the goal remains to train a high-quality centralized model. We refer to this setting as Federated Optimization. In this setting, communication efficiency is of utmost importance. A motivating example for federated optimization arises when we keep the training data locally on users' mobile devices rather than logging it to a data center for training. Instead, the mobile devices are used as nodes performing computation on their local data in order to update a global model. We suppose that we have an extremely large number of devices in our network, each of which has only a tiny fraction of data available totally; in particular, we expect the number of data points available locally to be much smaller than the number of devices. Additionally, since different users generate data with different patterns, we assume that no device has a representative sample of the overall distribution. We show that existing algorithms are not suitable for this setting, and propose a new algorithm which shows encouraging experimental results. This work also sets a path for future research needed in the context of federated optimization.