A Field Guide to Federated Optimization

Federated learning and analytics are a distributed approach for collaboratively learning models (or statistics) from decentralized data, motivated by and designed for privacy protection. The distributed learning process can be formulated as solving federated optimization problems, which emphasize communication efficiency, data heterogeneity, compatibility with privacy and system requirements, and other constraints that are not primary considerations in other problem settings. This paper provides recommendations and guidelines on formulating, designing, evaluating and analyzing federated optimization algorithms through concrete examples and practical implementation, with a focus on conducting effective simulations to infer real-world performance. The goal of this work is not to survey the current literature, but to inspire researchers and practitioners to design federated learning algorithms that can be used in various practical applications.

On the benefits of maximum likelihood estimation for Regression and Forecasting

We advocate for a practical Maximum Likelihood Estimation (MLE) approach for regression and forecasting, as an alternative to the typical approach of Empirical Risk Minimization (ERM) for a specific target metric. This approach is better suited to capture inductive biases such as prior domain knowledge in datasets, and can output post-hoc estimators at inference time that can optimize different types of target metrics. We present theoretical results to demonstrate that our approach is always competitive with any estimator for the target metric under some general conditions, and in many practical settings (such as Poisson Regression) can actually be much superior to ERM. We demonstrate empirically that our method instantiated with a well-designed general purpose mixture likelihood family can obtain superior performance over ERM for a variety of tasks across time-series forecasting and regression datasets with different data distributions.

On the Renyi Differential Privacy of the Shuffle Model

The central question studied in this paper is Renyi Differential Privacy (RDP) guarantees for general discrete local mechanisms in the shuffle privacy model. In the shuffle model, each of the $n$ clients randomizes its response using a local differentially private (LDP) mechanism and the untrusted server only receives a random permutation (shuffle) of the client responses without association to each client. The principal result in this paper is the first non-trivial RDP guarantee for general discrete local randomization mechanisms in the shuffled privacy model, and we develop new analysis techniques for deriving our results which could be of independent interest. In applications, such an RDP guarantee is most useful when we use it for composing several private interactions. We numerically demonstrate that, for important regimes, with composition our bound yields an improvement in privacy guarantee by a factor of $8\times$ over the state-of-the-art approximate Differential Privacy (DP) guarantee (with standard composition) for shuffled models. Moreover, combining with Poisson subsampling, our result leads to at least $10\times$ improvement over subsampled approximate DP with standard composition.

Communication-Efficient Agnostic Federated Averaging

In distributed learning settings such as federated learning, the training algorithm can be potentially biased towards different clients. Mohri et al. (2019) proposed a domain-agnostic learning algorithm, where the model is optimized for any target distribution formed by a mixture of the client distributions in order to overcome this bias. They further proposed an algorithm for the cross-silo federated learning setting, where the number of clients is small. We consider this problem in the cross-device setting, where the number of clients is much larger. We propose a communication-efficient distributed algorithm called Agnostic Federated Averaging (or AgnosticFedAvg) to minimize the domain-agnostic objective proposed in Mohri et al. (2019), which is amenable to other private mechanisms such as secure aggregation. We highlight two types of naturally occurring domains in federated learning and argue that AgnosticFedAvg performs well on both. To demonstrate the practical effectiveness of AgnosticFedAvg, we report positive results for large-scale language modeling tasks in both simulation and live experiments, where the latter involves training language models for Spanish virtual keyboard for millions of user devices.

Remember What You Want to Forget: Algorithms for Machine Unlearning

We study the problem of forgetting datapoints from a learnt model. In this case, the learner first receives a dataset $S$ drawn i.i.d. from an unknown distribution, and outputs a predictor $w$ that performs well on unseen samples from that distribution. However, at some point in the future, any training data point $z \in S$ can request to be unlearned, thus prompting the learner to modify its output predictor while still ensuring the same accuracy guarantees. In our work, we initiate a rigorous study of machine unlearning in the population setting, where the goal is to maintain performance on the unseen test loss. We then provide unlearning algorithms for convex loss functions. For the setting of convex losses, we provide an unlearning algorithm that can delete up to $O(n/d^{1/4})$ samples, where $d$ is the problem dimension. In comparison, in general, differentially private learningv(which implies unlearning) only guarantees deletion of $O(n/d^{1/2})$ samples. This shows that unlearning is at least polynomially more efficient than learning privately in terms of dependence on $d$ in the deletion capacity.

Learning with User-Level Privacy

We propose and analyze algorithms to solve a range of learning tasks under user-level differential privacy constraints. Rather than guaranteeing only the privacy of individual samples, user-level DP protects a user's entire contribution ($m \ge 1$ samples), providing more stringent but more realistic protection against information leaks. We show that for high-dimensional mean estimation, empirical risk minimization with smooth losses, stochastic convex optimization, and learning hypothesis class with finite metric entropy, the privacy cost decreases as $O(1/\sqrt{m})$ as users provide more samples. In contrast, when increasing the number of users $n$, the privacy cost decreases at a faster $O(1/n)$ rate. We complement these results with lower bounds showing the worst-case optimality of our algorithm for mean estimation and stochastic convex optimization. Our algorithms rely on novel techniques for private mean estimation in arbitrary dimension with error scaling as the concentration radius $\tau$ of the distribution rather than the entire range. Under uniform convergence, we derive an algorithm that privately answers a sequence of $K$ adaptively chosen queries with privacy cost proportional to $\tau$, and apply it to solve the learning tasks we consider.

Wyner-Ziv Estimators: Efficient Distributed Mean Estimation with Side Information

Communication efficient distributed mean estimation is an important primitive that arises in many distributed learning and optimization scenarios such as federated learning. Without any probabilistic assumptions on the underlying data, we study the problem of distributed mean estimation where the server has access to side information. We propose \emph{Wyner-Ziv estimators}, which are communication and computationally efficient and near-optimal when an upper bound for the distance between the side information and the data is known. As a corollary, we also show that our algorithms provide efficient schemes for the classic Wyner-Ziv problem in information theory. In a different direction, when there is no knowledge assumed about the distance between side information and the data, we present an alternative Wyner-Ziv estimator that uses correlated sampling. This latter setting offers {\em universal recovery guarantees}, and perhaps will be of interest in practice when the number of users is large and keeping track of the distances between the data and the side information may not be possible.

Robust hypothesis testing and distribution estimation in Hellinger distance

We propose a simple robust hypothesis test that has the same sample complexity as that of the optimal Neyman-Pearson test up to constants, but robust to distribution perturbations under Hellinger distance. We discuss the applicability of such a robust test for estimating distributions in Hellinger distance. We empirically demonstrate the power of the test on canonical distributions.

Multiple-Source Adaptation with Domain Classifiers

We consider the multiple-source adaptation (MSA) problem and improve a previously proposed MSA solution, where accurate density estimation per domain is required to obtain favorable learning guarantees. In this work, we replace the difficult task of density estimation per domain with a much easier task of domain classification, and show that the two solutions are equivalent given the true densities and domain classifier, yet the newer approach benefits from more favorable guarantees when densities and domain classifier are estimated from finite samples. Our experiments with real-world applications demonstrate that the new discriminative MSA solution outperforms the previous solution with density estimation, as well as other domain adaptation baselines.