Prompt Public Large Language Models to Synthesize Data for Private On-device Applications

Pre-training on public data is an effective method to improve the performance for federated learning (FL) with differential privacy (DP). This paper investigates how large language models (LLMs) trained on public data can improve the quality of pre-training data for the on-device language models trained with DP and FL. We carefully design LLM prompts to filter and transform existing public data, and generate new data to resemble the real user data distribution. The model pre-trained on our synthetic dataset achieves relative improvement of 19.0% and 22.8% in next word prediction accuracy compared to the baseline model pre-trained on a standard public dataset, when evaluated over the real user data in Gboard (Google Keyboard, a production mobile keyboard application). Furthermore, our method achieves evaluation accuracy better than or comparable to the baseline during the DP FL fine-tuning over millions of mobile devices, and our final model outperforms the baseline in production A/B testing. Our experiments demonstrate the strengths of LLMs in synthesizing data close to the private distribution even without accessing the private data, and also suggest future research directions to further reduce the distribution gap.

Profit: Benchmarking Personalization and Robustness Trade-off in Federated Prompt Tuning

In many applications of federated learning (FL), clients desire models that are personalized using their local data, yet are also robust in the sense that they retain general global knowledge. However, the presence of data heterogeneity across clients induces a fundamental trade-off between personalization (i.e., adaptation to a local distribution) and robustness (i.e., not forgetting previously learned general knowledge). It is critical to understand how to navigate this personalization vs robustness trade-off when designing federated systems, which are increasingly moving towards a paradigm of fine-tuning large foundation models. Due to limited computational and communication capabilities in most federated settings, this foundation model fine-tuning must be done using parameter-efficient fine-tuning (PEFT) approaches. While some recent work has studied federated approaches to PEFT, the personalization vs robustness trade-off of federated PEFT has been largely unexplored. In this work, we take a step towards bridging this gap by benchmarking fundamental FL algorithms -- FedAvg and FedSGD plus personalization (via client local fine-tuning) -- applied to one of the most ubiquitous PEFT approaches to large language models (LLMs) -- prompt tuning -- in a multitude of hyperparameter settings under varying levels of data heterogeneity. Our results show that federated-trained prompts can be surprisingly robust when using a small learning rate with many local epochs for personalization, especially when using an adaptive optimizer as the client optimizer during federated training. We also demonstrate that simple approaches such as adding regularization and interpolating two prompts are effective in improving the personalization vs robustness trade-off in computation-limited settings with few local updates allowed for personalization.

Motley: Benchmarking Heterogeneity and Personalization in Federated Learning

Personalized federated learning considers learning models unique to each client in a heterogeneous network. The resulting client-specific models have been purported to improve metrics such as accuracy, fairness, and robustness in federated networks. However, despite a plethora of work in this area, it remains unclear: (1) which personalization techniques are most effective in various settings, and (2) how important personalization truly is for realistic federated applications. To better answer these questions, we propose Motley, a benchmark for personalized federated learning. Motley consists of a suite of cross-device and cross-silo federated datasets from varied problem domains, as well as thorough evaluation metrics for better understanding the possible impacts of personalization. We establish baselines on the benchmark by comparing a number of representative personalized federated learning methods. These initial results highlight strengths and weaknesses of existing approaches, and raise several open questions for the community. Motley aims to provide a reproducible means with which to advance developments in personalized and heterogeneity-aware federated learning, as well as the related areas of transfer learning, meta-learning, and multi-task learning.

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.

Federated Reconstruction: Partially Local Federated Learning

Personalization methods in federated learning aim to balance the benefits of federated and local training for data availability, communication cost, and robustness to client heterogeneity. Approaches that require clients to communicate all model parameters can be undesirable due to privacy and communication constraints. Other approaches require always-available or stateful clients, impractical in large-scale cross-device settings. We introduce Federated Reconstruction, the first model-agnostic framework for partially local federated learning suitable for training and inference at scale. We motivate the framework via a connection to model-agnostic meta learning, empirically demonstrate its performance over existing approaches for collaborative filtering and next word prediction, and release an open-source library for evaluating approaches in this setting. We also describe the successful deployment of this approach at scale for federated collaborative filtering in a mobile keyboard application.

Implicit Regularization of Normalization Methods

Normalization methods such as batch normalization are commonly used in overparametrized models like neural networks. Here, we study the weight normalization (WN) method (Salimans & Kingma, 2016) and a variant called reparametrized projected gradient descent (rPGD) for overparametrized least squares regression and some more general loss functions. WN and rPGD reparametrize the weights with a scale $g$ and a unit vector such that the objective function becomes \emph{non-convex}. We show that this non-convex formulation has beneficial regularization effects compared to gradient descent on the original objective. We show that these methods adaptively regularize the weights and \emph{converge with exponential rate} to the minimum $\ell_2$ norm solution (or close to it) even for initializations \emph{far from zero}. This is different from the behavior of gradient descent, which only converges to the min norm solution when started at zero, and is more sensitive to initialization. Some of our proof techniques are different from many related works; for instance we find explicit invariants along the gradient flow paths. We verify our results experimentally and suggest that there may be a similar phenomenon for nonlinear problems such as matrix sensing.

Learning Distributions Generated by One-Layer ReLU Networks

We consider the problem of estimating the parameters of a $d$-dimensional rectified Gaussian distribution from i.i.d. samples. A rectified Gaussian distribution is defined by passing a standard Gaussian distribution through a one-layer ReLU neural network. We give a simple algorithm to estimate the parameters (i.e., the weight matrix and bias vector of the ReLU neural network) up to an error $\epsilon||W||_F$ using $\tilde{O}(1/\epsilon^2)$ samples and $\tilde{O}(d^2/\epsilon^2)$ time (log factors are ignored for simplicity). This implies that we can estimate the distribution up to $\epsilon$ in total variation distance using $\tilde{O}(\kappa^2d^2/\epsilon^2)$ samples, where $\kappa$ is the condition number of the covariance matrix. Our only assumption is that the bias vector is non-negative. Without this non-negativity assumption, we show that estimating the bias vector within any error requires the number of samples at least exponential in the infinity norm of the bias vector. Our algorithm is based on the key observation that vector norms and pairwise angles can be estimated separately. We use a recent result on learning from truncated samples. We also prove two sample complexity lower bounds: $\Omega(1/\epsilon^2)$ samples are required to estimate the parameters up to error $\epsilon$, while $\Omega(d/\epsilon^2)$ samples are necessary to estimate the distribution up to $\epsilon$ in total variation distance. The first lower bound implies that our algorithm is optimal for parameter estimation. Finally, we show an interesting connection between learning a two-layer generative model and non-negative matrix factorization. Experimental results are provided to support our analysis.

Sparse Logistic Regression Learns All Discrete Pairwise Graphical Models

We characterize the effectiveness of a natural and classic algorithm for recovering the Markov graph of a general discrete pairwise graphical model from i.i.d. samples. The algorithm is (appropriately regularized) conditional maximum likelihood, which involves solving a convex program for each node; for Ising models this is $\ell_1$-constrained logistic regression, while for more alphabets an $\ell_{2,1}$ group-norm constraint needs to be used. We show that this algorithm can recover any arbitrary discrete pairwise graphical model, and also characterize its sample complexity as a function of model width, alphabet size, edge parameter accuracy, and the number of variables. We show that along every one of these axes, it matches or improves on all existing results and algorithms for this problem. Our analysis applies a sharp generalization error bound for logistic regression when the weight vector has an $\ell_1$ constraint (or $\ell_{2,1}$ constraint) and the sample vector has an $\ell_{\infty}$ constraint (or $\ell_{2, \infty}$ constraint). We also show that the proposed convex programs can be efficiently optimized in $\tilde{O}(n^2)$ running time (where $n$ is the number of variables) under the same statistical guarantee. Our experimental results verify our analysis.

The Sparse Recovery Autoencoder

Linear encoding of sparse vectors is widely popular, but is most commonly data-independent -- missing any possible extra (but a-priori unknown) structure beyond sparsity. In this paper we present a new method to learn linear encoders that adapt to data, while still performing well with the widely used $\ell_1$ decoder. The convex $\ell_1$ decoder prevents gradient propagation as needed in standard autoencoder training. Our method is based on the insight that unfolding the convex decoder into $T$ projected gradient steps can address this issue. Our method can be seen as a data-driven way to learn a compressed sensing matrix. Our experiments show that there is indeed additional structure beyond sparsity in several real datasets. Our autoencoder is able to discover it and exploit it to create excellent reconstructions with fewer measurements compared to the previous state of the art methods.

Leveraging Sparsity for Efficient Submodular Data Summarization

The facility location problem is widely used for summarizing large datasets and has additional applications in sensor placement, image retrieval, and clustering. One difficulty of this problem is that submodular optimization algorithms require the calculation of pairwise benefits for all items in the dataset. This is infeasible for large problems, so recent work proposed to only calculate nearest neighbor benefits. One limitation is that several strong assumptions were invoked to obtain provable approximation guarantees. In this paper we establish that these extra assumptions are not necessary---solving the sparsified problem will be almost optimal under the standard assumptions of the problem. We then analyze a different method of sparsification that is a better model for methods such as Locality Sensitive Hashing to accelerate the nearest neighbor computations and extend the use of the problem to a broader family of similarities. We validate our approach by demonstrating that it rapidly generates interpretable summaries.