Methods with Local Steps and Random Reshuffling for Generally Smooth Non-Convex Federated Optimization

Non-convex Machine Learning problems typically do not adhere to the standard smoothness assumption. Based on empirical findings, Zhang et al. (2020b) proposed a more realistic generalized $(L_0, L_1)$-smoothness assumption, though it remains largely unexplored. Many existing algorithms designed for standard smooth problems need to be revised. However, in the context of Federated Learning, only a few works address this problem but rely on additional limiting assumptions. In this paper, we address this gap in the literature: we propose and analyze new methods with local steps, partial participation of clients, and Random Reshuffling without extra restrictive assumptions beyond generalized smoothness. The proposed methods are based on the proper interplay between clients' and server's stepsizes and gradient clipping. Furthermore, we perform the first analysis of these methods under the Polyak-{\L} ojasiewicz condition. Our theory is consistent with the known results for standard smooth problems, and our experimental results support the theoretical insights.

FRUGAL: Memory-Efficient Optimization by Reducing State Overhead for Scalable Training

With the increase in the number of parameters in large language models, the process of pre-training and fine-tuning increasingly demands larger volumes of GPU memory. A significant portion of this memory is typically consumed by the optimizer state. To overcome this challenge, recent approaches such as low-rank adaptation (LoRA (Hu et al., 2021)), low-rank gradient projection (GaLore (Zhao et al., 2024)), and blockwise optimization (BAdam (Luo et al., 2024)) have been proposed. However, in all these algorithms, the $\textit{effective rank of the weight updates remains low-rank}$, which can lead to a substantial loss of information from the gradient. This loss can be critically important, especially during the pre-training stage. In this paper, we introduce $\texttt{FRUGAL}$ ($\textbf{F}$ull-$\textbf{R}$ank $\textbf{U}$pdates with $\textbf{G}$r$\textbf{A}$dient sp$\textbf{L}$itting), a new memory-efficient optimization framework. $\texttt{FRUGAL}$ leverages gradient splitting to perform low-dimensional updates using advanced algorithms (such as Adam), while updates along the remaining directions are executed via state-free methods like SGD or signSGD (Bernstein et al., 2018). Our framework can be integrated with various low-rank update selection techniques, including GaLore and BAdam. We provide theoretical convergence guarantees for our framework when using SGDM for low-dimensional updates and SGD for state-free updates. Additionally, our method consistently outperforms concurrent approaches across various fixed memory budgets, achieving state-of-the-art results in pre-training and fine-tuning tasks while balancing memory efficiency and performance metrics.

Collaborative and Efficient Personalization with Mixtures of Adaptors

Non-iid data is prevalent in real-world federated learning problems. Data heterogeneity can come in different types in terms of distribution shifts. In this work, we are interested in the heterogeneity that comes from concept shifts, i.e., shifts in the prediction across clients. In particular, we consider multi-task learning, where we want the model to adapt to the task of the client. We propose a parameter-efficient framework to tackle this issue, where each client learns to mix between parameter-efficient adaptors according to its task. We use Low-Rank Adaptors (LoRAs) as the backbone and extend its concept to other types of layers. We call our framework Federated Low-Rank Adaptive Learning (FLoRAL). This framework is not an algorithm but rather a model parameterization for a multi-task learning objective, so it can work on top of any algorithm that optimizes this objective, which includes many algorithms from the literature. FLoRAL is memory-efficient, and clients are personalized with small states (e.g., one number per adaptor) as the adaptors themselves are federated. Hence, personalization is--in this sense--federated as well. Even though clients can personalize more freely by training an adaptor locally, we show that collaborative and efficient training of adaptors is possible and performs better. We also show that FLoRAL can outperform an ensemble of full models with optimal cluster assignment, which demonstrates the benefits of federated personalization and the robustness of FLoRAL to overfitting. We show promising experimental results on synthetic datasets, real-world federated multi-task problems such as MNIST, CIFAR-10, and CIFAR-100. We also provide a theoretical analysis of local SGD on a relaxed objective and discuss the effects of aggregation mismatch on convergence.

Low-Resource Machine Translation through the Lens of Personalized Federated Learning

We present a new approach based on the Personalized Federated Learning algorithm MeritFed that can be applied to Natural Language Tasks with heterogeneous data. We evaluate it on the Low-Resource Machine Translation task, using the dataset from the Large-Scale Multilingual Machine Translation Shared Task (Small Track #2) and the subset of Sami languages from the multilingual benchmark for Finno-Ugric languages. In addition to its effectiveness, MeritFed is also highly interpretable, as it can be applied to track the impact of each language used for training. Our analysis reveals that target dataset size affects weight distribution across auxiliary languages, that unrelated languages do not interfere with the training, and auxiliary optimizer parameters have minimal impact. Our approach is easy to apply with a few lines of code, and we provide scripts for reproducing the experiments at https://github.com/VityaVitalich/MeritFed

Gradient Clipping Improves AdaGrad when the Noise Is Heavy-Tailed

Methods with adaptive stepsizes, such as AdaGrad and Adam, are essential for training modern Deep Learning models, especially Large Language Models. Typically, the noise in the stochastic gradients is heavy-tailed for the later ones. Gradient clipping provably helps to achieve good high-probability convergence for such noises. However, despite the similarity between AdaGrad/Adam and Clip-SGD, the high-probability convergence of AdaGrad/Adam has not been studied in this case. In this work, we prove that AdaGrad (and its delayed version) can have provably bad high-probability convergence if the noise is heavy-tailed. To fix this issue, we propose a new version of AdaGrad called Clip-RAdaGradD (Clipped Reweighted AdaGrad with Delay) and prove its high-probability convergence bounds with polylogarithmic dependence on the confidence level for smooth convex/non-convex stochastic optimization with heavy-tailed noise. Our empirical evaluations, including NLP model fine-tuning, highlight the superiority of clipped versions of AdaGrad/Adam in handling the heavy-tailed noise.

Enhancing Policy Gradient with the Polyak Step-Size Adaption

Policy gradient is a widely utilized and foundational algorithm in the field of reinforcement learning (RL). Renowned for its convergence guarantees and stability compared to other RL algorithms, its practical application is often hindered by sensitivity to hyper-parameters, particularly the step-size. In this paper, we introduce the integration of the Polyak step-size in RL, which automatically adjusts the step-size without prior knowledge. To adapt this method to RL settings, we address several issues, including unknown f* in the Polyak step-size. Additionally, we showcase the performance of the Polyak step-size in RL through experiments, demonstrating faster convergence and the attainment of more stable policies.

Generalized Policy Learning for Smart Grids: FL TRPO Approach

The smart grid domain requires bolstering the capabilities of existing energy management systems; Federated Learning (FL) aligns with this goal as it demonstrates a remarkable ability to train models on heterogeneous datasets while maintaining data privacy, making it suitable for smart grid applications, which often involve disparate data distributions and interdependencies among features that hinder the suitability of linear models. This paper introduces a framework that combines FL with a Trust Region Policy Optimization (FL TRPO) aiming to reduce energy-associated emissions and costs. Our approach reveals latent interconnections and employs personalized encoding methods to capture unique insights, understanding the relationships between features and optimal strategies, allowing our model to generalize to previously unseen data. Experimental results validate the robustness of our approach, affirming its proficiency in effectively learning policy models for smart grid challenges.

Federated Learning Can Find Friends That Are Beneficial

In Federated Learning (FL), the distributed nature and heterogeneity of client data present both opportunities and challenges. While collaboration among clients can significantly enhance the learning process, not all collaborations are beneficial; some may even be detrimental. In this study, we introduce a novel algorithm that assigns adaptive aggregation weights to clients participating in FL training, identifying those with data distributions most conducive to a specific learning objective. We demonstrate that our aggregation method converges no worse than the method that aggregates only the updates received from clients with the same data distribution. Furthermore, empirical evaluations consistently reveal that collaborations guided by our algorithm outperform traditional FL approaches. This underscores the critical role of judicious client selection and lays the foundation for more streamlined and effective FL implementations in the coming years.

Flashback: Understanding and Mitigating Forgetting in Federated Learning

In Federated Learning (FL), forgetting, or the loss of knowledge across rounds, hampers algorithm convergence, particularly in the presence of severe data heterogeneity among clients. This study explores the nuances of this issue, emphasizing the critical role of forgetting in FL's inefficient learning within heterogeneous data contexts. Knowledge loss occurs in both client-local updates and server-side aggregation steps; addressing one without the other fails to mitigate forgetting. We introduce a metric to measure forgetting granularly, ensuring distinct recognition amid new knowledge acquisition. Leveraging these insights, we propose Flashback, an FL algorithm with a dynamic distillation approach that is used to regularize the local models, and effectively aggregate their knowledge. Across different benchmarks, Flashback outperforms other methods, mitigates forgetting, and achieves faster round-to-target-accuracy, by converging in 6 to 16 rounds.

Dirichlet-based Uncertainty Quantification for Personalized Federated Learning with Improved Posterior Networks

In modern federated learning, one of the main challenges is to account for inherent heterogeneity and the diverse nature of data distributions for different clients. This problem is often addressed by introducing personalization of the models towards the data distribution of the particular client. However, a personalized model might be unreliable when applied to the data that is not typical for this client. Eventually, it may perform worse for these data than the non-personalized global model trained in a federated way on the data from all the clients. This paper presents a new approach to federated learning that allows selecting a model from global and personalized ones that would perform better for a particular input point. It is achieved through a careful modeling of predictive uncertainties that helps to detect local and global in- and out-of-distribution data and use this information to select the model that is confident in a prediction. The comprehensive experimental evaluation on the popular real-world image datasets shows the superior performance of the model in the presence of out-of-distribution data while performing on par with state-of-the-art personalized federated learning algorithms in the standard scenarios.