Lingxiao Wang

Kumar Kshitij Patel, Margalit Glasgow, Ali Zindari et al.

Local SGD is a popular optimization method in distributed learning, often outperforming other algorithms in practice, including mini-batch SGD. Despite this success, theoretically proving the dominance of local SGD in settings with reasonable data heterogeneity has been difficult, creating a significant gap between theory and practice. In this paper, we provide new lower bounds for local SGD under existing first-order data heterogeneity assumptions, showing that these assumptions are insufficient to prove the effectiveness of local update steps. Furthermore, under these same assumptions, we demonstrate the min-max optimality of accelerated mini-batch SGD, which fully resolves our understanding of distributed optimization for several problem classes. Our results emphasize the need for better models of data heterogeneity to understand the effectiveness of local SGD in practice. Towards this end, we consider higher-order smoothness and heterogeneity assumptions, providing new upper bounds that imply the dominance of local SGD over mini-batch SGD when data heterogeneity is low.

Kumar Kshitij Patel, Weitong Zhang, Lingxiao Wang

The scarcity of accessible, compliant, and ethically sourced data presents a considerable challenge to the adoption of artificial intelligence (AI) in sensitive fields like healthcare, finance, and biomedical research. Furthermore, access to unrestricted public datasets is increasingly constrained due to rising concerns over privacy, copyright, and competition. Synthetic data has emerged as a promising alternative, and diffusion models -- a cutting-edge generative AI technology -- provide an effective solution for generating high-quality and diverse synthetic data. In this paper, we introduce a novel federated learning framework for training diffusion models on decentralized private datasets. Our framework leverages personalization and the inherent noise in the forward diffusion process to produce high-quality samples while ensuring robust differential privacy guarantees. Our experiments show that our framework outperforms non-collaborative training methods, particularly in settings with high data heterogeneity, and effectively reduces biases and imbalances in synthetic data, resulting in fairer downstream models.