Federated learning (FL) enables collaborative model training across multiple parties without sharing raw data, with semi-asynchronous FL (SAFL) emerging as a balanced approach between synchronous and asynchronous FL. However, SAFL faces significant challenges in optimizing both gradient-based (e.g., FedSGD) and model-based (e.g., FedAvg) aggregation strategies, which exhibit distinct trade-offs in accuracy, convergence speed, and stability. While gradient aggregation achieves faster convergence and higher accuracy, it suffers from pronounced fluctuations, whereas model aggregation offers greater stability but slower convergence and suboptimal accuracy. This paper presents FedQS, the first framework to theoretically analyze and address these disparities in SAFL. FedQS introduces a divide-andconquer strategy to handle client heterogeneity by classifying clients into four distinct types and adaptively optimizing their local training based on data distribution characteristics and available computational resources. Extensive experiments on computer vision, natural language processing, and real-world tasks demonstrate that FedQS achieves the highest accuracy, attains the lowest loss, and ranks among the fastest in convergence speed, outperforming state-of-the-art baselines.

Federated learning (FL) is a distributed paradigm that coordinates massive local clients to collaboratively train a global model via stage-wise local training processes on the heterogeneous dataset. Previous works have implicitly studied that FL suffers from the "client-drift" problem, which is caused by the inconsistent optimum across local clients. However, till now it still lacks solid theoretical analysis to explain the impact of this local inconsistency. To alleviate the negative impact of the "client drift" and explore its substance in FL, in this paper, we first design an efficient FL algorithm FedInit, which allows employing the personalized relaxed initialization state at the beginning of each local training stage.

We present more experiments and provide all missing proofs in the appendix. Concretely, Appendix A describes the experiment setup and contains additional numerical experiments. Appendix B and C provide the detailed proofs for our unified privacy guarantee in Theorem 2 and unified utility and communication complexity analysis in Theorem 3, respectively. Appendix D provides the proof for CDP-SGD (Theorem 1). Finally, Appendix E provides the proofs for Section 5, including Lemma 1 (showing that several local gradient estimators satisfy the generic Assumption 3) and Corollaries 1-3 (instantiating Lemma 1 in the unified Theorem 3) for the proposed SoteriaFL-style algorithms.

We first prove case (a).

Traditionally, federated learning (FL) aims to train a single global model while collaboratively using multiple clients and a server. Two natural challenges that FL algorithms face are heterogeneity in data across clients and collaboration of clients with diverse resources.

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