The standard Federated Averaging (FedAvg) algorithm serves as a foundational technique for combining model updates from multiple clients. However, its effectiveness can be limited, especially when dealing with non-identically distributed (Non-IID) data across clients or when facing unreliable participants. This chapter introduces aggregation algorithms designed to perform more effectively under these challenging, yet common, conditions.

You will examine:

• The specific weaknesses and failure modes of the standard FedAvg approach.
• Algorithms like FedProx, designed to mitigate the negative impact of statistical heterogeneity by adding a proximal term to the local client objective function, represented as $\frac{\mu}{2} ||w - w^t||^2$.
• SCAFFOLD, a method employing control variates to reduce client drift and variance, improving convergence speed.
• FedNova, which addresses systems heterogeneity by normalizing local updates before aggregation.
• Techniques such as Krum, Median, and Trimmed Mean that provide robustness against Byzantine clients submitting potentially malicious updates.
• The theoretical motivations and convergence properties of these advanced methods.
• Practical implementation considerations for integrating these algorithms into federated learning workflows.

Upon completing this chapter, you will be equipped to select, implement, and analyze aggregation strategies beyond FedAvg, enabling the development of more reliable and performant federated learning systems in diverse environments.