a new personalized FL algorithm paradigm by proposing Hybrid Pruning (structured + unstructured pruning) with averaging on the intersection of clients’ drawn subnetworks which simultaneously handles communication efficiency, resource constraints and personalized models accuracies. Sub-FedAvg is the first work which shows existence of personalized winning tickets for clients in federated learning through experiments. Moreover, it also proposes two algorithms on how to effectively draw the personalized subnetworks. Sub-FedAvg tries to extend "Lottery Ticket Hypothesis" which is for centrally trained neural networks to federated learning trained neural networks leading to this open research problem: “Do winning tickets exist for clients’ neural networks being trained in federated learning? If yes, how to effectively draw the personalized subnetworks for each client?” Dynamic Aggregation - Inverse Distance Aggregation IDA (Inverse Distance Aggregation) is a novel adaptive weighting approach for clients based on meta-information which handles unbalanced and non-iid data. It uses the distance of the model parameters as a strategy to minimize the effect of outliers and improve the model's convergence rate. Hybrid Federated Dual Coordinate Ascent (HyFDCA) Very few methods for hybrid federated learning, where clients only hold subsets of both features and samples, exist. Yet, this scenario is very important in practical settings. Hybrid Federated Dual Coordinate Ascent (HyFDCA) is a novel algorithm proposed in 2022 that solves convex problems in the hybrid FL setting. This algorithm extends CoCoA, a primal-dual distributed optimization algorithm introduced by Jaggi et al. (2014) and Smith et al. (2017), to the case where both samples and features are partitioned across clients. HyFDCA claims several improvement over existing algorithms: HyFDCA is a provably convergent primal-dual algorithm for hybrid FL in at least the following settings. Hybrid Federated Setting with Complete Client Participation Horizontal Federated Setting with Random Subsets of Available Clients The authors show HyFDCA enjoys a convergence rate of () which matches the convergence rate of FedAvg (see below). Vertical Federated Setting with Incomplete Client Participation The authors show HyFDCA enjoys a convergence rate of () whereas FedBCD exhibits a slower () convergence rate and requires full client participation. HyFDCA provides the privacy steps that ensure privacy of client data in the primal-dual setting. These principles apply to future efforts in developing primal-dual algorithms for FL. HyFDCA empirically outperforms FedAvg in loss function value and validation accuracy across a multitude of problem settings and datasets. The authors also introduce a hyperparameter selection framework for FL with