  Personalized Federated Learning (PFL) is proposed to find the greatest
personalized models for each client. To avoid the central failure and
communication bottleneck in the server-based FL, we concentrate on the
Decentralized Personalized Federated Learning (DPFL) that performs distributed
model training in a Peer-to-Peer (P2P) manner. Most personalized works in DPFL
are based on undirected and symmetric topologies, however, the data,
computation and communication resources heterogeneity result in large variances
in the personalized models, which lead the undirected aggregation to suboptimal
personalized performance and unguaranteed convergence. To address these issues,
we propose a directed collaboration DPFL framework by incorporating stochastic
gradient push and partial model personalized, called \textbf{D}ecentralized
\textbf{Fed}erated \textbf{P}artial \textbf{G}radient \textbf{P}ush
(\textbf{DFedPGP}). It personalizes the linear classifier in the modern deep
model to customize the local solution and learns a consensus representation in
a fully decentralized manner. Clients only share gradients with a subset of
neighbors based on the directed and asymmetric topologies, which guarantees
flexible choices for resource efficiency and better convergence. Theoretically,
we show that the proposed DFedPGP achieves a superior convergence rate of
$\mathcal{O}(\frac{1}{\sqrt{T}})$ in the general non-convex setting, and prove
the tighter connectivity among clients will speed up the convergence. The
proposed method achieves state-of-the-art (SOTA) accuracy in both data and
computation heterogeneity scenarios, demonstrating the efficiency of the
directed collaboration and partial gradient push.
