Distributed Adaptive Multi-Task Learning Based on Partially Observed Graph Signals

In this paper, we consider the clustered multi-task learning (MTL) problem with partial observations and develop a diffusion least-mean-square (LMS) algorithm with a distributed cluster-wise sampling strategy. The proposed algorithm converges at the steady-state with the measurements observed only at a subset of the vertices, instead of the entire graph, without significant loss of the steady-state performance. We analyze the performance of the proposed algorithm and further devise a tractable cost function with respect to the sampling probability based on an approximate network Mean-Square-Deviation (MSD) of the learning objectives. We further develop a feasible selection scheme of the sampling probability set to bolster the distributed cluster-wise sampling strategy such that the convergence of the proposed diffusion LMS algorithm is accelerated. Illustrative simulations show the efficiency and the robustness of the proposed algorithm and validate the theoretical results.