Deep Unfolding Aided Parameter Optimization for Multi-task Diffusion LMS Algorithm

The paper proposes a novel algorithm termed TMDLMS (Trainable Multi-task Diffusion Least Mean Squares) to collaboratively estimate multiple vectors, which are assumed to have certain correlations, from observations obtained at multiple nodes in the network. Adopting the concept of deep unfolding, the proposed algorithm is obtained by unfolding iterative process of the conventional MDLMS (Multi-task Diffusion Least Mean Squares) algorithm, resulting in a multi-layered signal flow graph reminiscent of neural networks. In this structure, the parameters in the algorithm such as the step size of each layer are considered as trainable parameters, allowing for optimization via machine learning techniques, such as stochastic gradient descent (SGD). Numerical experimental results indicate that, compared to the conventional MDLMS using fixed parameters, the proposed algorithm can boast the convergence rates and achieve lower steady-state errors at the same time. The results demonstrate the validity of the proposed approach under various conditions.