Performance Enhancement on Sparse Federated Learning Supported by RIS-Aided Communication in the Finite Blocklength Regime

Federated learning (FL) has been considered as a promising way to train distributed wireless systems in a privacy-preserving manner. However, the significant communications overheads caused by uploading local parameters and the potential unreliability of wireless links emerged as one of the bottlenecks of FL. To address this challenge, this paper investigates a reconfigurable intelligent surface (RIS)-assisted sparse FL network, where the RIS is utilized for wireless transmission reliability enhancement, and the sparsification operation is used to reduce the communications overheads. Considering that the wireless transmissions of the FL uploads are carried by finite blocklength (FBL) codes, we <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">for the first time</i> investigate the convergence of sparse FL while taking into account both the FBL decoding errors and FL sparsification errors. Following such a model, a novel joint learning and communication design framework is provided. In particular, an optimization problem is formulated to minimize the impacts of the above errors on the convergence via jointly determining the coding rate, transmit power, and RIS phase shift. To tackle the formulated non-convex problem, a block coordinate descent (BCD)-based algorithm is proposed, which decomposes the problem into two sub-ones and solves them alternately. On the one hand, for the resource allocation sub-problem, we derive a closed-form expression of optimal coding rate with respect to power that drastically reduces the optimization problem dimension, and shows the convexity of the resulting power allocation problem. For the RIS phase shift design sub-problem, on the other hand, a trust-region based linear approximation is used, along with problem transformations and tight successive convex approximations, to derive a highly effective iterative algorithm based on the closed-form expression for each variable. The entire proposed iterative algorithm converges efficiently to a suboptimal solution. Then, we extend the proposed algorithm to the imperfect channel state information (CSI) scenarios by using second-order Taylor approximation. Numerical results demonstrate that the proposed design significantly improves the FL performance in comparison to benchmark schemes.