Prior study on automatically identifying complaints on social media has relied on extensive feature engineering in centralized settings, with no consideration for the decentralized, non-identically independently distributed (Non-IID), and privacy-conscious aspect of complaints, which can hinder data collection, distribution, and learning. In this work, we propose a Graph Attention Network (GAT) based multi-task framework that intends to learn two closely related tasks, complaint detection (primary task) and sentiment classification (auxiliary task), simultaneously in federated-learning scenarios. We propose the Federated Combination (FedComb) algorithm, a two-sided adaptive optimization technique that simultaneously optimizes global and local models. The proposed methodology outperforms several baselines for the intended task of recognizing complaints in decentralized settings, according to quantitative and qualitative studies on two benchmark datasets. The resources are available at <uri xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">https://github.com/appy1608/IEEE-TAI_FedCI_GAT</uri> .