A deep learning approach for distributed aggregative optimization with users' feedback

This thesis focuses on distributed aggregative optimization, a recently emerged framework where a network of agents cooperate to solve a global optimization problem characterized by local cost functions depending on both the local decision variable and an aggregation of all of them (e.g., the mean of the decision variables of all the agents). The focus is on a so-called personalized version of this scenario in which the local costs consist of a (possibly) time-varying known term and a fixed unknown part, respectively representing the so-called engineering function (concerning measuring quantities such as, e.g., energy or time) and the user’s satisfaction (concerning human preferences whose model cannot be known in advance). In order to compensate for the lack of knowledge about the unknown part of each cost, this work enhances an existing distributed optimization scheme with an automatic differentiation procedure applied to neural networks. More in detail, the designed algorithm combines two independent loops devoted to performing optimization and learning steps. In turn, the distributed optimization algorithm embeds a consensus mechanism aimed at reconstructing in each agent the global information, namely the aggregative variable and the gradient of the cost function with respect to the aggregative variable. Finally, numerical examples involving a quadratic scenario are reported to show the effectiveness of the proposed method comparing already existing algorithms.