Federated Learning (FL) is a distributed machine learning framework in which a set of local communities collaboratively learn a shared global model while retaining all training data locally within each community. Two notions of fairness have recently emerged as important issues for federated learning: group fairness and community fairness. Group fairness requires that a model's decisions do not favor any particular group based on a set of legally protected attributes such as race or gender. Community fairness requires that global models exhibit similar levels of performance (accuracy) across all collaborating communities. Both fairness concepts can coexist within an FL framework, but the existing literature has focused on either one concept or the other. This paper proposes and analyzes a post-processing fair federated learning (FFL) framework called post-FFL. Post-FFL uses a linear program to simultaneously enforce group and community fairness while maximizing the utility of the global model. Because Post-FFL is a post-processing approach, it can be used with existing FL training pipelines whose convergence properties are well understood. This paper uses post-FFL on real-world datasets to mimic how hospital networks, for example, use federated learning to deliver community health care. Theoretical results bound the accuracy lost when post-FFL enforces both notion of fairness. Experimental results illustrate that post-FFL simultaneously improves both group and community fairness in FL. Moreover, post-FFL outperforms the existing in-processing fair federated learning in terms of improving both notions of fairness, communication efficiency and computation cost.

AM techniques were first introduced in soft-competitive learning algorithms[l]. This training procedure was later shown to be closely related to Expectation-Maximization algorithms used by the statistical estimation community[2]. Alternating minimizations search for optimal network weights by breaking the search into two distinct minimization problems. A given network performance functional is extremalized first with respect to one set of network weights and then with respect to the remaining weights. These learning procedures have found applications in the training of local expert systems [3], and in Boltzmann machine training [4]. More recently, convergence rates have been derived by viewing the AM 570 Michael Lemmon.

AM techniques were first introduced in soft-competitive learning algorithms[l]. Thistraining procedure was later shown to be closely related to Expectation-Maximization algorithms used by the statistical estimation community[2].

A neural network solution is proposed for solving path planning problems The proposed network is a two-dimensional sheetfaced by mobile robots. of neurons forming a distributed representation of the robot's workspace. Lateral interconnections between neurons are "cooperative", so that the network exhibits oscillatory behaviour. These oscillations are used to generate solutions of Bellman's dynamic programming equation in the context of path planning. Simulation experiments imply that these networks locate paths even in the presence of substantial levels of circuitglobal optimal nOlse. 1 Dynamic Programming and Path Planning Consider a 2-DOF robot moving about in a 2-dimensional world. A robot's location is denoted by the real vector, p.

A neural network solution is proposed for solving path planning problems faced by mobile robots. The proposed network is a two-dimensional sheet of neurons forming a distributed representation of the robot's workspace. Lateral interconnections between neurons are "cooperative", so that the network exhibits oscillatory behaviour. These oscillations are used to generate solutions of Bellman's dynamic programming equation in the context of path planning. Simulation experiments imply that these networks locate global optimal paths even in the presence of substantial levels of circuit nOlse. 1 Dynamic Programming and Path Planning Consider a 2-DOF robot moving about in a 2-dimensional world. A robot's location is denoted by the real vector, p.