Federated learning (FL) enables collaborative learning across multiple clients. In most FL work, all clients train a single learning task. However, the recent proliferation of FL applications may increasingly require multiple FL tasks to be trained simultaneously, sharing clients' computing and communication resources, which we call Multiple-Model Federated Learning (MMFL). Current MMFL algorithms use naive average-based client-task allocation schemes that can lead to unfair performance when FL tasks have heterogeneous difficulty levels, e.g., tasks with larger models may need more rounds and data to train. Just as naively allocating resources to generic computing jobs with heterogeneous resource needs can lead to unfair outcomes, naive allocation of clients to FL tasks can lead to unfairness, with some tasks having excessively long training times, or lower converged accuracies. Furthermore, in the FL setting, since clients are typically not paid for their training effort, we face a further challenge that some clients may not even be willing to train some tasks, e.g., due to high computational costs, which may exacerbate unfairness in training outcomes across tasks. We address both challenges by firstly designing FedFairMMFL, a difficulty-aware algorithm that dynamically allocates clients to tasks in each training round. We provide guarantees on airness and FedFairMMFL's convergence rate. We then propose a novel auction design that incentivizes clients to train multiple tasks, so as to fairly distribute clients' training efforts across the tasks. We show how our fairness-based learning and incentive mechanisms impact training convergence and finally evaluate our algorithm with multiple sets of learning tasks on real world datasets.
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