Present-day federated learning (FL) systems deployed over edge networks have to consistently deal with a large number of workers with high degrees of heterogeneity in data and/or computing capabilities. This diverse set of workers necessitates the development of FL algorithms that allow: (1) flexible worker participation that grants the workers capability to engage in training at will, (2) varying number of local updates (based on computational resources) at each worker along with asynchronous communication with the server, and (3) heterogeneous data across workers. To address these challenges, in this work, we propose a new paradigm in FL called ``Anarchic Federated Learning (AFL). In stark contrast to conventional FL models, each worker in AFL has complete freedom to choose i) when to participate in FL, and ii) the number of local steps to perform in each round based on its current situation (e.g., battery level, communication channels, privacy concerns). However, AFL also introduces significant challenges in algorithmic design because the server needs to handle the chaotic worker behaviors. Toward this end, we propose two Anarchic FedAvg-like algorithms with two-sided learning rates for both cross-device and cross-silo settings, which are named AFedAvg-TSLR-CD and AFedAvg-TSLR-CS, respectively. For general worker information arrival processes, we show that both algorithms retain the highly desirable linear speedup effect in the new AFL paradigm. Moreover, we show that our AFedAvg-TSLR algorithmic framework can be viewed as a {em meta-algorithm} for AFL in the sense that they can utilize advanced FL algorithms as worker- and/or server-side optimizers to achieve enhanced performance under AFL. We validate the proposed algorithms with extensive experiments on real-world datasets.
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