State-of-the-art federated learning algorithms such as FedAvg require carefully tuned stepsizes to achieve their best performance. The improvements proposed by existing adaptive federated methods involve tuning of additional hyperparameters such as momentum parameters, and consider adaptivity only in the server aggregation round, but not locally. These methods can be inefficient in many practical scenarios because they require excessive tuning of hyperparameters and do not capture local geometric information. In this work, we extend the recently proposed stochastic Polyak stepsize (SPS) to the federated learning setting, and propose new locally adaptive and nearly parameter-free distributed SPS variants (FedSPS and FedDecSPS). We prove that FedSPS converges linearly in strongly convex and sublinearly in convex settings when the interpolation condition (overparametrization) is satisfied, and converges to a neighborhood of the solution in the general case. We extend our proposed method to a decreasing stepsize version FedDecSPS, that converges also when the interpolation condition does not hold. We validate our theoretical claims by performing illustrative convex experiments. Our proposed algorithms match the optimization performance of FedAvg with the best tuned hyperparameters in the i.i.d. case, and outperform FedAvg in the non-i.i.d. case.

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