Locally Adaptive Federated Learning via Stochastic Polyak Stepsizes

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.

Fingertip Detection and Tracking for Recognition of Air-Writing in Videos

Air-writing is the process of writing characters or words in free space using finger or hand movements without the aid of any hand-held device. In this work, we address the problem of mid-air finger writing using web-cam video as input. In spite of recent advances in object detection and tracking, accurate and robust detection and tracking of the fingertip remains a challenging task, primarily due to small dimension of the fingertip. Moreover, the initialization and termination of mid-air finger writing is also challenging due to the absence of any standard delimiting criterion. To solve these problems, we propose a new writing hand pose detection algorithm for initialization of air-writing using the Faster R-CNN framework for accurate hand detection followed by hand segmentation and finally counting the number of raised fingers based on geometrical properties of the hand. Further, we propose a robust fingertip detection and tracking approach using a new signature function called distance-weighted curvature entropy. Finally, a fingertip velocity-based termination criterion is used as a delimiter to mark the completion of the air-writing gesture. Experiments show the superiority of the proposed fingertip detection and tracking algorithm over state-of-the-art approaches giving a mean precision of 73.1 % while achieving real-time performance at 18.5 fps, a condition which is of vital importance to air-writing. Character recognition experiments give a mean accuracy of 96.11 % using the proposed air-writing system, a result which is comparable to that of existing handwritten character recognition systems.