Distributed Conditional Gradient Online Learning for IoT Optimization

Many problems in Internet of Things (IoT) can be cast as distributed optimization problems. For this reason, this paper considers a distributed online constrained optimization problem in IoT, where the local objective functions change with time. In order to solve this problem, distributed projected gradient descent methods are employed frequently. However, the computation of the projection operators is prohibitive in high-dimensional constrained optimization problem. To address the issue, we propose a distributed online learning algorithm based on the conditional gradient method over IoT systems, which avoids the costly projection steps. Moreover, when the local objective functions are strongly convex, we show that the regret bound of O(T) is achieved, where T is a time horizon. When the local objective functions are potentially non-convex, we also show that the algorithm converges to some stationary points at rate of O(T). In addition, we present simulation experiments to confirm the theoretical results.