Distributed First-Order and Second-Order Adaptive Hybrid Optimization for Multi-Robot Learning

We present a distributed first-order and second-order adaptive hybrid optimization algorithm (DAHO) for multi-robot systems. A team of robots collaboratively trains a shared deep neural network using only local data while exchanging model updates via peer-to-peer robot communication. Raw data never leaves the device, which preserves privacy and conserves communication bandwidth. The method blends a second-order Limited-memory Broyden–Fletcher–Goldfarb–Shann (LBFGS) method with an alternating direction method of multipliers (ADMM) based first-order method to obtain both the fast convergence of second-order methods and the robustness of first-order schemes. An automatic switching policy, guided by a convergence analysis rooted in trust region theory, selects the update type at each round. A soft switch mechanism derived from the same analysis mitigates oscillations during mode changes. Compared with four single-method baselines that range from first-order to second-order optimization, the proposed hybrid approach achieves faster convergence, superior accuracy, and near centralized performance on robotics related deep learning tasks.