Theoretical Analysis of Divide-and-Conquer ERM: Beyond Square Loss and RKHS
This work addresses a gap in learning theory for distributed machine learning, but it is incremental as it extends existing analysis to broader settings.
The paper tackles the limited theoretical analysis of distributed learning for general loss functions and hypothesis spaces beyond square loss and RKHS, deriving tight risk bounds for distributed ERM under various assumptions and a more general bound without strong convexity.
Theoretical analysis of the divide-and-conquer based distributed learning with least square loss in the reproducing kernel Hilbert space (RKHS) have recently been explored within the framework of learning theory. However, the studies on learning theory for general loss functions and hypothesis spaces remain limited. To fill the gap, we study the risk performance of distributed empirical risk minimization (ERM) for general loss functions and hypothesis spaces. The main contributions are two-fold. First, we derive two tight risk bounds under certain basic assumptions on the hypothesis space, as well as the smoothness, Lipschitz continuity, strong convexity of the loss function. Second, we further develop a more general risk bound for distributed ERM without the restriction of strong convexity.