Importance sampling strategy for non-convex randomized block-coordinate descent
This incremental improvement addresses convergence efficiency for large-scale optimization problems in statistics and machine learning.
The authors tackled the problem of slow convergence in randomized block-coordinate descent for high-dimensional optimization by introducing an importance sampling strategy that prioritizes blocks far from convergence, resulting in clear experimental benefits compared to uniform sampling and cyclic methods.
As the number of samples and dimensionality of optimization problems related to statistics an machine learning explode, block coordinate descent algorithms have gained popularity since they reduce the original problem to several smaller ones. Coordinates to be optimized are usually selected randomly according to a given probability distribution. We introduce an importance sampling strategy that helps randomized coordinate descent algorithms to focus on blocks that are still far from convergence. The framework applies to problems composed of the sum of two possibly non-convex terms, one being separable and non-smooth. We have compared our algorithm to a full gradient proximal approach as well as to a randomized block coordinate algorithm that considers uniform sampling and cyclic block coordinate descent. Experimental evidences show the clear benefit of using an importance sampling strategy.