Distributed Proximal Splitting Algorithms with Rates and Acceleration
This work provides improved theoretical understanding and practical algorithms for distributed optimization, but it is incremental as it builds on existing proximal splitting methods.
The paper tackles large-scale convex nonsmooth optimization by analyzing proximal splitting algorithms, deriving new sublinear and linear convergence rates for function value suboptimality and distance to solutions, and proposing distributed and accelerated variants.
We analyze several generic proximal splitting algorithms well suited for large-scale convex nonsmooth optimization. We derive sublinear and linear convergence results with new rates on the function value suboptimality or distance to the solution, as well as new accelerated versions, using varying stepsizes. In addition, we propose distributed variants of these algorithms, which can be accelerated as well. While most existing results are ergodic, our nonergodic results significantly broaden our understanding of primal-dual optimization algorithms.