Consensus-based distributed learning for robust convex optimization with a scenario approach

This paper aims to solve the robust convex optimization (RCO) problem, where the constraints of RCO are parameterized with uncertainties, and the scenario approach is applied to transform RCO into standard convex optimization with a finite number of constraints through probabilistic approximation. The transformed problem is called a scenario problem (SP). Two consensus-based distributed learning algorithms for SP are designed in consideration of a large number of sampled constraints. One is based on the distributed average consensus (DAC), and the other is based on the alternating direction method of multipliers (ADMM). It has regulated that data distributed to nodes are not allowed to communicate. Simulation results indicate that the proposed algorithms are suitable for handling large-scale data and achieve excellent performance, with the ADMM-based algorithm performing the best. Furthermore, the DAC-based algorithm has certain advantages in terms of computational time and complexity. In addition, to improve the communicative efficiency based on a DAC, an efficient distributed average consensus (EDAC) is put forward. The average time for every node when using an EDAC is less than that of a DAC, despite the exact same performance.