Accelerated Distributed Aggregative Optimization
This work addresses optimization challenges in multi-agent systems where agents' costs depend on aggregated states, offering accelerated convergence for applications like optimal placement, though it is incremental as it builds on existing acceleration techniques.
The paper tackles the distributed aggregative optimization problem in networks by proposing two novel algorithms, DAGT-HB and DAGT-NES, which combine heavy ball and Nesterov's accelerated methods with distributed aggregative gradient tracking, achieving global R-linear convergence to an optimal solution under smooth and strongly convex conditions.
In this paper, we investigate a distributed aggregative optimization problem in a network, where each agent has its own local cost function which depends not only on the local state variable but also on an aggregated function of state variables from all agents. To accelerate the optimization process, we combine heavy ball and Nesterov's accelerated methods with distributed aggregative gradient tracking, and propose two novel algorithms named DAGT-HB and DAGT-NES for solving the distributed aggregative optimization problem. We analyse that the DAGT-HB and DAGT-NES algorithms can converge to an optimal solution at a global $\mathbf{R}-$linear convergence rate when the objective function is smooth and strongly convex, and when the parameters (e.g., step size and momentum coefficients) are selected within certain ranges. A numerical experiment on the optimal placement problem is given to verify the effectiveness and superiority of our proposed algorithms.