Automatic Performance Estimation for Decentralized Optimization

We present a methodology to automatically compute worst-case performance bounds for large class of first-order decentralized optimization algorithms. These algorithms aim at minimizing the average local functions that are distributed across network agents. They typically combine computations and consensus steps. Our is based on approach Performance Estimation Problem (PEP), which allows computing instance by solving an SDP. propose two ways representing steps in PEPs, allow writing PEPs optimization. The first formulation exact but specific given averaging matrix. second relaxation provides guarantees valid over entire matrices, characterized their spectral range. This often recovering posteriori worst possible matrix algorithm. apply our three different methods. For each them, we obtain numerically tight significantly improve existing ones, as well insights about parameters tuning communication networks.