Nonlinear-Gain Distributed Zeroth-Order Optimization for Networked Black-Box Control
arXiv:2605.25306
The paper proposes ZOOM-PB, a distributed zeroth‑order optimization algorithm that mixes raw gradient estimates with a nonlinear fractional‑power response to improve convergence on peer‑to‑peer networks.
Abstract
This letter studies distributed stochastic optimization over a peer-to-peer network when agents can query only zeroth-order function values. We propose ZOOM-PB, a coordinate-sampling method that blends each local ZO estimate with a fractional-power response while maintaining only a primal state. The raw estimate is retained as a linear anchor, and the nonlinear mixing weight is coupled to the optimization stepsize. This design is motivated by a basic obstruction: transforming heterogeneous or noisy local estimates before averaging can reverse the network direction. We bound that nonlinear residual directly from the raw oracle assumptions instead of imposing an aggregate-alignment condition. With a smooth stochastic-function oracle and a connected graph, ZOOM-PB attains the nonconvex stationarity order and a Polyak--Åojasiewicz statistical term of order , after an explicit initialization transient. Numerical examples compare ZOOM-PB with seven distributed ZO baselines under matched query and message budgets.