  Distribution grids are currently challenged by frequent voltage excursions
induced by intermittent solar generation. Smart inverters have been advocated
as a fast-responding means to regulate voltage and minimize ohmic losses. Since
optimal inverter coordination may be computationally challenging and preset
local control rules are subpar, the approach of customized control rules
designed in a quasi-static fashion features as a golden middle. Departing from
affine control rules, this work puts forth non-linear inverter control
policies. Drawing analogies to multi-task learning, reactive control is posed
as a kernel-based regression task. Leveraging a linearized grid model and given
anticipated data scenarios, inverter rules are jointly designed at the feeder
level to minimize a convex combination of voltage deviations and ohmic losses
via a linearly-constrained quadratic program. Numerical tests using real-world
data on a benchmark feeder demonstrate that nonlinear control rules driven also
by a few non-local readings can attain near-optimal performance.
