  We study model-free learning methods for the output-feedback Linear Quadratic
(LQ) control problem in finite-horizon subject to subspace constraints on the
control policy. Subspace constraints naturally arise in the field of
distributed control and present a significant challenge in the sense that
standard model-based optimization and learning leads to intractable numerical
programs in general. Building upon recent results in zeroth-order optimization,
we establish model-free sample-complexity bounds for the class of distributed
LQ problems where a local gradient dominance constant exists on any sublevel
set of the cost function. %which admit a local gradient dominance constant
valid on the sublevel set of the cost function. We prove that a fundamental
class of distributed control problems - commonly referred to as Quadratically
Invariant (QI) problems - as well as others possess this property. To the best
of our knowledge, our result is the first sample-complexity bound guarantee on
learning globally optimal distributed output-feedback control policies.
