  Electronically tunable metasurfaces, or Intelligent Reflective Surfaces
(IRSs), are a popular technology for achieving high spectral efficiency in
modern wireless systems by shaping channels using a multitude of tunable
passive reflective elements. Capitalizing on key practical limitations of
IRS-aided beamforming pertaining to system modeling and channel
sensing/estimation, we propose a novel, fully data-driven Zeroth-order
Stochastic Gradient Ascent (ZoSGA) algorithm for general two-stage (i.e.,
short/long-term), fully-passive IRS-aided stochastic utility maximization.
ZoSGA learns long-term optimal IRS beamformers jointly with short-term optimal
precoders (e.g., WMMSE-based) via minimal zeroth-order reinforcement and in a
strictly model-free fashion, relying solely on the \textit{effective} compound
channels observed at the terminals, while being independent of channel models
or network/IRS configurations. Another remarkable feature of ZoSGA is being
amenable to analysis, enabling us to establish a state-of-the-art (SOTA)
convergence rate of the order of $\boldsymbol{O}(\sqrt{S}\epsilon^{-4})$ under
minimal assumptions, where $S$ is the total number of IRS elements, and
$\epsilon$ is a desired suboptimality target. Our numerical results on a
standard MISO downlink IRS-aided sumrate maximization setting establish SOTA
empirical behavior of ZoSGA as well, consistently and substantially
outperforming standard fully model-based baselines. Lastly, we demonstrate that
ZoSGA can in fact operate \textit{in the field}, by directly optimizing the
capacitances of a varactor-based electromagnetic IRS model (unknown to ZoSGA)
on a multiple user/IRS, compute-heavy network setting, with essentially no
computational overheads or performance degradation.
