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Electronically tunable metasurfaces, or Intelligent Reflecting Surfaces (IRSs), are a popular technology for achieving high spectral efficiency in modern wireless systems by shaping channels using a multitude of tunable passive reflecting 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 Zerothorder 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 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 O( S −4) under minimal assumptions, where S is the total number of IRS elements, and   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 in the field, by directly optimizing the capacitances of a varactor-based electromagnetic IRS model (unknown to ZoSGA) on a multiple user/IRS, link-dense network setting, with essentially no computational overheads or performance degradation.