Data-Driven Learning of Two-Stage Beamformers in Passive IRS-Assisted Systems With Inexact Oracles

The purpose of this work is the development of an efficient data-driven and model-free unsupervised learning framework for achieving fully passive intelligent reflective surface (IRS)-assisted optimal joint short/long-term beamforming in wireless communication networks. Under this challenging setting, our contribution amounts to the design of novel <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">IRS training schemes</i> —termed <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">iZoSGA</i> herein— relying on a zeroth-order stochastic gradient ascent methodology, suitable for tackling nonconvex twostage stochastic optimization problems with continuous uncertainty and unknown (or ‘‘black-box’’) terms present in the corresponding objective function, via utilization of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">inexact short-term evaluation oracles</i>. Our findings are as follows:We showcase that iZoSGA can operate under realistic and general assumptions, and establish its (non-asymptotic) convergence rate close to some stationary point of the associated two-stage (i.e., short/long-term) problem, particularly in cases where the second-stage (i.e., short-term) beamforming problem (e.g., transmit precoding) is solved <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">inexactly</i> using an arbitrary (inexact) algorithm. iZoSGA is applicable on a wide variety of IRS-assisted optimal beamforming settings, while also being able to operate without (cascaded) channel model assumptions or knowledge of channel statistics, and over arbitrary IRS physical configurations; thus, no active sensing capability at the IRS(s) is needed. Additionally, our approach bypasses the need of imposing challenging nonconvex unit-modulus constraints, typically associated with IRS parameter optimization. Several algorithmic variants of iZoSGA are numerically demonstrated to be particularly effective in a range of experiments pertaining to a well-studied MISO downlink model, including scenarios demanding physical IRS tuning (e.g., directly through varactor capacitances), even in large-scale regimes. Overall we demonstrate that, by leveraging the developed theory and its insights on the propagation of oracle errors, we can create highly efficient and scalable algorithms for the solution of general (possibly large-scale) IRS-assisted optimal beamforming problems, under realistic assumptions.