This paper studies a reconfigurable intelligent surface (RIS)-assisted indoor architecture for extended reality (XR) applications, where multiple access points (APs) simultaneously serve multiple users over a shared frequency channel under a centralized AP controller. We formulate a non-convex sum-rate maximization problem with coupled AP precoders and RIS phase shifts, and develop a centralized alternating optimization (AO) framework for joint design. We rigorously prove that the proposed AO guarantees monotonic improvement of the sum rate that converges to a coordinate-wise stationary point, despite the non-convexity of the resulting subproblems. Although AO provides reliable performance, its iterative nature limits real-time applicability as the system dimension grows. To overcome this limitation, we propose a supervised learning-assisted approach that leverages AO-generated solutions to significantly accelerate convergence. Simulation results demonstrate that the proposed framework achieves near-optimal performance with substantially fewer AO iterations, which makes it well-suited for latency-critical RIS-assisted XR deployments.

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