<p>This paper introduces a novel multivariable Newton-based stochastic extremum-seeking control method for real-time optimization in multi-input systems with distinct input delays. The proposed approach integrates predictor-based feedback and Hessian inverse estimation, achieved through stochastic sinusoidal perturbations, to allow delay compensation while ensuring user-defined convergence rates. This method preserves exponential stability and guarantees convergence to a small neighborhood around the unknown extremum point, even under arbitrarily long delays in actuator channels. The control scheme is further extended to accommodate multi-input, single-output maps with cross-coupled channels, thereby addressing complex, delayed interactions that frequently arise in real-world control systems. Stability analysis is rigorously derived using backstepping transformations and infinite-dimensional averaging techniques, establishing a strong theoretical foundation for robust performance in dynamic settings. Numerical simulations illustrate the proposed method’s effectiveness in delay compensation, highlighting both the challenges and the benefits of managing time-delayed channels in real-time optimization.</p>