Uncertainty-Aware Kernels as a Practical Alternative to Moment Matching in Gaussian-Process MPC

Analytic Moment Matching enables multistep uncertainty propagation in Gaussian-Process Model Predictive Control, but requires specialised derivations. We study an uncertainty-aware RBF kernel over Gaussian-distributed inputs as a practical alternative. For deterministic training inputs, we show that the resulting GP predictor has exactly the same posterior mean and marginal-likelihood objective as analytic Moment Matching. On Pendulum-v1 our method shows comparable performance with an $8\times$ wall-clock speedup and an $11\times$ lower memory footprint.