Learning-Augmented Strategyproof Facility Location in $\mathbb{R}^d$ with $\ell_p$ Distances

We study learning-augmented mechanism design for locating a single facility in $\mathbb{R}^d$ to minimize the sum of the agents' $\ell_p$ distances to the facility. We analyze the coordinate-wise median with predictions (CMP) mechanism, which adds $cn$ virtual agents at a predicted optimal facility