Multi-Constrained Randomized Smoothing Certificates

Randomized Smoothing (RS) is a principled and widely adopted approach for certifying the robustness of black-box models, such as neural networks, against adversarial perturbations. We propose an optimization perspective that unifies several prior randomized smoothing certificates. We then show how to reduce the underlying high-dimensional worst-case optimization problem to an equivalent two-dimensional formulation under a double- or multi-sampling scheme, enabling efficient solutions via convex optimization. By exploiting additional information about the variance of the smoothed classifier across different smoothing distributions, we derive certified bounds that improve upon standard certificates. We show results on both classification and regression tasks.