Wealsoproposeawayto regularize this MMD flow, based on an injection of noise in the gradient. This algorithmic fix comes with theoretical and empirical evidence.

Several classical results have shown that, forρ-Hessian Lipschitz functions (see Definition 1), using the second-order information like computing the Hessian [33] or Hessian-vector products [1, 9, 2], one can find anϵ-approximate second-order stationary point (SOSP, f(x) ϵ and 2f(x) ρϵI).

We assume that the lower-level objective functiong is convex but notstrongly convex,sothelower-levelproblem mayhavemultiple optimal solutions.

While recent developments in autonomous vehicle (AV) technology highlight substantial progress, we lack tools for rigorous and scalable testing.

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