A sliced controller steers Gaussian measures to targets via averaged 1D projections and equates its energy cost exactly to the sliced Wasserstein distance.
In other words, lim tր T ∫ S n− 1 √ θ⊤ Σ f θ θ⊤ Σ( t)θ θθ⊤ σ (dθ) − 1 n I = 0
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Sliced Wasserstein Steering between Gaussian Measures
A sliced controller steers Gaussian measures to targets via averaged 1D projections and equates its energy cost exactly to the sliced Wasserstein distance.