Sampling a random hypersphere point from a von Mises-Fisher distribution around the state and retrieving its nearest neighbor asymptotically reproduces Boltzmann exploration probabilities at sublinear cost.
(28) Replacing g and g′ by their respective values, we obtain: √n h 1 Dn − Cd(κ)A(S d−1) i D − → N(0, σ2(A(S d−1)Cd(κ))4)
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Exploring Large Action Sets with Hyperspherical Embeddings using von Mises-Fisher Sampling
Sampling a random hypersphere point from a von Mises-Fisher distribution around the state and retrieving its nearest neighbor asymptotically reproduces Boltzmann exploration probabilities at sublinear cost.