Defines diffusion processes on implicit data manifolds via proximity-graph approximations to the infinitesimal generator and carré-du-champ operator, proves convergence in law to the continuous manifold process, and provides an Euler-Maruyama integrator validated on synthetic and MNIST manifolds.
Springer, 2007
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Solutions to the regularized exploratory equilibrium HJB equation converge in suitable norms to a strong solution of the original EHJB as the entropy parameter vanishes, yielding existence of equilibria without conventional stringent regularity assumptions.
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Diffusion Processes on Implicit Manifolds
Defines diffusion processes on implicit data manifolds via proximity-graph approximations to the infinitesimal generator and carré-du-champ operator, proves convergence in law to the continuous manifold process, and provides an Euler-Maruyama integrator validated on synthetic and MNIST manifolds.
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Equilibrium under Time-Inconsistency: A New Existence Theory by Vanishing Entropy Regularization
Solutions to the regularized exploratory equilibrium HJB equation converge in suitable norms to a strong solution of the original EHJB as the entropy parameter vanishes, yielding existence of equilibria without conventional stringent regularity assumptions.