  It is well known that adding any skew symmetric matrix to the gradient of
Langevin dynamics algorithm results in a non-reversible diffusion with improved
convergence rate. This paper presents a gradient algorithm to adaptively
optimize the choice of the skew symmetric matrix. The resulting algorithm
involves a non-reversible diffusion algorithm cross coupled with a stochastic
gradient algorithm that adapts the skew symmetric matrix. The algorithm uses
the same data as the classical Langevin algorithm. A weak convergence proof is
given for the optimality of the choice of the skew symmetric matrix. The
improved convergence rate of the algorithm is illustrated numerically in
Bayesian learning and tracking examples.
