  We present a computational strategy for reducing the sign problem in the
evaluation of high dimensional integrals with non-positive definite weights.
The method involves stochastic sampling with a positive semidefinite weight
that is adaptively and optimally determined during the course of a simulation.
The optimal criterion, which follows from a variational principle for analytic
actions S(z), is a global stationary phase condition that the average gradient
of the phase Im(S) along the sampling path vanishes. Numerical results are
presented from simulations of a model adapted from statistical field theories
of classical fluids.
