  The complex Langevin method, a numerical method used to compute the ensemble
average with a complex partition function, often suffers from runaway
instability. We study the regularization of the complex Langevin method via
augmenting the action with a stabilization term. Since the regularization
introduces biases to the numerical result, two approaches, named 2R and 3R
methods, are introduced to recover the unbiased result. The 2R method
supplements the regularization with regression to estimate the unregularized
ensemble average, and the 3R method reduces the computational cost by coupling
the regularization with a reweighting strategy before regression. Both methods
can be generalized to the SU(n) theory and are assessed from several
perspectives. Several numerical experiments in the lattice field theory are
carried out to show the effectiveness of our approaches.
