Physical Review Letters

Optimization in the presence of noise is a difficult task. Most of the optimization methods available are totally deterministic in nature, and, when applied to problems affected by noise, they are either unable to reach an optimum or they may reach a false one. In this Letter we present a novel optimization scheme, called the stochastic gradient approximation (SGA). The method has its roots in the mathematics of automatic control theory [1,2], but to the authors’ knowledge it has not been applied for optimization problems in physics before. The algorithm belongs to the class of probabilistic iterative methods with variable step size. We consider one important application, namely, the optimization of manybody wave functions using the variational Monte Carlo (VMC) method. The results obtained show conclusively that the SGA constitutes a method tailor-made for quantum Monte Carlo (QMC) techniques. The excellent performance obtained makes the SGA an attractive tool to other difficult optimization problems as well. Quantum Monte Carlo methods are powerful tools for studying interacting many-particle systems. For fermion systems, the fixed-node diffusion QMC (DMC) can be thought of as a supervariational approach with an energy which is guaranteed to be closer to the exact answer than the starting VMC parent wave function [3]. For a given nodal surface the DMC provides the lowest energy compatible with such a constraint. In atomic