Convergence and efficiency of adaptive importance sampling techniques with partial biasing
Résumé
We consider a generalization of the discrete-time Self Healing Umbrella
Sampling method, which is an adaptive importance technique useful to sample
multimodal target distributions. The importance function is based on the
weights of disjoint sets which form a partition of the space. In the context of
computational statistical physics, the logarithm of these weights is, up to a
multiplicative constant, the free energy, and the discrete valued function
defining the partition is called the reaction coordinate. The algorithm is a
generalization of the original Self Healing Umbrella Sampling method in two
ways: (i) the updating strategy leads to a larger penalization strength of
already visited sets and (ii) the target distribution is biased using only a
fraction of the free energy, in order to increase the effective sample size and
reduce the variance of importance sampling estimators. The algorithm can also
be seen as a generalization of well-tempered metadynamics. We prove the
convergence of the algorithm and analyze numerically its efficiency on a toy
example.