Dynamic weighting in Monte Carlo and optimization

Abstract

Dynamic importance weighting is proposed as a Monte Carlo method that has the capability to sample relevant parts of the configuration space even in the presence of many steep energy minima. The method relies on an additional dynamic variable (the importance weight) to help the system overcome steep barriers. A non-Metropolis theory is developed for the construction of such weighted samplers. Algorithms based on this method are designed for simulation and global optimization tasks arising from multimodal sampling, neural network training, and the traveling salesman problem. Numerical tests on these problems confirm the effectiveness of the method.

Annealing Stochastic Approximation Monte Carlo for Global Optimization

“…Although ASAMC and AESAMC are proposed as optimization techniques, they can also be used as importance sampling techniques by keeping the sample space unshrinked through iterations. AESAMC has provided a general framework on how to incorporate crossover operations into dynamically weighted MCMC simulations, e.g., dynamic weighting (Wong & Liang, 1997;Liang, 2002) and population Monte Carlo (Cappé et al, 2004). This framework is potentially more useful than the conventional MCMC framework provided by evolutionary Monte Carlo (Liang & Wong, 2000, 2001.…”

Partitioning the Data Domain of Combinatorial Problems for Sequential Optimization

“…This waiting time dilemma [21] is due to a stringent requirement for equilibrium. To escape, the process must generate subsequent states with higher energy and the probability for such a move declines roughly exponentially with the energy differences that has to be overcome.…”

“…Thus, the expected waiting time for such escape grows also exponentially. For high-dimensional problems like the one that we scrutinize here, this problem is even more prevalent [21]. Several techniques have been proposed to overcome the problem of getting trapped, e.g.…”

“…Several techniques have been proposed to overcome the problem of getting trapped, e.g. [22], [21], [23]; one is the concept of Simulated Annealing (SA).…”

Annealing stochastic approximation Monte Carlo algorithm for neural network training

“…Fahlman and Lebiere (1990) solved the problem using cascadecorrelation networks with 12-19 hidden units, the smallest network having 114 connections. Wong and Liang (1997) solved the problem using a 2-14-4-1 MLP without shortcut connections. It is generally believed that this problem is very difficult to solve using the standard one-hidden-layer MLP, because it requires the MLP to learn a highly nonlinear separation of the input space.…”