Simulated annealing method optimizes partition function estimation efficiently
Optimal Simulated Annealing for Partition Function Estimation
Data Structures and Algorithms
Summary
Estimating the partition function is important in many areas like physics and machine learning but can be very hard to do quickly and accurately. The authors analyzed a specific version of simulated annealing, a method inspired by cooling metal slowly, to estimate these partition functions more efficiently without needing to adapt as they run. They also proved that their approach is as good as possible for a wide range of cases, meaning it can’t be improved much further. This helps make some complex calculations faster and more predictable.
What this means in practice
- •For machine learning engineers: Use optimized simulated annealing to estimate probability models' partition functions faster in probabilistic model training.
- •For operations research practitioners: Improve estimation of complex system states modeled by Gibbs distributions for better decision-making under uncertainty.
Authors
Heng Guo, Hongyang Liu, Xiongxin Yang, Yitong Yin, Yiyao Zhang
Abstract
In this note, we give a simple analysis of a non-adaptive simulated annealing algorithm for estimating the partition function of Gibbs distributions. This yields the most efficient reduction of this kind so far. We also establish lower bounds for both general and non-adaptive algorithms, showing that our algorithm is optimal over a broad range of parameters.