# Monte Carlo optimisation

September 30, 2020 — September 30, 2020

Bayes

density

estimator distribution

Monte Carlo

probabilistic algorithms

probability

statistics

statmech

stochastic processes

Optimisation via Monte Carlo Simulation, typically with MCMC plus annealing TBD.

## 1 References

Abernethy, and Hazan. 2016. “Faster Convex Optimization: Simulated Annealing with an Efficient Universal Barrier.” In

*International Conference on Machine Learning*.
Botev, and Kroese. 2008. “An Efficient Algorithm for Rare-Event Probability Estimation, Combinatorial Optimization, and Counting.”

*Methodology and Computing in Applied Probability*.
Dalalyan. 2017. “Further and Stronger Analogy Between Sampling and Optimization: Langevin Monte Carlo and Gradient Descent.”

*arXiv:1704.04752 [Math, Stat]*.
de Freitas, Niranjan, Gee, et al. 1998. “Sequential Monte Carlo Methods for Optimisation of Neural Network Models.”

*Cambridge University Engineering Department, Cambridge, England, Technical Report TR-328*.
Devlin, Horridge, Green, et al. 2021. “The No-U-Turn Sampler as a Proposal Distribution in a Sequential Monte Carlo Sampler with a Near-Optimal L-Kernel.”

Drovandi, Nott, and Pagendam. 2017. “New Insights into History Matching via Sequential Monte Carlo.”

*arXiv:1710.03133 [Stat]*.
Duan, and Kroese. 2016. “Splitting for Optimization.”

*Computers & Operations Research*.
Elvira, and Chouzenoux. 2021. “Optimized Population Monte Carlo.”

Goffe, Ferrier, and Rogers. 1994. “Global Optimization of Statistical Functions with Simulated Annealing.”

*Journal of Econometrics*.
Mandt, Hoffman, and Blei. 2017. “Stochastic Gradient Descent as Approximate Bayesian Inference.”

*JMLR*.
Mıguez, Crisan, and Djuric. 2010. “Sequential Monte Carlo Methods for the Optimization of a General Class of Objective Functions.”

Robert, and Casella. 2004.

*Monte Carlo Statistical Methods*. Springer Texts in Statistics.
Rubinstein, Reuven Y, and Kroese. 2004.

*The Cross-Entropy Method a Unified Approach to Combinatorial Optimization, Monte-Carlo Simulation and Machine Learning*.
Rubinstein, Reuven Y., and Kroese. 2016.

*Simulation and the Monte Carlo Method*. Wiley series in probability and statistics.
Rubinstein, Reuven Y., Ridder, and Vaisman. 2014.

*Fast Sequential Monte Carlo Methods for Counting and Optimization*. Wiley Series in Probability and Statistics.