Monte Carlo optimisation

September 30, 2020 — September 30, 2020

Bayes
density
estimator distribution
Monte Carlo
probabilistic algorithms
probability
statistics
statmech
stochastic processes

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Figure 1

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.