A global stochastic optimization particle filter algorithm

Parallel sequential Monte Carlo for stochastic gradient-free nonconvex optimization

M Gerber and R Douc

Biometrika, 2022, vol. 109, issue 4, 937-955

Abstract: SummaryWe introduce a new online algorithm for expected loglikelihood maximization in situations where the objective function is multimodal or has saddle points. The key element underpinning the algorithm is a probability distribution that concentrates on the target parameter value as the sample size increases and can be efficiently estimated by means of a standard particle filter algorithm. This distribution depends on a learning rate, such that the faster the learning rate the quicker the distribution concentrates on the desired element of the search space, but the less likely the algorithm is to escape from a local optimum of the objective function. In order to achieve a fast convergence rate with a slow learning rate, our algorithm exploits the acceleration property of averaging, which is well known from the stochastic gradient literature. Considering several challenging estimation problems, our numerical experiments show that with high probability, the algorithm successfully finds the highest mode of the objective function and converges to the global maximizer at the optimal rate. While the focus of this work is expected loglikelihood maximization, the proposed methodology and its theory apply more generally to optimization of a function defined through an expectation.

Keywords: Global optimization; Inference in large datasets; Particle filtering; Stochastic optimization (search for similar items in EconPapers)
Date: 2022
References: Add references at CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://hdl.handle.net/10.1093/biomet/asab067 (application/pdf)
Access to full text is restricted to subscribers.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:oup:biomet:v:109:y:2022:i:4:p:937-955.

Ordering information: This journal article can be ordered from
https://academic.oup.com/journals

Access Statistics for this article

Biometrika is currently edited by Paul Fearnhead

More articles in Biometrika from Biometrika Trust Oxford University Press, Great Clarendon Street, Oxford OX2 6DP, UK.
Bibliographic data for series maintained by Oxford University Press ().