{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/online-approximate-bayesian-learning","title":"A Global Stochastic Optimization Particle Filter Algorithm","arxiv_id":"2007.04803","date":"2020-07-09","proceeding":null,"authors":["Mathieu Gerber","Randal Douc"],"abstract":"We introduce a new online algorithm for expected log-likelihood maximization in situations where the objective function is multi-modal and/or has saddle points, that we term G-PFSO. The key element underpinning G-PFSO is a probability distribution which (a) is shown to concentrate on the target parameter value as the sample size increases and (b) can be efficiently estimated by means of a standard particle filter algorithm. This distribution depends on a learning rate, where the faster the learning rate the quicker it concentrates on the desired element of the search space, but the less likely G-PFSO is to escape from a local optimum of the objective function. In order to achieve a fast convergence rate with a slow learning rate, G-PFSO exploits the acceleration property of averaging, well-known in the stochastic gradient literature. Considering several challenging estimation problems, the numerical experiments show that, with high probability, G-PFSO successfully finds the highest mode of the objective function and converges to its global maximizer at the optimal rate. While the focus of this work is expected log-likelihood maximization, the proposed methodology and its theory apply more generally for optimizing a function defined through an expectation.","url_abs":"https://arxiv.org/abs/2007.04803v9","url_pdf":"https://arxiv.org/pdf/2007.04803v9.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"online-approximate-bayesian-learning","repo_url":"https://github.com/mathgerberch/gpfso","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null},{"paper_slug":"online-approximate-bayesian-learning","repo_url":"https://github.com/mathieugerber/PFoptim","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null},{"paper_slug":"online-approximate-bayesian-learning","repo_url":"https://github.com/mathieugerber/gpfso-paper","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[{"task_slug":"stochastic-optimization","task_name":"Stochastic Optimization"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2007.04803","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}