{"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/langevin-dynamics-based-algorithm-e-th","title":"Langevin dynamics based algorithm e-TH$\\varepsilon$O POULA for stochastic optimization problems with discontinuous stochastic gradient","arxiv_id":"2210.13193","date":"2022-10-24","proceeding":null,"authors":["Dong-Young Lim","Ariel Neufeld","Sotirios Sabanis","Ying Zhang"],"abstract":"We introduce a new Langevin dynamics based algorithm, called e-TH$\\varepsilon$O POULA, to solve optimization problems with discontinuous stochastic gradients which naturally appear in real-world applications such as quantile estimation, vector quantization, CVaR minimization, and regularized optimization problems involving ReLU neural networks. We demonstrate both theoretically and numerically the applicability of the e-TH$\\varepsilon$O POULA algorithm. More precisely, under the conditions that the stochastic gradient is locally Lipschitz in average and satisfies a certain convexity at infinity condition, we establish non-asymptotic error bounds for e-TH$\\varepsilon$O POULA in Wasserstein distances and provide a non-asymptotic estimate for the expected excess risk, which can be controlled to be arbitrarily small. Three key applications in finance and insurance are provided, namely, multi-period portfolio optimization, transfer learning in multi-period portfolio optimization, and insurance claim prediction, which involve neural networks with (Leaky)-ReLU activation functions. Numerical experiments conducted using real-world datasets illustrate the superior empirical performance of e-TH$\\varepsilon$O POULA compared to SGLD, TUSLA, ADAM, and AMSGrad in terms of model accuracy.","url_abs":"https://arxiv.org/abs/2210.13193v3","url_pdf":"https://arxiv.org/pdf/2210.13193v3.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":"langevin-dynamics-based-algorithm-e-th","repo_url":"https://github.com/dongyounglim/etheopoula","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"pytorch","reach":{"status":"ok"}}],"tasks":[{"task_slug":"portfolio-optimization","task_name":"Portfolio Optimization"},{"task_slug":"quantization","task_name":"Quantization"},{"task_slug":"stochastic-optimization","task_name":"Stochastic Optimization"},{"task_slug":"transfer-learning","task_name":"Transfer Learning"}],"methods":[{"method_slug":"amsgrad","method_name":"AMSGrad"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2210.13193","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}