{"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/regret-optimal-federated-transfer-learning","title":"Regret-Optimal Federated Transfer Learning for Kernel Regression with Applications in American Option Pricing","arxiv_id":"2309.04557","date":"2023-09-08","proceeding":null,"authors":["Xuwei Yang","Anastasis Kratsios","Florian Krach","Matheus Grasselli","Aurelien Lucchi"],"abstract":"We propose an optimal iterative scheme for federated transfer learning, where a central planner has access to datasets ${\\cal D}_1,\\dots,{\\cal D}_N$ for the same learning model $f_{\\theta}$. Our objective is to minimize the cumulative deviation of the generated parameters $\\{\\theta_i(t)\\}_{t=0}^T$ across all $T$ iterations from the specialized parameters $\\theta^\\star_{1},\\ldots,\\theta^\\star_N$ obtained for each dataset, while respecting the loss function for the model $f_{\\theta(T)}$ produced by the algorithm upon halting. We only allow for continual communication between each of the specialized models (nodes/agents) and the central planner (server), at each iteration (round). For the case where the model $f_{\\theta}$ is a finite-rank kernel regression, we derive explicit updates for the regret-optimal algorithm. By leveraging symmetries within the regret-optimal algorithm, we further develop a nearly regret-optimal heuristic that runs with $\\mathcal{O}(Np^2)$ fewer elementary operations, where $p$ is the dimension of the parameter space. Additionally, we investigate the adversarial robustness of the regret-optimal algorithm showing that an adversary which perturbs $q$ training pairs by at-most $\\varepsilon>0$, across all training sets, cannot reduce the regret-optimal algorithm's regret by more than $\\mathcal{O}(\\varepsilon q \\bar{N}^{1/2})$, where $\\bar{N}$ is the aggregate number of training pairs. To validate our theoretical findings, we conduct numerical experiments in the context of American option pricing, utilizing a randomly generated finite-rank kernel.","url_abs":"https://arxiv.org/abs/2309.04557v2","url_pdf":"https://arxiv.org/pdf/2309.04557v2.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":"regret-optimal-federated-transfer-learning","repo_url":"https://github.com/floriankrach/regretoptimalfederatedtransferlearning","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"pytorch","reach":null}],"tasks":[{"task_slug":"adversarial-robustness","task_name":"Adversarial Robustness"},{"task_slug":"transfer-learning","task_name":"Transfer Learning"},{"task_slug":"regression-1","task_name":"regression"}],"methods":[{"method_slug":null,"method_name":"American"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}