Regret-Optimal Federated Transfer Learning for Kernel Regression with Applications in American Option Pricing

• URL: http://arxiv.org/abs/2309.04557v2
• Date: Thu, 03 Oct 2024 14:08:12 GMT
• Title: Regret-Optimal Federated Transfer Learning for Kernel Regression with Applications in American Option Pricing
• Authors: Xuwei Yang, Anastasis Kratsios, Florian Krach, Matheus Grasselli, Aurelien Lucchi,
• Abstract summary: We propose an optimal iterative scheme for federated transfer learning, where a central planner has access to datasets. Our objective is to minimize the cumulative deviation of the generated parameters $thetai(t)_t=0T$ across all $T$ iterations. By leveraging symmetries within the regret-optimal algorithm, we develop a nearly regret $_optimal that runs with $mathcalO(Np2)$ fewer elementary operations.
• Score: 8.723136784230906
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• 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.

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