On characterizing optimal learning trajectories in a class of learning problems
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | |
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| _version_ | 1866916599928193024 |
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| author | Befekadu, Getachew K |
| author_facet | Befekadu, Getachew K |
| contents | In this brief paper, we provide a mathematical framework that exploits the relationship between the maximum principle and dynamic programming for characterizing optimal learning trajectories in a class of learning problem, which is related to point estimations for modeling of high-dimensional nonlinear functions. Here, such characterization for the optimal learning trajectories is associated with the solution of an optimal control problem for a weakly-controlled gradient system with small parameters, whose time-evolution is guided by a model training dataset and its perturbed version, while the optimization problem consists of a cost functional that summarizes how to gauge the quality/performance of the estimated model parameters at a certain fixed final time w.r.t. a model validating dataset. Moreover, using a successive Galerkin approximation method, we provide an algorithmic recipe how to construct the corresponding optimal learning trajectories leading to the optimal estimated model parameters for such a class of learning problem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_16521 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On characterizing optimal learning trajectories in a class of learning problems Befekadu, Getachew K Optimization and Control Machine Learning In this brief paper, we provide a mathematical framework that exploits the relationship between the maximum principle and dynamic programming for characterizing optimal learning trajectories in a class of learning problem, which is related to point estimations for modeling of high-dimensional nonlinear functions. Here, such characterization for the optimal learning trajectories is associated with the solution of an optimal control problem for a weakly-controlled gradient system with small parameters, whose time-evolution is guided by a model training dataset and its perturbed version, while the optimization problem consists of a cost functional that summarizes how to gauge the quality/performance of the estimated model parameters at a certain fixed final time w.r.t. a model validating dataset. Moreover, using a successive Galerkin approximation method, we provide an algorithmic recipe how to construct the corresponding optimal learning trajectories leading to the optimal estimated model parameters for such a class of learning problem. |
| title | On characterizing optimal learning trajectories in a class of learning problems |
| topic | Optimization and Control Machine Learning |
| url | https://arxiv.org/abs/2501.16521 |