148. Probabilistic Trust Region Method for solving Multi-Objective Problems
Invited abstract in session WD-4: Large scale optimization and applications 2, stream Large scale optimization and applications.
Wednesday, 12:00 - 13:30Room: C105
Authors (first author is the speaker)
| 1. | Luka Rutešić
|
| Mathematics and Informatics, Faculty of Sciences | |
| 2. | Natasa Krejic
|
| Department of Mathematics and Informatics, University of Novi Sad Faculty of Science | |
| 3. | Nataša Krklec Jerinkić
|
| Department of Mathematics and Informatics, Faculty of Sciences, University of Novi Sad |
Abstract
The problem considered is a multi-objective optimization problem, in which the goal is to find an optimal value of a vector function representing various criteria. An algorithm which utilizes trust region framework with probabilistic model functions able to cope with noisy problems and approximate functions and their derivatives is derived and analysed. We prove the almost sure convergence of the proposed algorithm to a Pareto critical point if the model functions are good approximations in probabilistic sense. Numerical results demonstrate effectiveness of the probabilistic trust region by comparing it to competitive stochastic multi-objective solvers. The application in supervised machine learning is showcased by training non discriminatory Logistic Regression models on different size data groups. Additionally, we use several test examples with irregularly shaped fronts to exibit the efficiency of the algorithm.
Keywords
- Data driven optimization
- Optimization for learning and data analysis
- SS - Advances in Nonlinear Optimization and Applications
Status: accepted
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