Adaptive multi-gradient methods for quasiconvex vector optimization and applications to multi-task learning
<|reference_start|>Adaptive multi-gradient methods for quasiconvex vector optimization and applications to multi-task learning: We present an adaptive step-size method, which does not include line-search techniques, for solving a wide class of nonconvex multiobjective programming problems on an unbounded constraint set. We also prove convergence of a general approach under modest assumptions. More specifically, the convexity criterion might not be satisfied by the objective function. Unlike descent line-search algorithms, it does not require an initial step-size to be determined by a previously determined Lipschitz constant. The process's primary characteristic is its gradual step-size reduction up until a predetermined condition is met. It can be specifically applied to offer an innovative multi-gradient projection method for unbounded constrained optimization issues. Preliminary findings from a few computational examples confirm the accuracy of the strategy. We apply the proposed technique to some multi-task learning experiments to show its efficacy for large-scale challenges.<|reference_end|>
@article{minh2024adaptive,
    title={Adaptive multi-gradient methods for quasiconvex vector optimization and
  applications to multi-task learning},
    author={Nguyen Anh Minh and Le Dung Muu and Tran Ngoc Thang},
    journal={arXiv preprint arXiv:2402.06224},
    year={2024},
    archivePrefix={arXiv},
    eprint={2402.06224},
    primaryClass={math.OC cs.LG}
}