Adaptive multi-gradient methods for quasiconvex vector optimization and applications to multi-task learning
This work addresses optimization challenges in multi-task learning, but it appears incremental as it builds on existing multi-gradient methods with adaptive step-sizes.
The authors tackled the problem of solving nonconvex multiobjective programming on unbounded constraint sets by developing an adaptive step-size method without line-search, proving convergence under modest assumptions and applying it to multi-task learning experiments to demonstrate efficacy for large-scale challenges.
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.