Bézier Flow: a Surface-wise Gradient Descent Method for Multi-objective Optimization

Akiyoshi Sannai, Yasunari Hikima, Ken Kobayashi, Akinori Tanaka, Naoki Hamada

Abstract:

This paper proposes a framework to construct a multi-objective optimization algorithm from a single-objective optimization algorithm by using the Bézier simplex model. Additionally, we extend the stability of optimization algorithms in the sense of Probably Approximately Correct (PAC) learning and define the PAC stability. We prove that it leads to an upper bound on the generalization error with high probability.
Furthermore, we show that multi-objective optimization algorithms derived from a gradient descent-based single-objective optimization algorithm are PAC stable. We conducted numerical experiments with synthetic and real multi-objective optimization problem instances and demonstrated that our method achieved lower generalization errors than the existing multi-objective optimization algorithms.

Submission Length: Regular submission (no more than 12 pages of main content)

Code: https://github.com/hikimay/bezier-flow

Assigned Action Editor: ~Roman_Garnett1

Submission Number: 3320