B\'zier Flow: a Surface-wise Gradient Descent Method for Multi-objective Optimization

TMLR Paper3320 Authors

Abstract:

This paper proposes a strategy to construct a multi-objective optimization algorithm from a single-objective optimization algorithm by using the B\'ezier 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 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 and demonstrated that our method achieved lower generalization errors than the existing multi-objective optimization algorithm.

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

Assigned Action Editor: ~Roman_Garnett1

Submission Number: 3320