Bézier Flow: a Surface-wise Gradient Descent Method for Multi-objective Optimization
This work addresses multi-objective optimization problems, which are common in machine learning and engineering, but it appears incremental as it builds on existing single-objective techniques.
The paper tackles multi-objective optimization by constructing algorithms from single-objective ones using the Bézier simplex model, and it demonstrates lower generalization errors than existing methods in numerical experiments.
In this paper, we propose a strategy to construct a multi-objective optimization algorithm from a single-objective optimization algorithm by using the Bézier simplex model. Also, we extend the stability of optimization algorithms in the sense of Probability 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.