论文标题
Bézier流量：用于多目标优化的地表梯度下降方法
Bézier Flow: a Surface-wise Gradient Descent Method for Multi-objective Optimization
论文作者
论文摘要
在本文中，我们提出了一种通过使用BézierSimplex模型来构建单目标优化算法的多目标优化算法的策略。同样，我们从概率上近似正确的（PAC）学习并定义PAC稳定性的概率上扩展了优化算法的稳定性。我们证明，它以高概率导致对概括的上限。此外，我们表明，从基于梯度下降的单目标优化算法得出的多目标优化算法是PAC稳定的。我们进行了数值实验，并证明我们的方法比现有的多目标优化算法达到了较低的概括误差。
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.
