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In this paper, we propose a strategy to construct a multi-objectiveoptimization algorithm from a single-objective optimization algorithm by usingthe B\'ezier simplex model. Also, we extend the stability of optimizationalgorithms in the sense of Probability Approximately Correct (PAC) learning anddefine the PAC stability. We prove that it leads to an upper bound on thegeneralization with high probability. Furthermore, we show that multi-objectiveoptimization algorithms derived from a gradient descent-based single-objectiveoptimization algorithm are PAC stable. We conducted numerical experiments anddemonstrated that our method achieved lower generalization errors than theexisting multi-objective optimization algorithm.

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