Joint Gradient Balancing for Data Ordering in Finite-Sum Multi-Objective Optimization

In finite-sum optimization problems, the sample orders for parameter updates can significantly influence the convergence rate of optimization algorithms. While numerous sample ordering techniques have been proposed in the context of single-objective optimization, the problem of sample ordering in finite-sum multiobjective optimization has not been thoroughly explored. To address this gap, we propose a sample ordering method called JoGBa (Joint Gradient Balancing), which finds the sample orders for multiple objectives by jointly performing online vector balancing on the gradients of all objectives. Our theoretical analysis demonstrates that this approach outperforms the standard baseline of random ordering and accelerates the convergence rate for the MGDA algorithm. Empirical evaluation across various datasets with different multi-objective optimization algorithms further demonstrates that JoGBa can achieve faster convergence and superior final performance than other data ordering strategies.