Stochastic block coordinate and function alternation for multi-objective optimization and learning
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866917487000420352 |
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| author | Tran, Trang H. Vicente, Luis Nunes |
| author_facet | Tran, Trang H. Vicente, Luis Nunes |
| contents | Multi-objective optimization is central to many engineering and machine learning applications, where multiple objectives must be optimized in balance. While multi-gradient based optimization methods combine these objectives in each step, such methods require computing gradients with respect to all variables at every iteration, resulting in high computational costs in large-scale settings. In this work, we propose a framework that simultaneously alternates the optimization of each objective and the (stochastic) gradient update with respect to each variable block. Our framework reduces per-iteration computational cost while enabling exploration of the Pareto front by allocating a prescribed number of gradient steps to each objective. We establish rigorous convergence guarantees across several stochastic smooth settings, including convex, non-convex, and Polyak-Lojasiewicz conditions, recovering classical convergence rates of single-objective methods. Numerical experiments demonstrate that our framework outperforms non-alternating methods on multi-target regression and produces a competitive Pareto front approximation, highlighting its computational efficiency and practical effectiveness. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_12432 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Stochastic block coordinate and function alternation for multi-objective optimization and learning Tran, Trang H. Vicente, Luis Nunes Optimization and Control 90C29, 90C06, 90C15 Multi-objective optimization is central to many engineering and machine learning applications, where multiple objectives must be optimized in balance. While multi-gradient based optimization methods combine these objectives in each step, such methods require computing gradients with respect to all variables at every iteration, resulting in high computational costs in large-scale settings. In this work, we propose a framework that simultaneously alternates the optimization of each objective and the (stochastic) gradient update with respect to each variable block. Our framework reduces per-iteration computational cost while enabling exploration of the Pareto front by allocating a prescribed number of gradient steps to each objective. We establish rigorous convergence guarantees across several stochastic smooth settings, including convex, non-convex, and Polyak-Lojasiewicz conditions, recovering classical convergence rates of single-objective methods. Numerical experiments demonstrate that our framework outperforms non-alternating methods on multi-target regression and produces a competitive Pareto front approximation, highlighting its computational efficiency and practical effectiveness. |
| title | Stochastic block coordinate and function alternation for multi-objective optimization and learning |
| topic | Optimization and Control 90C29, 90C06, 90C15 |
| url | https://arxiv.org/abs/2605.12432 |