Neural Predictor-Corrector: Solving Homotopy Problems with Reinforcement Learning
The Homotopy paradigm, a general principle for solving challenging problems, appears across diverse domains such as robust optimization, global optimization, polynomial root-finding, and sampling. Practical solvers for these problems typically follow a predictor-corrector (PC) structure, but rely on hand-crafted heuristics for step sizes and iteration termination, which are often suboptimal and task-specific. To address this, we unify these problems under a single framework, which enables the design of a general neural solver. Building on this unified view, we propose Neural Predictor-Corrector (NPC), which replaces hand-crafted heuristics with automatically learned policies. NPC formulates policy selection as a sequential decision-making problem and leverages reinforcement learning to automatically discover efficient strategies. To further enhance generalization, we introduce an amortized training mechanism, enabling one-time offline training for a class of problems and efficient online inference on new instances. Experiments on four representative homotopy problems demonstrate that our method generalizes effectively to unseen instances. It consistently outperforms classical and specialized baselines in efficiency while demonstrating superior stability across tasks, highlighting the value of unifying homotopy methods into a single neural framework.
6983585c37bca54cd0587d64
Jiayao Mai
6983585c37bca54cd0587d65
Bangyan Liao
6983585c37bca54cd0587d66
Zhenjun Zhao
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Yingping Zeng
6983585c37bca54cd0587d68
Haoang Li
6983585c37bca54cd0587d69
Javier Civera
6983585c37bca54cd0587d6a
Tailin Wu
6983585c37bca54cd0587d6b
Yi Zhou
6983585c37bca54cd0587d6c
Peidong Liu
Neural Predictor-Corrector: Solving Homotopy Problems with Reinforcement Learning
The Homotopy paradigm, a general principle for solving challenging problems, appears across diverse domains such as robust optimization, global optimization, polynomial root-finding, and sampling. Practical solvers for these problems typically follow a predictor-corrector (PC) structure, but rely on hand-crafted heuristics for step sizes and iteration termination, which are often suboptimal and task-specific. To address this, we unify these problems under a single framework, which enables the design of a general neural solver. Building on this unified view, we propose Neural Predictor-Corrector (NPC), which replaces hand-crafted heuristics with automatically learned policies. NPC formulates policy selection as a sequential decision-making problem and leverages reinforcement learning to automatically discover efficient strategies. To further enhance generalization, we introduce an amortized training mechanism, enabling one-time offline training for a class of problems and efficient online inference on new instances. Experiments on four representative homotopy problems demonstrate that our method generalizes effectively to unseen instances. It consistently outperforms classical and specialized baselines in efficiency while demonstrating superior stability across tasks, highlighting the value of unifying homotopy methods into a single neural framework.
Neural Predictor-Corrector framework unifies homotopy methods across multiple domains and outperforms classical approaches through learned policies and amortized training.
predictor-corrector reinforcement learning sequential decision-making amortized training neural solver homotopy paradigm optimization sampling