Neural Predictor-Corrector: Solving Homotopy Problems with Reinforcement Learning
This addresses inefficiencies in homotopy solvers for domains like optimization and root-finding, though it is incremental as it builds on existing predictor-corrector frameworks.
The paper tackled the problem of suboptimal hand-crafted heuristics in predictor-corrector solvers for homotopy problems by proposing Neural Predictor-Corrector, which uses reinforcement learning to learn efficient policies, resulting in consistent outperformance of classical baselines in efficiency and stability across tasks.
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.