Natural Hypergradient Descent: Algorithm Design, Convergence Analysis, and Parallel Implementation
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| Acceso en línea: | |
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| _version_ | 1866912994305245184 |
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| author | Kong, Deyi Chen, Zaiwei Zhang, Shuzhong Mou, Shancong |
| author_facet | Kong, Deyi Chen, Zaiwei Zhang, Shuzhong Mou, Shancong |
| contents | In this work, we propose Natural Hypergradient Descent (NHGD), a new method for solving bilevel optimization problems. To address the computational bottleneck in hypergradient estimation--namely, the need to compute or approximate Hessian inverse--we exploit the statistical structure of the inner optimization problem and use the empirical Fisher information matrix as an asymptotically consistent surrogate for the Hessian. This design enables a parallel optimize-and-approximate framework in which the Hessian-inverse approximation is updated synchronously with the stochastic inner optimization, reusing gradient information at negligible additional cost. Our main theoretical contribution establishes high-probability error bounds and sample complexity guarantees for NHGD that match those of state-of-the-art optimize-then-approximate methods, while significantly reducing computational time overhead. Empirical evaluations on representative bilevel learning tasks further demonstrate the practical advantages of NHGD, highlighting its scalability and effectiveness in large-scale machine learning settings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_10905 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Natural Hypergradient Descent: Algorithm Design, Convergence Analysis, and Parallel Implementation Kong, Deyi Chen, Zaiwei Zhang, Shuzhong Mou, Shancong Machine Learning Optimization and Control In this work, we propose Natural Hypergradient Descent (NHGD), a new method for solving bilevel optimization problems. To address the computational bottleneck in hypergradient estimation--namely, the need to compute or approximate Hessian inverse--we exploit the statistical structure of the inner optimization problem and use the empirical Fisher information matrix as an asymptotically consistent surrogate for the Hessian. This design enables a parallel optimize-and-approximate framework in which the Hessian-inverse approximation is updated synchronously with the stochastic inner optimization, reusing gradient information at negligible additional cost. Our main theoretical contribution establishes high-probability error bounds and sample complexity guarantees for NHGD that match those of state-of-the-art optimize-then-approximate methods, while significantly reducing computational time overhead. Empirical evaluations on representative bilevel learning tasks further demonstrate the practical advantages of NHGD, highlighting its scalability and effectiveness in large-scale machine learning settings. |
| title | Natural Hypergradient Descent: Algorithm Design, Convergence Analysis, and Parallel Implementation |
| topic | Machine Learning Optimization and Control |
| url | https://arxiv.org/abs/2602.10905 |