Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2604.06837 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866914457602490368 |
|---|---|
| author | Yang, Hyukjun Lim, Han-Dong Lee, Donghwan |
| author_facet | Yang, Hyukjun Lim, Han-Dong Lee, Donghwan |
| contents | The problem of solving Markov decision processes under function approximation remains a fundamental challenge, even under linear function approximation settings. A key difficulty arises from a geometric mismatch: while the Bellman optimality operator is contractive in the Linfty-norm, commonly used objectives such as projected value iteration and Bellman residual minimization rely on L2-based formulations. To enable gradient-based optimization, we consider a soft formulation of Bellman residual minimization and extend it to a generalized weighted Lp -norm. We show that this formulation aligns the optimization objective with the contraction geometry of the Bellman operator as p increases, and derive corresponding performance error bounds. Our analysis provides a principled connection between residual minimization and Bellman contraction, leading to improved control of error propagation while remaining compatible with gradient-based optimization. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_06837 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Contraction-Aligned Analysis of Soft Bellman Residual Minimization with Weighted Lp-Norm for Markov Decision Problem Yang, Hyukjun Lim, Han-Dong Lee, Donghwan Machine Learning The problem of solving Markov decision processes under function approximation remains a fundamental challenge, even under linear function approximation settings. A key difficulty arises from a geometric mismatch: while the Bellman optimality operator is contractive in the Linfty-norm, commonly used objectives such as projected value iteration and Bellman residual minimization rely on L2-based formulations. To enable gradient-based optimization, we consider a soft formulation of Bellman residual minimization and extend it to a generalized weighted Lp -norm. We show that this formulation aligns the optimization objective with the contraction geometry of the Bellman operator as p increases, and derive corresponding performance error bounds. Our analysis provides a principled connection between residual minimization and Bellman contraction, leading to improved control of error propagation while remaining compatible with gradient-based optimization. |
| title | Contraction-Aligned Analysis of Soft Bellman Residual Minimization with Weighted Lp-Norm for Markov Decision Problem |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2604.06837 |