Beyond the Bellman Recursion: A Pontryagin-Guided Framework for Non-Exponential Discounting
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866911701246410752 |
|---|---|
| author | Ko, Hojin Huh, Jeonggyu |
| author_facet | Ko, Hojin Huh, Jeonggyu |
| contents | Most value-based and actor--critic reinforcement learning methods rely on Bellman-style recursions, yet these recursions collapse under non-exponential discounting common in human preferences and survival processes. We show the breakdown is structural: exponential discounting sits at a fragile intersection of multiplicativity and time homogeneity, and violating either property breaks standard dynamic programming. To overcome this, we propose Pontryagin-Guided Direct Policy Optimization (PG-DPO), a variational framework that abandons recursion and couples the Pontryagin Maximum Principle with Monte Carlo rollouts via an Adjoint-MC projection enforcing pointwise Hamiltonian maximization. Across multi-dimensional hyperbolic and survival-discount benchmarks, PG-DPO improves accuracy and stability where equation-driven solvers and critic-based baselines diverge. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_20996 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Beyond the Bellman Recursion: A Pontryagin-Guided Framework for Non-Exponential Discounting Ko, Hojin Huh, Jeonggyu Machine Learning Optimization and Control Most value-based and actor--critic reinforcement learning methods rely on Bellman-style recursions, yet these recursions collapse under non-exponential discounting common in human preferences and survival processes. We show the breakdown is structural: exponential discounting sits at a fragile intersection of multiplicativity and time homogeneity, and violating either property breaks standard dynamic programming. To overcome this, we propose Pontryagin-Guided Direct Policy Optimization (PG-DPO), a variational framework that abandons recursion and couples the Pontryagin Maximum Principle with Monte Carlo rollouts via an Adjoint-MC projection enforcing pointwise Hamiltonian maximization. Across multi-dimensional hyperbolic and survival-discount benchmarks, PG-DPO improves accuracy and stability where equation-driven solvers and critic-based baselines diverge. |
| title | Beyond the Bellman Recursion: A Pontryagin-Guided Framework for Non-Exponential Discounting |
| topic | Machine Learning Optimization and Control |
| url | https://arxiv.org/abs/2605.20996 |