Strategies in POMDPs with Stage Duration
Fuente:
arXiv
Salvato in:
| Autore principale: | |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2026
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866912969574580224 |
|---|---|
| author | Novikov, Ivan |
| author_facet | Novikov, Ivan |
| contents | Partially observable Markov decision processes (POMDPs) with stage duration provide a framework for approximating continuous-time behavior by scaling transition probabilities with a stage duration parameter $h \in (0,1]$. While previous literature has primarily focused on the limit of the discounted value as the stage duration $h$ vanishes, this paper investigates the global behavior of the asymptotic value, $V(h)$, across varying stage durations. Our main result demonstrates that any strategy in a POMDP with stage duration $h$ can be mimicked in the base POMDP ($h=1$). Specifically, we provide an explicit construction showing that for any strategy in the POMDP with stage duration $h$, there exists a strategy in the base POMDP that secures the same asymptotic payoff. As a consequence of this theorem, we establish that the value function $V(h)$ is nondecreasing with respect to $h$, and that the continuous-time limit $\lim_{h \to 0} V(h)$ exists. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_16055 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Strategies in POMDPs with Stage Duration Novikov, Ivan Optimization and Control Partially observable Markov decision processes (POMDPs) with stage duration provide a framework for approximating continuous-time behavior by scaling transition probabilities with a stage duration parameter $h \in (0,1]$. While previous literature has primarily focused on the limit of the discounted value as the stage duration $h$ vanishes, this paper investigates the global behavior of the asymptotic value, $V(h)$, across varying stage durations. Our main result demonstrates that any strategy in a POMDP with stage duration $h$ can be mimicked in the base POMDP ($h=1$). Specifically, we provide an explicit construction showing that for any strategy in the POMDP with stage duration $h$, there exists a strategy in the base POMDP that secures the same asymptotic payoff. As a consequence of this theorem, we establish that the value function $V(h)$ is nondecreasing with respect to $h$, and that the continuous-time limit $\lim_{h \to 0} V(h)$ exists. |
| title | Strategies in POMDPs with Stage Duration |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2603.16055 |