Mixing Any Cocktail with Limited Ingredients: On the Structure of Payoff Sets in Multi-Objective POMDPs and its Impact on Randomised Strategies
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2025
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866911183163883520 |
|---|---|
| author | Main, James C. A. Randour, Mickael |
| author_facet | Main, James C. A. Randour, Mickael |
| contents | We consider multi-dimensional payoff functions in partially observable Markov decision processes. We study the structure of the set of expected payoff vectors of all strategies (policies) and study what kind are needed to achieve a given expected payoff vector. In general, pure strategies (i.e., not resorting to randomisation) do not suffice for this problem.
We prove that for any payoff for which the expectation is well-defined under all strategies, it is sufficient to mix (i.e., randomly select a pure strategy at the start of a play and committing to it for the rest of the play) finitely many pure strategies to approximate any expected payoff vector up to any precision. Furthermore, for any payoff for which the expected payoff is finite under all strategies, any expected payoff can be obtained exactly by mixing finitely many strategies. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_18296 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Mixing Any Cocktail with Limited Ingredients: On the Structure of Payoff Sets in Multi-Objective POMDPs and its Impact on Randomised Strategies Main, James C. A. Randour, Mickael Computer Science and Game Theory Artificial Intelligence Formal Languages and Automata Theory Logic in Computer Science Probability We consider multi-dimensional payoff functions in partially observable Markov decision processes. We study the structure of the set of expected payoff vectors of all strategies (policies) and study what kind are needed to achieve a given expected payoff vector. In general, pure strategies (i.e., not resorting to randomisation) do not suffice for this problem. We prove that for any payoff for which the expectation is well-defined under all strategies, it is sufficient to mix (i.e., randomly select a pure strategy at the start of a play and committing to it for the rest of the play) finitely many pure strategies to approximate any expected payoff vector up to any precision. Furthermore, for any payoff for which the expected payoff is finite under all strategies, any expected payoff can be obtained exactly by mixing finitely many strategies. |
| title | Mixing Any Cocktail with Limited Ingredients: On the Structure of Payoff Sets in Multi-Objective POMDPs and its Impact on Randomised Strategies |
| topic | Computer Science and Game Theory Artificial Intelligence Formal Languages and Automata Theory Logic in Computer Science Probability |
| url | https://arxiv.org/abs/2502.18296 |