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| Format: | Preprint |
| Veröffentlicht: |
2025
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| Online-Zugang: | https://arxiv.org/abs/2506.09499 |
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| _version_ | 1866909645981876224 |
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| author | Ringstrom, Thomas J. Schrater, Paul R. |
| author_facet | Ringstrom, Thomas J. Schrater, Paul R. |
| contents | We introduce Option Kernel Bellman Equations (OKBEs) for a new reward-free Markov Decision Process. Rather than a value function, OKBEs directly construct and optimize a predictive map called a state-time option kernel (STOK) to maximize the probability of completing a goal while avoiding constraint violations. STOKs are compositional, modular, and interpretable initiation-to-termination transition kernels for policies in the Options Framework of Reinforcement Learning. This means: 1) STOKs can be composed using Chapman-Kolmogorov equations to make spatiotemporal predictions for multiple policies over long horizons, 2) high-dimensional STOKs can be represented and computed efficiently in a factorized and reconfigurable form, and 3) STOKs record the probabilities of semantically interpretable goal-success and constraint-violation events, needed for formal verification. Given a high-dimensional state-transition model for an intractable planning problem, we can decompose it with local STOKs and goal-conditioned policies that are aggregated into a factorized goal kernel, making it possible to forward-plan at the level of goals in high-dimensions to solve the problem. These properties lead to highly flexible agents that can rapidly synthesize meta-policies, reuse planning representations across many tasks, and justify goals using empowerment, an intrinsic motivation function. We argue that reward-maximization is in conflict with the properties of compositionality, modularity, and interpretability. Alternatively, OKBEs facilitate these properties to support verifiable long-horizon planning and intrinsic motivation that scales to dynamic high-dimensional world-models. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_09499 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Unified Theory of Compositionality, Modularity, and Interpretability in Markov Decision Processes Ringstrom, Thomas J. Schrater, Paul R. Machine Learning Artificial Intelligence We introduce Option Kernel Bellman Equations (OKBEs) for a new reward-free Markov Decision Process. Rather than a value function, OKBEs directly construct and optimize a predictive map called a state-time option kernel (STOK) to maximize the probability of completing a goal while avoiding constraint violations. STOKs are compositional, modular, and interpretable initiation-to-termination transition kernels for policies in the Options Framework of Reinforcement Learning. This means: 1) STOKs can be composed using Chapman-Kolmogorov equations to make spatiotemporal predictions for multiple policies over long horizons, 2) high-dimensional STOKs can be represented and computed efficiently in a factorized and reconfigurable form, and 3) STOKs record the probabilities of semantically interpretable goal-success and constraint-violation events, needed for formal verification. Given a high-dimensional state-transition model for an intractable planning problem, we can decompose it with local STOKs and goal-conditioned policies that are aggregated into a factorized goal kernel, making it possible to forward-plan at the level of goals in high-dimensions to solve the problem. These properties lead to highly flexible agents that can rapidly synthesize meta-policies, reuse planning representations across many tasks, and justify goals using empowerment, an intrinsic motivation function. We argue that reward-maximization is in conflict with the properties of compositionality, modularity, and interpretability. Alternatively, OKBEs facilitate these properties to support verifiable long-horizon planning and intrinsic motivation that scales to dynamic high-dimensional world-models. |
| title | A Unified Theory of Compositionality, Modularity, and Interpretability in Markov Decision Processes |
| topic | Machine Learning Artificial Intelligence |
| url | https://arxiv.org/abs/2506.09499 |