Generalised Bellman recurrence and three dualities in sequential decision-making
What gives the Bellman equation its form? We show that the recursive properties of optimal value functions follow from three conditions: that the dynamics decomposes through sufficient statistics, that the return decomposes recursively, and that the aggregation of uncertainty is compatible with both. When all three conditions hold on a common state, the Bellman equation arises from their mutual consistency; when one fails, tractability can often be recovered by augmenting the state or by deforming return or dynamics. The same conditions are shown to give rise to three dualities: one between probability and return, one between return and aggregation, and one between aggregation and probabi...
| Authors | Fernando E. Rosas, David Hyland, Daniel Polani |
|---|---|
| Primary category | cs.LG |
| Published | 20 July 2026 |
| Last updated at source | 20 July 2026 |
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