New v-CMC paper generalizes Bellman recursion to causal DAGs
A novel causal value theory links causality and utility with mathematical rigor.
In a new paper accepted at UAI 2026, philosopher and computer scientist Olav Benjamin Vassend introduces the value Causal Markov Condition (v-CMC), a formal principle that extends the logic of causal inference to the domain of value and utility. The work establishes a rigorous duality between probability distributions and value functions, allowing standard causal-inference results—such as the Causal Markov Condition and d-separation—to be translated into a value setting. Vassend defines local, global, and decomposition formulations of the v-CMC and proves their equivalence, and introduces v-separation as a sound and complete criterion for conditional value independence.
A key result is the derivation of a Bellman-type recursion as a special case of the v-CMC, generalizing the classic dynamic programming recurrence from linear chains to arbitrary causal directed acyclic graphs (DAGs). This opens the door to more flexible planning and value iteration in structured environments. The paper also presents algorithms for causally structured utility elicitation and canonical influence-diagram construction, enabling modular transfer and updating of utility information across different causal contexts. The work has immediate relevance for AI alignment, causal reinforcement learning, and decision-making under uncertainty.
- Introduces v-CMC: a causal independence principle for value, with local, global, and decomposition variants proven equivalent.
- Defines v-separation as a sound and complete criterion for conditional value independence, analogous to d-separation in causality.
- Generalizes Bellman recursion from linear chains to causal DAGs, enabling structured value iteration in complex causal models.
Why It Matters
Bridges causality and utility theory, enabling principled decision-making AI that transfers value knowledge across contexts.