A Causal Markov Condition for Value
Artificial IntelligenceMachine Learning
Summary
The authors introduce a principle called the value Causal Markov Condition (v-CMC), which connects the ideas of cause-and-effect with how we assign value or utility. They build mathematical tools to describe how values relate causally, similar to how probabilities usually do in standard causal inference. They show different versions of their principle are equivalent and define new ways to think about value independence using v-separation. The authors also link their idea to a well-known recursion formula (Bellman recursion) and demonstrate how their approach helps update and transfer value information in complex decision problems.
Authors
Olav Benjamin Vassend
Abstract
This paper proposes a causal independence principle for value -- the value Causal Markov Condition (v-CMC) -- and develops the conceptual and mathematical foundations of a "causal value theory" linking causality and utility. After motivating a local formulation of the v-CMC, we introduce a probability-value duality that translates standard causal-inference results into the value setting. In particular, we formulate local, global, and decomposition versions of the v-CMC and prove their equivalence. We also define v-separation and show that it is sound and complete for conditional value independence. Furthermore, we derive a Bellman-type recursion as a special case of the v-CMC, thereby generalizing standard Bellman recursion from linear chains to causal DAGs. Finally, we show how the v-CMC supports modular transfer and updating of utility information across causal contexts and develop algorithms for causally structured utility elicitation and canonical influence-diagram construction.