73. Relational irreducibility

For \(A\subseteq V\), the coalition statistic is \(\mathbf H_t^A\). Given an action space \(\mathsf A\) and loss \(\ell\), define its unrestricted Bayes risk by \[\boxed{ \mathcal R_\ell(A) = \inf_d \mathbb E\!\left[ \ell\bigl(Y_t^+,d(\mathbf H_t^A)\bigr) \right]. }\] The infimum is over measurable decision rules for which the expectation is defined. The full-system risk is \(\mathcal R_\ell(V)\).