Supplementary material for Dynamic Causal Bayesian Optimisation

In this section we give the proof for Theorem 1 in the main text. W. This means that W includes those variables that are parents of Y Eq. (1) follows from Y Eq. (2) follows from the Eq. Exploiting Eq. (8) we can rewrite Eq. (6) as: We can further expand Eq. (11) noticing that in this case W = {Z In this section we give the proof for Proposition 3.1 in the main text. This section contains additional experimental details associated to the experiments discussed in Section 4 of the main text. Notice how the location of the optimum changes significantly both in terms of optimal set and intervention value when going from t = 0 to t = 1.