Certified Policy Optimisation for Nested Causal Bandits via PAC-Bayes Risk

Critical sequential decisions are rarely single-timescale: a strategic decision causally shapes the context in which every subsequent tactical choice is made; standard bandit and reinforcement-learning theory does not capture this causal coupling between timescales. We formalise the problem class as Nested Contextual Causal Bandits (NCCBs), a hierarchical SCM where each level's action sets the next level's context distribution, and propose Nested Causal Thompson Sampling (NCTS), which draws one mechanism-factorised belief per episode and acts recursively under it. Our main theoretical result is a causal PAC-Bayesian excess-risk bound that certifies any candidate deployment policy from historic data alone, off-policy and anytime, answering the deployment question: can we trust this agent here, and at what risk? Experiments on a hierarchical SCM show that, against a matched RFF-GP joint regression on the same function class, the factorised SCM-mechanism posterior transfers significantly better zero-shot under exogenous distribution shifts, the recursive meta-to-inner commit significantly dominates the joint-commit alternative in distribution, and the certificate significantly contracts as offline data accumulates. Combining these results, we establish progressive certified handover, a safe-deployment method: each timescale flips from a legacy controller to NCTS when gains can be certified, independently of the others.

Multi-Objective Causal Bayesian Optimization

In decision-making problems, the outcome of an intervention often depends on the causal relationships between system components and is highly costly to evaluate. In such settings, causal Bayesian optimization (CBO) can exploit the causal relationships between the system variables and sequentially perform interventions to approach the optimum with minimal data. Extending CBO to the multi-outcome setting, we propose Multi-Objective Causal Bayesian Optimization (MO-CBO), a paradigm for identifying Pareto-optimal interventions within a known multi-target causal graph. We first derive a graphical characterization for potentially optimal sets of variables to intervene upon. Showing that any MO-CBO problem can be decomposed into several traditional multi-objective optimization tasks, we then introduce an algorithm that sequentially balances exploration across these tasks using relative hypervolume improvement. The proposed method will be validated on both synthetic and real-world causal graphs, demonstrating its superiority over traditional (non-causal) multi-objective Bayesian optimization in settings where causal information is available.