Graph Agnostic Causal Bayesian Optimisation

TL;DR

This work is the first to study causal Bayesian optimization with cumulative regret objectives in scenarios where the graph is unknown or partially known, and proposes Graph Agnostic Causal Bayesian Optimisation (GACBO), an algorithm that actively discovers the causal structure that contributes to achieving optimal rewards.

Abstract

We study the problem of globally optimising a target variable of an unknown causal graph on which a sequence of soft or hard interventions can be performed. The problem of optimising the target variable associated with a causal graph is formalised as Causal Bayesian Optimisation (CBO). We study the CBO problem under the cumulative regret objective with unknown causal graphs for two settings, namely structural causal models with hard interventions and function networks with soft interventions. We propose Graph Agnostic Causal Bayesian Optimisation (GACBO), an algorithm that actively discovers the causal structure that contributes to achieving optimal rewards. GACBO seeks to balance exploiting the actions that give the best rewards against exploring the causal structures and functions. To the best of our knowledge, our work is the first to study causal Bayesian optimization with cumulative regret objectives in scenarios where the graph is unknown or partially known. We show our proposed algorithm outperforms baselines in simulated experiments and real-world applications.

Figures (8)

• Figure 1: Graph Agnostic Causal Bayesian Optimisation (gacbo) workflow. Top: Select plausible graphs based on data collected so far, Right: Perform Causal Bayesian Optimisation on plausible graphs, Bottom: Select the action based on the highest reward among all plausible graphs, Left: Execute selected action, collect Data and repeat steps.
• Figure 2: Problem Settings and Causal Structures: (a) Bayesian optimisation; (b) Structural causal models and hard interventions; (c) Function networks and soft interventions; (c-w1) Incomplete graph for (c), missing X1; (c-w2) Incorrect graph for (c), reversing order of X1 and X2. The blue circles $X1$ and $X2$ represent non-manipulative variables, the orange squares $A1$ and $A2$ represent actions that can be taken, and $Y$ is the outcome of interest.
• Figure 3: Simulation Results. We compare our method (gacbo) with mcbo with true graph and wrong graphs (missing edges and extra edges), and gp-ucb. As discussed in Section \ref{['sec: experiments']}, gp-ucb is inappropriate for ToyGraph. For soft intervention, we tested on Dropwave, Alpine3 and Rosenbrock. For hard intervention, we tested on ToyGraph.
• Figure 4: Real-world applications: Epidemiology. We show the true causal graph on the left top, where the T,R are potential treatments and Y is the target to be optimised. B,L are non-manipulative. The left bottom shows the designed wrong causal structure for mcbo. The right-hand side shows the performance of our experiments.
• Figure 5: Dropwave: True DAG structure, and Incorrect DAG structures used in Experiment