Randomized Experimental Design for Causal Graph Discovery

We examine the number of controlled experiments required to discover a causal graph. Hauser and Buhlmann [1] showed that the number of experiments required is logarithmic in the cardinality of maximum undirected clique in the essential graph. Their lower bounds, however, assume that the experiment designer cannot use randomization in selecting the experiments. We show that significant improvements are possible with the aid of randomization - in an adversarial (worst-case) setting, the designer can then recover the causal graph using at most O(log log n) experiments in expectation. This bound cannot be improved; we show it is tight for some causal graphs.