Linear Causal Bandits: Unknown Graph and Soft Interventions

Designing causal bandit algorithms depends on two central categories of assumptions: (i) the extent of information about the underlying causal graphs and (ii) the extent of information about interventional statistical models. There have been extensive recent advances in dispensing with assumptions on either category. These include assuming known graphs but unknown interventional distributions, and the converse setting of assuming unknown graphs but access to restrictive hard/do interventions, which removes the stochasticity and ancestral dependencies. Nevertheless, the problem in its general form, i.e., unknown graph and unknown stochastic intervention models, remains open.