TY - GEN

T1 - Causal bandits with propagating inference

AU - Yabe, Akihiro

AU - Hatano, Daisuke

AU - Sumita, Hanna

AU - Ito, Shinji

AU - Kakimura, Naonori

AU - Fukunaga, Takuro

AU - Kawarabayashi, Ken Ichi

PY - 2018/1/1

Y1 - 2018/1/1

N2 - Bandit is a framework for designing sequential experiments, where a learner selects an arm A ϵ A and obtains an observation corresponding to A in each experiment. Theoretically, the tight regret lower-bound for the general bandit is polynomial with respect to the number of arms |A|, and thus, to overcome this bound, the bandit problem with side-information is often considered. Recently, a bandit framework over a causal graph was introduced, where the structure of the causal graph is available as side-information and the arms are identified with interventions on the causal graph. Existing algorithms for causal bandit overcame the Ω(√\A\/T) simple-regret lower-bound; however, their algorithms work only when the interventions A are localized around a single node (i.e., an intervention propagates only to its neighbors). We then propose a novel causal bandit algorithm for an arbitrary set of interventions, which can propagate throughout the causal graph. We also show that it achieves O(√γ∗ log(|A|T)/T) regret bound, where γ∗ is determined by using a causal graph structure. In particular, if the maximum in-degree of the causal graph is a constant, then γ∗ = O(N2), where N is the number of nodes.

AB - Bandit is a framework for designing sequential experiments, where a learner selects an arm A ϵ A and obtains an observation corresponding to A in each experiment. Theoretically, the tight regret lower-bound for the general bandit is polynomial with respect to the number of arms |A|, and thus, to overcome this bound, the bandit problem with side-information is often considered. Recently, a bandit framework over a causal graph was introduced, where the structure of the causal graph is available as side-information and the arms are identified with interventions on the causal graph. Existing algorithms for causal bandit overcame the Ω(√\A\/T) simple-regret lower-bound; however, their algorithms work only when the interventions A are localized around a single node (i.e., an intervention propagates only to its neighbors). We then propose a novel causal bandit algorithm for an arbitrary set of interventions, which can propagate throughout the causal graph. We also show that it achieves O(√γ∗ log(|A|T)/T) regret bound, where γ∗ is determined by using a causal graph structure. In particular, if the maximum in-degree of the causal graph is a constant, then γ∗ = O(N2), where N is the number of nodes.

UR - http://www.scopus.com/inward/record.url?scp=85057298452&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85057298452&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:85057298452

T3 - 35th International Conference on Machine Learning, ICML 2018

SP - 8761

EP - 8781

BT - 35th International Conference on Machine Learning, ICML 2018

A2 - Dy, Jennifer

A2 - Krause, Andreas

PB - International Machine Learning Society (IMLS)

T2 - 35th International Conference on Machine Learning, ICML 2018

Y2 - 10 July 2018 through 15 July 2018

ER -