  In a sequential decision-making problem, having a structural dependency
amongst the reward distributions associated with the arms makes it challenging
to identify a subset of alternatives that guarantees the optimal collective
outcome. Thus, besides individual actions' reward, learning the causal
relations is essential to improve the decision-making strategy. To solve the
two-fold learning problem described above, we develop the 'combinatorial
semi-bandit framework with causally related rewards', where we model the causal
relations by a directed graph in a stationary structural equation model. The
nodal observation in the graph signal comprises the corresponding base arm's
instantaneous reward and an additional term resulting from the causal
influences of other base arms' rewards. The objective is to maximize the
long-term average payoff, which is a linear function of the base arms' rewards
and depends strongly on the network topology. To achieve this objective, we
propose a policy that determines the causal relations by learning the network's
topology and simultaneously exploits this knowledge to optimize the
decision-making process. We establish a sublinear regret bound for the proposed
algorithm. Numerical experiments using synthetic and real-world datasets
demonstrate the superior performance of our proposed method compared to several
benchmarks.
