Online planning algorithms are typically a tool of choice for dealing with sequential decision problems in combinatorial search spaces. Many such problems, however, also exhibit combinatorial actions, yet standard planning algorithms do not cope well with this type of “the curse of dimensionality”. Following a recently opened line of related work on combinatorial multi-armed bandit (CMAB) problems, we propose a novel CMAB planning scheme, as well as two specific instances of this scheme, dedicated to exploiting what is called linear side information. Using a representative strategy game as a benchmark, we show that the resulting algorithms very favorably compete with the state-of-the-art.