  In this paper, a single user multiple input single output downlink wireless
communication system is investigated, in which multiple reconfigurable
intelligent surfaces (RISs) are deployed to improve the propagation condition.
Our objective is to optimize the phase shift matrices of all the RISs by
exploiting the statistical channel state information (CSI). In particular, two
model-free algorithms are proposed, which are applicable for any channel
statistical assumptions. Numerical results show that the proposed algorithms
significantly outperform the random phase shift scheme, especially when the
channel randomness is low.
