  We examine holographic complexity in the doubly holographic model introduced
in [arXiv:2006.04851][arXiv:2010.00018] to study quantum extremal islands. We
focus on the holographic complexity=volume (CV) proposal for boundary
subregions in the island phase. Exploiting the Fefferman-Graham expansion of
the metric and other geometric quantities near the brane, we derive the leading
contributions to the complexity and interpret these in terms of the generalized
volume of the island derived from the induced higher-curvature gravity action
on the brane. Motivated by these results, we propose a generalization of the CV
proposal for higher curvature theories of gravity. Further, we provide two
consistency checks of our proposal by studying Gauss-Bonnet gravity and f(R)
gravity in the bulk.
