  Sparse reduced rank regression is an essential statistical learning method.
In the contemporary literature, estimation is typically formulated as a
nonconvex optimization that often yields to a local optimum in numerical
computation. Yet, their theoretical analysis is always centered on the global
optimum, resulting in a discrepancy between the statistical guarantee and the
numerical computation. In this research, we offer a new algorithm to address
the problem and establish an almost optimal rate for the algorithmic solution.
We also demonstrate that the algorithm achieves the estimation with a
polynomial number of iterations. In addition, we present a generalized
information criterion to simultaneously ensure the consistency of support set
recovery and rank estimation. Under the proposed criterion, we show that our
algorithm can achieve the oracle reduced rank estimation with a significant
probability. The numerical studies and an application in the ovarian cancer
genetic data demonstrate the effectiveness and scalability of our approach.
