Many recently proposed methods for Neural Architecture Search (NAS) can be formulated as bilevel optimization. For efficient implementation, its solution requires approximations of second-order methods. In this paper, we demonstrate that gradient errors caused by such approximations lead to suboptimality, in the sense that the optimization procedure fails to converge to a (locally) optimal solution. To remedy this, this paper proposes mldas, a mixed-level reformulation for NAS that can be optimized efficiently and reliably. It is shown that even when using a simple first-order method on the mixed-level formulation, mldas can achieve a lower validation error for NAS problems. Consequently, architectures obtained by our method achieve consistently higher accuracies than those obtained from bilevel optimization. Moreover, mldas proposes a framework beyond DARTS. It is upgraded via model size-based search and early stopping strategies to complete the search process in around 5 hours. Extensive experiments within the convolutional architecture search space validate the effectiveness of our approach.
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