This paper analyzes the convergence deviation of surrogate assisted (1+1)EA. A model of surrogate assisted (1+1)EA can be built by the finite markov chain, then we got the transition matrix of this algorithm. The deviation of surrogate model can be expressed by the perturbation of transition matrix. So we can estimate the convergence deviation with the method of matrix perturbation analysis. Analyzing of the convergence changes brought by surrogate model’s deviations can help us to have a better select of the surrogate model.
Differentiable architecture search (DARTS) marks a milestone in Neural Architecture Search (NAS), boasting simplicity and small search costs. However, DARTS still suffers from frequent performance collapse, which happens when some operations, such as skip connections, zeroes and poolings, dominate the architecture. In this paper, we are the first to point out that the phenomenon is attributed to bi-level optimization.We propose Single-DARTS which merely uses singlelevel optimization, updating network weights and architecture parameters simultaneously with the same data batch. Even single-level optimization has been previously attempted, no literature provides a systematic explanation on this essential point. Replacing the bi-level optimization, Single-DARTS obviously alleviates performance collapse as well as enhances the stability of architecture search. Experiment results show that Single-DARTS achieves state-of-the-art performance on mainstream search spaces. For instance, on NAS-Benchmark-201, the searched architectures are nearly optimal ones. We also validate that the single-level optimization framework is much more stable than the bi-level one. We hope that this simple yet effective method will give some insights on differential architecture search. The code is available at https://github.com/PencilAndBike/Single-DARTS.git.
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