  Defense models against adversarial attacks have grown significantly, but the
lack of practical evaluation methods has hindered progress. Evaluation can be
defined as looking for defense models' lower bound of robustness given a budget
number of iterations and a test dataset. A practical evaluation method should
be convenient (i.e., parameter-free), efficient (i.e., fewer iterations) and
reliable (i.e., approaching the lower bound of robustness). Towards this
target, we propose a parameter-free Adaptive Auto Attack (A$^3$) evaluation
method which addresses the efficiency and reliability in a test-time-training
fashion. Specifically, by observing that adversarial examples to a specific
defense model follow some regularities in their starting points, we design an
Adaptive Direction Initialization strategy to speed up the evaluation.
Furthermore, to approach the lower bound of robustness under the budget number
of iterations, we propose an online statistics-based discarding strategy that
automatically identifies and abandons hard-to-attack images. Extensive
experiments demonstrate the effectiveness of our A$^3$. Particularly, we apply
A$^3$ to nearly 50 widely-used defense models. By consuming much fewer
iterations than existing methods, i.e., $1/10$ on average (10$\times$ speed
up), we achieve lower robust accuracy in all cases. Notably, we won
$\textbf{first place}$ out of 1681 teams in CVPR 2021 White-box Adversarial
Attacks on Defense Models competitions with this method. Code is available at:
$\href{https://github.com/liuye6666/adaptive_auto_attack}{https://github.com/liuye6666/adaptive\_auto\_attack}$
