Paper:
Adversarial example generation becomes a viable method for evaluating the robustness of a machine learning model. In this paper, we consider hard-label blackbox attacks (a.k.a. decision-based attacks), which is a challenging setting that generates adversarial examples based on only a series of black-box hard-label queries. This type of attacks can be used to attack discrete and complex models, such as Gradient Boosting Decision Tree (GBDT) and detection-based defense models. Existing decision-based attacks based on iterative local updates often get stuck in a local minimum and fail to generate the optimal adversarial example with the smallest perturbation. To remedy this issue, we propose an efficient meta algorithm called BOSH-attack, which tremendously improves existing algorithms through Bayesian Optimization (BO) and Successive Halving (SH). In particular, instead of traversing a single solution path when searching an adversarial example, we maintain a pool of solution paths to explore important regions. We show empirically that the proposed algorithm converges to a better solution than existing approaches, while the query count is smaller than applying multiple random initializations by a factor of 10.

Review:
This paper proposes a meta-algorithm for the so-called "decision-based attack" problem, where a model that can be accessed only via label queries for a given input is attacked by a minimal perturbation to the input that changes the predicted label. The algorithm, BOSH, augments any iterative algorithm for this problem with a diversification strategy based on bayesian optimization and throwing away bad solutions. Empirically, it is shown that BOSH can improve the performance of recently developed algorithms for this problem, by exploring more solutions and refining them intelligently.
Overall, the decision-based attack problem is very practically relevant as it assumes minimal access to the classifier. I also really like that the authors looked into tree-based models in addition to neural networks. The algorithmic ideas that are proposed are simple and effective, as supported by the experimental results.
However, I have some serious comments about the experimental evaluation that I believe can substantially improve the quality of the paper, if addressed. Whether I raise my score or not will depend on how well the authors address these questions. I also have concerns about related work in heuristic algorithms.
Questions:
- Related work: the ideas of diversifying solution paths and throwing away bad solutions are very popular in combinatorial heuristics. You should do a thorough review of work in that area and in Genetic Algorithms (GA). You could look into the following classical/survey papers as starting points, in particular the first survey's chapter 4.
Glover, Fred, and Manuel Laguna. "Tabu search." Handbook of combinatorial optimization. Springer, Boston, MA, 1998. 2093-2229.
Feo, Thomas A., and Mauricio GC Resende. "Greedy randomized adaptive search procedures." Journal of global optimization 6.2 (1995): 109-133.
- Other Black-Box algorithms: you should compare against well-established black-box optimization algorithms such as NOMAD and RBF-OPT. Both are based on very solid mathematical foundations and have high-quality open source implementations:
NOMAD: https://www.gerad.ca/nomad/
rbf-opt: https://github.com/coin-or/rbfopt
- Runtime comparison: your analysis with respect to number of queries is very good and insightful. In addition, we should get a sense of the runtime performance. If you run each of the approaches with the same time limit, how do they fare?
- Comparing to "optimal" attacks: we need to know how well the solutions are compared to the best possible, or a close-enough approximation. You could run white-box attacks and compare the relative error to the quality of the white-box attack. Otherwise, it is hard to tell what gap remains to be closed algorithmically and it is difficult for other researchers to know whether it's worth trying to improve what you propose here in the future.
- Time complexity: please give a time complexity analysis of BOSH as a function of all its hyperparameters.
Clarity:
- Figure 1: I don't understand what this figure shows. Where are the 2 minima? Please clarify further.
- You minimize l(.) / g(.) in Algorithm 2, but maximize it in Appendix B.2. Maximizing makes more sense. Which one is it?
- Theorem 1: Is that your result or Bergstra et al.'s?
Minor comments:
- "Adversarial example generation becomes a viable method for evaluating the robustness of a machine learning model." --> "Adversarial example generation has become a viable method for evaluating the robustness of a machine learning model."
- "when searching an adversarial" --> "when searching for an adversarial"
- "Distortion" is used in the literature much less than "Perturbation"; consider switching them.
- "our mega algorithm" --> "our meta-algorithm"
- Please use consistent notation: SignOPT or Sign-OPT.
- Appendix B.1: "undifferentiable" --> "non-differentiable"
- "are the t − x1 samples" --> "are the t − 1 samples"