Paper:
With the prevalence of machine learning services, crowdsourced data containing sensitive information poses substantial privacy challenges. Existing work focusing on protecting against membership inference attacks under the rigorous framework of differential privacy are vulnerable to attribute inference attacks. In light of the current gap between theory and practice, we develop a novel theoretical framework for privacy-preservation under the attack of attribute inference. Under our framework, we propose a minimax optimization formulation to protect the given attribute and analyze its privacy guarantees against arbitrary adversaries. On the other hand, it is clear that privacy constraint may cripple utility when the protected attribute is correlated with the target variable. To this end, we also prove an informationtheoretic lower bound to precisely characterize the fundamental trade-off between utility and privacy. Empirically, we extensively conduct experiments to corroborate our privacy guarantee and validate the inherent trade-offs in different privacy preservation algorithms. Our experimental results indicate that the adversarial representation learning approaches achieve the best trade-off in terms of privacy preservation and utility maximization.

Review:
Overall, this paper provides valuable insight into the trade-off between privacy preservation and utility when training a representation to fight against attribute inference attack.
Detail comments:
Strength:
+ The whole paper is well organized with logic. Notations are well defined and distinguished.
+ The final results have a good intuitive explanation.
+ The most impressive part of this paper is the analysis of the trade-off between privacy and utility from which the upper bound is quantified.
Weakness:
+ The minimax method looks trivial. The difficulty of using such an objective should be emphasized for practical implementation.
+ The major weakness is the experiments. The experiments only on two datasets may not be convincing for me. And the repetition times, 5 or 3, for each dataset are pretty small. Considering the experiments are conducted with random noise, e.g., DP methods, such a small repetition time is not fair since there a large chance these results could be selected.
+ Which DP Laplacian mechanism is used is not specified. Since there are already many improvements on the DP Laplacian mechanism, e.g., [A], it is necessary to make sure the baseline should be state-of-the-art for a fair comparison.
+ The result is not intuitively surprising that the privacy loss and utility loss will be balanced toward an upper bound (Theorem 4.2). I am not sure how the Jensen-Shannon entropy between D^Y_0 and D^Y_1 can be calculated in practice since the true conditional distribution is not observed. For example, when the data distribution is heavily biased, then the conditional distribution might show less correlation between Y and A. Then, the privacy protection will be a pretty simple task with a very high upper bound. Based on this, it is worth to ask what the upper bound looks like in the dataset used in the experiments.
+ How efficient this algorithm could be? In comparison to other baselines, does this method provide a more efficient solution?
[A] Phan, N., Wu, X., Hu, H., & Dou, D. (2017). Adaptive Laplace Mechanism: Differential Privacy Preservation in Deep Learning. 2017 IEEE International Conference on Data Mining (ICDM), 385–394. https://doi.org/10.1109/ICDM.2017.48