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Title: Poisoning Attacks with Generative Adversarial Nets

Paper content:
Machine learning algorithms are vulnerable to poisoning attacks: An adversary can inject malicious points in the training dataset to influence the learning process and degrade the algorithm's performance.
Optimal poisoning attacks have already been proposed to evaluate worst-case scenarios, modelling attacks as a bi-level optimization problem.
Solving these problems is computationally demanding and has limited applicability for some models such as deep networks.
In this paper we introduce a novel generative model to craft systematic poisoning attacks against machine learning classifiers generating adversarial training examples, i.e. samples that look like genuine data points but that degrade the classifier's accuracy when used for training.
We propose a Generative Adversarial Net with three components: generator, discriminator, and the target classifier.
This approach allows us to model naturally the detectability constrains that can be expected in realistic attacks and to identify the regions of the underlying data distribution that can be more vulnerable to data poisoning.
Our experimental evaluation shows the effectiveness of our attack to compromise machine learning classifiers, including deep networks.
Despite the advancements and the benefits of machine learning, it has been shown that learning algorithms are vulnerable and can be the target of attackers, who can gain a significant advantage by exploiting these vulnerabilities (Huang et al., 2011) .
At training time, learning algorithms are vulnerable to poisoning attacks, where small fractions of malicious points injected in the training set can subvert the learning process and degrade the performance of the system in an indiscriminate or targeted way.
Data poisoning is one of the most relevant and emerging security threats in applications that rely upon the collection of large amounts of data in the wild (Joseph et al., 2013) .
Some applications rely on the data from users' feedback or untrusted sources of information that often collude towards the same malicious goal.
For example, in IoT environments sensors can be compromised and adversaries can craft coordinated attacks manipulating the measurements of neighbour sensors evading detection (Illiano et al., 2016) .
In many applications curation of the whole training dataset is not possible, exposing machine learning systems to poisoning attacks.
In the research literature optimal poisoning attack strategies have been proposed against different machine learning algorithms (Biggio et al., 2012; Mei & Zhu, 2015; Muñoz-González et al., 2017; Jagielski et al., 2018) , allowing to assess their performance in worst-case scenarios.
These attacks can be modelled as a bi-level optimization problem, where the outer objective represents the attacker's goal and the inner objective corresponds to the training of the learning algorithm with the poisoned dataset.
Solving these bi-level optimization problems is challenging and can be computationally demanding, especially for generating poisoning points at scale.
This limits its applicability against some learning algorithms such as deep networks or where the training set is large.
In many cases, if no detectability constraints are considered, the poisoning points generated are outliers that can be removed with data filtering (Paudice et al., 2018a) .
Furthermore, such attacks are not realistic as real attackers would aim to remain undetected in order to be able to continue subverting the system in the future.
As shown in (Koh et al., 2018) , detectability constraints for these optimal attack strategies can be modelled, however they further increase the complexity of the attack, limiting even more the application of these techniques.
Taking an entirely different and novel approach, in this paper we propose a poisoning attack strategy against machine learning classifiers with Generative Adversarial Nets (GANs) (Goodfellow et al., 2014) .
This allows us to craft poisoning points in a more systematic way, looking for regions of the data distribution where the poisoning points are more influential and, at the same time, difficult to detect.
Our proposed scheme, pGAN, consists on three components: generator, discriminator and target classifier.
The generator aims to generate poisoning points that maximize the error of the target classifier but minimize the discriminator's ability to distinguish them from genuine data points.
The classifier aims to minimize some loss function evaluated on a training dataset that contains a fraction of poisoning points.
As in a standard GAN, the problem can be formulated as a minimax game.
pGAN allows to systematically generate adversarial training examples , which are similar to genuine data points but that can degrade the performance of the system when used for training.
The use of a generative model allows us to produce poisoning points at scale, enabling poisoning attacks against learning algorithms where the number of training points is large or in situations where optimal attack strategies with bi-level optimization are intractable or difficult to compute, as it can be the case for deep networks.
Additionally, our proposed model also includes a mechanism to control the detectability of the generated poisoning points.
For this, the generator maximizes a convex combination of the losses for the discriminator and the classifier evaluated on the poisoning data points.
Our model allows to control the aggressiveness of the attack through a parameter that controls the weighted sum of the two losses.
This induces a trade-off between effectiveness and detectability of the attack.
In this way, pGAN can be applied for systematic testing of machine learning classifiers at different risk levels.
Our experimental evaluation in synthetic and real datasets shows that pGAN is capable of compromising different machine learning classifiers bypassing different defence mechanisms, including outlier detection Paudice et al. (2018a) , Sever Diakonikolas et al. (2019) , PCA-based defences Rubinstein et al. (2009) and label sanitization Paudice et al. (2018b) .
We analyse the trade-off between detectability and effectiveness of the attack: Too conservative strategies will have a reduced impact on the target classifier but, if the attack is too aggressive, most poisoning points can be detected as outliers.
The pGAN approach we introduce in this paper allows to naturally model attackers with different levels of aggressiveness and the effect of different detectability constraints on the robustness of the algorithms.
This allows to
a) study the characteristics of the attacks and identify regions of the data distributions where poisoning points are more influential, yet more difficult to detect,
b) systematically generate in an efficient and scalable way attacks that correspond to different types of threats and
c) study the effect of mitigation measures such as improving detectability.
In addition to studying the tradeoffs involved in the adversarial model, pGAN also allows to naturally study the tradeoffs between performance and robustness of the system as the fraction of poisoning points increases.
Our experimental evaluation shows that pGAN effectively bypasses different strategies to mitigate poisoning attacks, including outlier detection, label sanitization, PCA-based defences and Sever algorithm.

assistant: text: In this paper we propose a novel generative model to craft systematic poisoning attacks with detectability constraints against machine learning classifiers, including deep networks.