The Curse of Concentration in Robust Learning: Evasion and Poisoning Attacks from Concentration of Measure

Many modern machine learning classifiers are shown to be vulnerable to adversarial perturbations of the instances. Despite a massive amount of work focusing on making classifiers robust, the task seems quite challenging. In this work, through a theoretical study, we investigate the adversarial risk and robustness of classifiers and draw a connection to the well-known phenomenon of concentration of measure in metric measure spaces. We show that if the metric probability space of the test instance is concentrated, any classifier with some initial constant error is inherently vulnerable to adversarial perturbations. One class of concentrated metric probability spaces are the so-called Levy families that include many natural distributions. In this special case, our attacks only need to perturb the test instance by at most $O(\sqrt n)$ to make it misclassified, where $n$ is the data dimension. Using our general result about Levy instance spaces, we first recover as special case some of the previously proved results about the existence of adversarial examples. However, many more Levy families are known (e.g., product distribution under the Hamming distance) for which we immediately obtain new attacks that find adversarial examples of distance $O(\sqrt n)$. Finally, we show that concentration of measure for product spaces implies the existence of forms of "poisoning" attacks in which the adversary tampers with the training data with the goal of degrading the classifier. In particular, we show that for any learning algorithm that uses $m$ training examples, there is an adversary who can increase the probability of any "bad property" (e.g., failing on a particular test instance) that initially happens with non-negligible probability to $\approx 1$ by substituting only $\tilde{O}(\sqrt m)$ of the examples with other (still correctly labeled) examples

TrojDRL: Trojan Attacks on Deep Reinforcement Learning Agents

Recent work has identified that classification models implemented as neural networks are vulnerable to data-poisoning and Trojan attacks at training time. In this work, we show that these training-time vulnerabilities extend to deep reinforcement learning (DRL) agents and can be exploited by an adversary with access to the training process. In particular, we focus on Trojan attacks that augment the function of reinforcement learning policies with hidden behaviors. We demonstrate that such attacks can be implemented through minuscule data poisoning (as little as 0.025% of the training data) and in-band reward modification that does not affect the reward on normal inputs. The policies learned with our proposed attack approach perform imperceptibly similar to benign policies but deteriorate drastically when the Trojan is triggered in both targeted and untargeted settings. Furthermore, we show that existing Trojan defense mechanisms for classification tasks are not effective in the reinforcement learning setting