How can we design agents that pursue a given objective when all feedback mechanisms are influenceable by the agent? Standard RL algorithms assume a secure reward function, and can thus perform poorly in settings where agents can tamper with the reward-generating mechanism. We present a principled solution to the problem of learning from influenceable feedback, which combines approval with a decoupled feedback collection procedure. For a natural class of corruption functions, decoupled approval algorithms have aligned incentives both at convergence and for their local updates. Empirically, they also scale to complex 3D environments where tampering is possible.
This paper describes REALab, a platform for embedded agency research in reinforcement learning (RL). REALab is designed to model the structure of tampering problems that may arise in real-world deployments of RL. Standard Markov Decision Process (MDP) formulations of RL and simulated environments mirroring the MDP structure assume secure access to feedback (e.g., rewards). This may be unrealistic in settings where agents are embedded and can corrupt the processes producing feedback (e.g., human supervisors, or an implemented reward function). We describe an alternative Corrupt Feedback MDP formulation and the REALab environment platform, which both avoid the secure feedback assumption. We hope the design of REALab provides a useful perspective on tampering problems, and that the platform may serve as a unit test for the presence of tampering incentives in RL agent designs.
Convex relaxations have emerged as a promising approach for verifying desirable properties of neural networks like robustness to adversarial perturbations. Widely used Linear Programming (LP) relaxations only work well when networks are trained to facilitate verification. This precludes applications that involve verification-agnostic networks, i.e., networks not specially trained for verification. On the other hand, semidefinite programming (SDP) relaxations have successfully be applied to verification-agnostic networks, but do not currently scale beyond small networks due to poor time and space asymptotics. In this work, we propose a first-order dual SDP algorithm that (1) requires memory only linear in the total number of network activations, (2) only requires a fixed number of forward/backward passes through the network per iteration. By exploiting iterative eigenvector methods, we express all solver operations in terms of forward and backward passes through the network, enabling efficient use of hardware like GPUs/TPUs. For two verification-agnostic networks on MNIST and CIFAR-10, we significantly improve L-inf verified robust accuracy from 1% to 88% and 6% to 40% respectively. We also demonstrate tight verification of a quadratic stability specification for the decoder of a variational autoencoder.
Adversarial training and its variants have become de facto standards for learning robust deep neural networks. In this paper, we explore the landscape around adversarial training in a bid to uncover its limits. We systematically study the effect of different training losses, model sizes, activation functions, the addition of unlabeled data (through pseudo-labeling) and other factors on adversarial robustness. We discover that it is possible to train robust models that go well beyond state-of-the-art results by combining larger models, Swish/SiLU activations and model weight averaging. We demonstrate large improvements on CIFAR-10 and CIFAR-100 against $\ell_\infty$ and $\ell_2$ norm-bounded perturbations of size $8/255$ and $128/255$, respectively. In the setting with additional unlabeled data, we obtain an accuracy under attack of 65.88% against $\ell_\infty$ perturbations of size $8/255$ on CIFAR-10 (+6.35% with respect to prior art). Without additional data, we obtain an accuracy under attack of 57.20% (+3.46%). To test the generality of our findings and without any additional modifications, we obtain an accuracy under attack of 80.53% (+7.62%) against $\ell_2$ perturbations of size $128/255$ on CIFAR-10, and of 36.88% (+8.46%) against $\ell_\infty$ perturbations of size $8/255$ on CIFAR-100.
Adversarial testing methods based on Projected Gradient Descent (PGD) are widely used for searching norm-bounded perturbations that cause the inputs of neural networks to be misclassified. This paper takes a deeper look at these methods and explains the effect of different hyperparameters (i.e., optimizer, step size and surrogate loss). We introduce the concept of MultiTargeted testing, which makes clever use of alternative surrogate losses, and explain when and how MultiTargeted is guaranteed to find optimal perturbations. Finally, we demonstrate that MultiTargeted outperforms more sophisticated methods and often requires less iterative steps than other variants of PGD found in the literature. Notably, MultiTargeted ranks first on MadryLab's white-box MNIST and CIFAR-10 leaderboards, reducing the accuracy of their MNIST model to 88.36% (with $\ell_\infty$ perturbations of $\epsilon = 0.3$) and the accuracy of their CIFAR-10 model to 44.03% (at $\epsilon = 8/255$). MultiTargeted also ranks first on the TRADES leaderboard reducing the accuracy of their CIFAR-10 model to 53.07% (with $\ell_\infty$ perturbations of $\epsilon = 0.031$).
Prior work on neural network verification has focused on specifications that are linear functions of the output of the network, e.g., invariance of the classifier output under adversarial perturbations of the input. In this paper, we extend verification algorithms to be able to certify richer properties of neural networks. To do this we introduce the class of convex-relaxable specifications, which constitute nonlinear specifications that can be verified using a convex relaxation. We show that a number of important properties of interest can be modeled within this class, including conservation of energy in a learned dynamics model of a physical system; semantic consistency of a classifier's output labels under adversarial perturbations and bounding errors in a system that predicts the summation of handwritten digits. Our experimental evaluation shows that our method is able to effectively verify these specifications. Moreover, our evaluation exposes the failure modes in models which cannot be verified to satisfy these specifications. Thus, emphasizing the importance of training models not just to fit training data but also to be consistent with specifications.
This paper addresses the problem of evaluating learning systems in safety critical domains such as autonomous driving, where failures can have catastrophic consequences. We focus on two problems: searching for scenarios when learned agents fail and assessing their probability of failure. The standard method for agent evaluation in reinforcement learning, Vanilla Monte Carlo, can miss failures entirely, leading to the deployment of unsafe agents. We demonstrate this is an issue for current agents, where even matching the compute used for training is sometimes insufficient for evaluation. To address this shortcoming, we draw upon the rare event probability estimation literature and propose an adversarial evaluation approach. Our approach focuses evaluation on adversarially chosen situations, while still providing unbiased estimates of failure probabilities. The key difficulty is in identifying these adversarial situations -- since failures are rare there is little signal to drive optimization. To solve this we propose a continuation approach that learns failure modes in related but less robust agents. Our approach also allows reuse of data already collected for training the agent. We demonstrate the efficacy of adversarial evaluation on two standard domains: humanoid control and simulated driving. Experimental results show that our methods can find catastrophic failures and estimate failures rates of agents multiple orders of magnitude faster than standard evaluation schemes, in minutes to hours rather than days.
State-of-the-art classifiers have been shown to be largely vulnerable to adversarial perturbations. One of the most effective strategies to improve robustness is adversarial training. In this paper, we investigate the effect of adversarial training on the geometry of the classification landscape and decision boundaries. We show in particular that adversarial training leads to a significant decrease in the curvature of the loss surface with respect to inputs, leading to a drastically more "linear" behaviour of the network. Using a locally quadratic approximation, we provide theoretical evidence on the existence of a strong relation between large robustness and small curvature. To further show the importance of reduced curvature for improving the robustness, we propose a new regularizer that directly minimizes curvature of the loss surface, and leads to adversarial robustness that is on par with adversarial training. Besides being a more efficient and principled alternative to adversarial training, the proposed regularizer confirms our claims on the importance of exhibiting quasi-linear behavior in the vicinity of data points in order to achieve robustness.