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Register a new userGeneralizable Adversarial Training via Spectral Normalization
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Deep neural networks (DNNs) have set benchmarks on a wide array of supervised learning tasks. Trained DNNs, however, often lack robustness to minor adversarial perturbations to the input, which undermines their true practicality. Recent works have increased the robustness of DNNs by fitting networks using adversarially-perturbed training samples, but the improved performance can still be far below the performance seen in non-adversarial settings. A significant portion of this gap can be attributed to the decrease in generalization performance due to adversarial training. In this work, we extend the notion of margin loss to adversarial settings and bound the generalization error for DNNs trained under several well-known gradient-based attack schemes, motivating an effective regularization scheme based on spectral normalization of the DNNs weight matrices. We also provide a computationally-efficient method for normalizing the spectral norm of convolutional layers with arbitrary stride and padding schemes in deep convolutional networks. We evaluate the power of spectral normalization extensively on combinations of datasets, network architectures, and adversarial training schemes. The code is available at https://github.com/jessemzhang/dl_spectral_normalization.
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We introduce a sampling perspective to tackle the challenging task of training robust Reinforcement Learning (RL) agents. Leveraging the powerful Stochastic Gradient Langevin Dynamics, we present a novel, scalable two-player RL algorithm, which is a sampling variant of the two-player policy gradient method. Our algorithm consistently outperforms existing baselines, in terms of generalization across different training and testing conditions, on several MuJoCo environments. Our experiments also show that, even for objective functions that entirely ignore potential environmental shifts, our sampling approach remains highly robust in comparison to standard RL algorithms.
Adoption of machine learning (ML)-enabled cyber-physical systems (CPS) are becoming prevalent in various sectors of modern society such as transportation, industrial, and power grids. Recent studies in deep reinforcement learning (DRL) have demonstrated its benefits in a large variety of data-driven decisions and control applications. As reliance on ML-enabled systems grows, it is imperative to study the performance of these systems under malicious state and actuator attacks. Traditional control systems employ resilient/fault-tolerant controllers that counter these attacks by correcting the system via error observations. However, in some applications, a resilient controller may not be sufficient to avoid a catastrophic failure. Ideally, a robust approach is more useful in these scenarios where a system is inherently robust (by design) to adversarial attacks. While robust control has a long history of development, robust ML is an emerging research area that has already demonstrated its relevance and urgency. However, the majority of robust ML research has focused on perception tasks and not on decision and control tasks, although the ML (specifically RL) models used for control applications are equally vulnerable to adversarial attacks. In this paper, we show that a well-performing DRL agent that is initially susceptible to action space perturbations (e.g. actuator attacks) can be robustified against similar perturbations through adversarial training.
Adversarially trained models exhibit a large generalization gap: they can interpolate the training set even for large perturbation radii, but at the cost of large test error on clean samples. To investigate this gap, we decompose the test risk into its bias and variance components and study their behavior as a function of adversarial training perturbation radii ($varepsilon$). We find that the bias increases monotonically with $varepsilon$ and is the dominant term in the risk. Meanwhile, the variance is unimodal as a function of $varepsilon$, peaking near the interpolation threshold for the training set. This characteristic behavior occurs robustly across different datasets and also for other robust training procedures such as randomized smoothing. It thus provides a test for proposed explanations of the generalization gap. We find that some existing explanations fail this test--for instance, by predicting a monotonically increasing variance curve. This underscores the power of bias-variance decompositions in modern settings-by providing two measurements instead of one, they can rule out more explanations than test accuracy alone. We also show that bias and variance can provide useful guidance for scalably reducing the generalization gap, highlighting pre-training and unlabeled data as promising routes.
Robust training methods against perturbations to the input data have received great attention in the machine learning literature. A standard approach in this direction is adversarial training which learns a model using adversarially-perturbed training samples. However, adversarial training performs suboptimally against perturbations structured across samples such as universal and group-sparse shifts that are commonly present in biological data such as gene expression levels of different tissues. In this work, we seek to close this optimality gap and introduce Group-Structured Adversarial Training (GSAT) which learns a model robust to perturbations structured across samples. We formulate GSAT as a non-convex concave minimax optimization problem which minimizes a group-structured optimal transport cost. Specifically, we focus on the applications of GSAT for group-sparse and rank-constrained perturbations modeled using group and nuclear norm penalties. In order to solve GSATs non-smooth optimization problem in those cases, we propose a new minimax optimization algorithm called GDADMM by combining Gradient Descent Ascent (GDA) and Alternating Direction Method of Multipliers (ADMM). We present several applications of the GSAT framework to gain robustness against structured perturbations for image recognition and computational biology datasets.
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