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Register a new userDeformRS: Certifying Input Deformations with Randomized Smoothing
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Deep neural networks are vulnerable to input deformations in the form of vector fields of pixel displacements and to other parameterized geometric deformations e.g. translations, rotations, etc. Current input deformation certification methods either (i) do not scale to deep networks on large input datasets, or (ii) can only certify a specific class of deformations, e.g. only rotations. We reformulate certification in randomized smoothing setting for both general vector field and parameterized deformations and propose DeformRS-VF and DeformRS-Par, respectively. Our new formulation scales to large networks on large input datasets. For instance, DeformRS-Par certifies rich deformations, covering translations, rotations, scaling, affine deformations, and other visually aligned deformations such as ones parameterized by Discrete-Cosine-Transform basis. Extensive experiments on MNIST, CIFAR10 and ImageNet show that DeformRS-Par outperforms existing state-of-the-art in certified accuracy, e.g. improved certified accuracy of 6% against perturbed rotations in the set [-10,10] degrees on ImageNet.
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Randomized smoothing is a recently proposed defense against adversarial attacks that has achieved SOTA provable robustness against $ell_2$ perturbations. A number of publications have extended the guarantees to other metrics, such as $ell_1$ or $ell_infty$, by using different smoothing measures. Although the current framework has been shown to yield near-optimal $ell_p$ radii, the total safety region certified by the current framework can be arbitrarily small compared to the optimal. In this work, we propose a framework to improve the certified safety region for these smoothed classifiers without changing the underlying smoothing scheme. The theoretical contributions are as follows: 1) We generalize the certification for randomized smoothing by reformulating certified radius calculation as a nested optimization problem over a class of functions. 2) We provide a method to calculate the certified safety region using $0^{th}$-order and $1^{st}$-order information for Gaussian-smoothed classifiers. We also provide a framework that generalizes the calculation for certification using higher-order information. 3) We design efficient, high-confidence estimators for the relevant statistics of the first-order information. Combining the theoretical contribution 2) and 3) allows us to certify safety region that are significantly larger than the ones provided by the current methods. On CIFAR10 and Imagenet datasets, the new regions certified by our approach achieve significant improvements on general $ell_1$ certified radii and on the $ell_2$ certified radii for color-space attacks ($ell_2$ restricted to 1 channel) while also achieving smaller improvements on the general $ell_2$ certified radii. Our framework can also provide a way to circumvent the current impossibility results on achieving higher magnitude of certified radii without requiring the use of data-dependent smoothing techniques.
Randomized smoothing is a recent technique that achieves state-of-art performance in training certifiably robust deep neural networks. While the smoothing family of distributions is often connected to the choice of the norm used for certification, the parameters of these distributions are always set as global hyper parameters independent of the input data on which a network is certified. In this work, we revisit Gaussian randomized smoothing and show that the variance of the Gaussian distribution can be optimized at each input so as to maximize the certification radius for the construction of the smoothed classifier. This new approach is generic, parameter-free, and easy to implement. In fact, we show that our data dependent framework can be seamlessly incorporated into 3 randomized smoothing approaches, leading to consistent improved certified accuracy. When this framework is used in the training routine of these approaches followed by a data dependent certification, we achieve 9% and 6% improvement over the certified accuracy of the strongest baseline for a radius of 0.5 on CIFAR10 and ImageNet.
We present the first framework of Certifying Robust Policies for reinforcement learning (CROP) against adversarial state perturbations. We propose two particular types of robustness certification criteria: robustness of per-state actions and lower bound of cumulative rewards. Specifically, we develop a local smoothing algorithm which uses a policy derived from Q-functions smoothed with Gaussian noise over each encountered state to guarantee the robustness of actions taken along this trajectory. Next, we develop a global smoothing algorithm for certifying the robustness of a finite-horizon cumulative reward under adversarial state perturbations. Finally, we propose a local smoothing approach which makes use of adaptive search in order to obtain tight certification bounds for reward. We use the proposed RL robustness certification framework to evaluate six methods that have previously been shown to yield empirically robust RL, including adversarial training and several forms of regularization, on two representative Atari games. We show that RegPGD, RegCVX, and RadialRL achieve high certified robustness among these. Furthermore, we demonstrate that our certifications are often tight by evaluating these algorithms against adversarial attacks.
Federated learning is an emerging data-private distributed learning framework, which, however, is vulnerable to adversarial attacks. Although several heuristic defenses are proposed to enhance the robustness of federated learning, they do not provide certifiable robustness guarantees. In this paper, we incorporate randomized smoothing techniques into federated adversarial training to enable data-private distributed learning with certifiable robustness to test-time adversarial perturbations. Our experiments show that such an advanced federated adversarial learning framework can deliver models as robust as those trained by the centralized training. Further, this enables provably-robust classifiers to $ell_2$-bounded adversarial perturbations in a distributed setup. We also show that one-point gradient estimation based training approach is $2-3times$ faster than popular stochastic estimator based approach without any noticeable certified robustness differences.
Federated learning aims to protect data privacy by collaboratively learning a model without sharing private data among users. However, an adversary may still be able to infer the private training data by attacking the released model. Differential privacy provides a statistical protection against such attacks at the price of significantly degrading the accuracy or utility of the trained models. In this paper, we investigate a utility enhancement scheme based on Laplacian smoothing for differentially private federated learning (DP-Fed-LS), where the parameter aggregation with injected Gaussian noise is improved in statistical precision without losing privacy budget. Our key observation is that the aggregated gradients in federated learning often enjoy a type of smoothness, i.e. sparsity in the graph Fourier basis with polynomial decays of Fourier coefficients as frequency grows, which can be exploited by the Laplacian smoothing efficiently. Under a prescribed differential privacy budget, convergence error bounds with tight rates are provided for DP-Fed-LS with uniform subsampling of heterogeneous Non-IID data, revealing possible utility improvement of Laplacian smoothing in effective dimensionality and variance reduction, among others. Experiments over MNIST, SVHN, and Shakespeare datasets show that the proposed method can improve model accuracy with DP-guarantee and membership privacy under both uniform and Poisson subsampling mechanisms.
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