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isanunbiasedstochasticgradientdescentupdateruleforthefollowingempiricalrisk: R(θ) = X

Neural Information Processing Systems

This section contains the theoretical analysis of the loss functions of offline experience replay (Proposition 2),augmented experience replay (Proposition 3),andonline experience replay with reservoirsampling(Proposition1). For all experiments, we use the learning rate of 0.1 following the same setting as in Aljundi et al. [2019], Shimetal.[2021], This paper uses Randaugment [Cubuk et al., 2020], which is an auto augmentation method. It randomly selectsP augmentation operators from a set of 14 operators and applies them to the images. ToapplyBPGintheOCLenvironment,weproposeto determine the better/worse action set based on the feedback in the form of current memory batch accuracyAM,which reflects the memory overfitting level of the CL agent.



SupplementaryMaterial: DualManifoldAdversarialRobustness: Defense againstLpandnon-LpAdversarialAttacks AOM-ImageNetDetails

Neural Information Processing Systems

As pre-processing, each image was center-cropped to produce a square image, and convertedto256 256resolution. In Figure 1, we presentxi (Original) andg(wi)(Projected). Figure 1: Visual comparison between original images and projected images. Weuse the SGD optimizer with the cyclic learning rate scheduling strategyin[10](see Figure 2), momentum0.9,andweightdecay5 For the unseen attacks proposed in [11], we consider attack parameters presented in Table 3. We study how different choices affect the robustness of the trained networks against unseen attacks.


9 SupplementaryMaterial

Neural Information Processing Systems

We use the default train/validation split from nuScenes. All numbers reported in the paper are on the validation split ofnuScenes. Adapt Version (Images) To solve the minimax objective in a single forward-backward pass we usethegradient-reversal layer GRL andwarm-up schedule from [16,15]. Adapt Version (Lidar) Similar to the image version, we solve the minimax objective in a single forward-backward pass using the gradient-reversal layer GRL and the warm-up schedule from [16,15]. We remove the rotation operation from the augmentation pool.