Using this estimator, we propose a perturbation-based exploration strategy and develop a generalized regret analysis scheme that provides upper and lower regret bounds by revealing the relationship between the regret and the cumulative density function of the perturbation. From the proposed analysis scheme, we obtain gap-dependent and gap-independent upper and lower regret bounds of various perturbations. We also find the optimal hyperparameters for each perturbation, which can achieve the minimax optimal regret bound with respect to total rounds. In simulation, the proposed estimator shows favorable performance compared to existing robust estimators for various p values and, for MAB problems, the proposed perturbation strategy outperforms existing exploration methods.

Active Learning (AL) aims to reduce the labeling burden by interactively selecting the most informative samples from a pool of unlabeled data. While there has been extensive research on improving AL query methods in recent years, some studies have questioned the effectiveness of AL compared to emerging paradigms such as semi-supervised (Semi-SL) and self-supervised learning (Self-SL), or a simple optimization of classifier configurations. Thus, today's AL literature presents an inconsistent and contradictory landscape, leaving practitioners uncertain about whether and how to use AL in their tasks. In this work, we make the case that this inconsistency arises from a lack of systematic and realistic evaluation of AL methods. Specifically, we identify five key pitfalls in the current literature that reflect the delicate considerations required for AL evaluation. Further, we present an evaluation framework that overcomes these pitfalls and thus enables meaningful statements about the performance of AL methods. To demonstrate the relevance of our protocol, we present a large-scale empirical study and benchmark for image classification spanning various data sets, query methods, AL settings, and training paradigms. Our findings clarify the inconsistent picture in the literature and enable us to give hands-on recommendations for practitioners.

Solving inverse problems, such as parameter estimation and optimal control, is a vital part of science. Many experiments repeatedly collect data and rely on machine learning algorithms to quickly infer solutions to the associated inverse problems. We find that state-of-the-art training techniques are not well-suited to many problems that involve physical processes. The highly nonlinear behavior, common in physical processes, results in strongly varying gradients that lead first-order optimizers like SGD or Adam to compute suboptimal optimization directions. We propose a novel hybrid training approach that combines higherorder optimization methods with machine learning techniques. We take updates from a scale-invariant inverse problem solver and embed them into the gradientdescent-based learning pipeline, replacing the regular gradient of the physical process. We demonstrate the capabilities of our method on a variety of canonical physical systems, showing that it yields significant improvements on a wide range of optimization and learning problems.

We analyze the dynamics of finite width effects in wide but finite feature learning neural networks. Starting from a dynamical mean field theory description of infinite width deep neural network kernel and prediction dynamics, we provide a characterization of the O(1/ width) fluctuations of the DMFT order parameters over random initializations of the network weights. Our results, while perturbative in width, unlike prior analyses, are non-perturbative in the strength of feature learning. In the lazy limit of network training, all kernels are random but static in time and the prediction variance has a universal form. However, in the rich, feature learning regime, the fluctuations of the kernels and predictions are dynamically coupled with a variance that can be computed self-consistently.

Convolutional neural networks perform a local and translationally-invariant treatment of the data: quantifying which of these two aspects is central to their success remains a challenge. We study this problem within a teacher-student framework for kernel regression, using'convolutional' kernels inspired by the neural tangent kernel of simple convolutional architectures of given filter size.

Training deep neural network classifiers that are certifiably robust against adversarial attacks is critical to ensuring the security and reliability of AI-controlled systems. Although numerous state-of-the-art certified training methods have been developed, they are computationally expensive and scale poorly with respect to both dataset and network complexity. Widespread usage of certified training is further hindered by the fact that periodic retraining is necessary to incorporate new data and network improvements. In this paper, we propose Certified Robustness Transfer (CRT), a general-purpose framework for reducing the computational overhead of any certifiably robust training method through knowledge transfer. Given a robust teacher, our framework uses a novel training loss to transfer the teacher's robustness to the student. We provide theoretical and empirical validation of CRT. Our experiments on CIFAR-10 show that CRT speeds up certified robustness training by 8 on average across three different architecture generations while achieving comparable robustness to state-of-the-art methods. We also show that CRT can scale to large-scale datasets like ImageNet.

While reinforcement learning algorithms can learn effective policies for complex tasks, these policies are often brittle to even minor task variations, especially when variations are not explicitly provided during training. One natural approach to this problem is to train agents with manually specified variation in the training task or environment. However, this may be infeasible in practical situations, either because making perturbations is not possible, or because it is unclear how to choose suitable perturbation strategies without sacrificing performance. The key insight of this work is that learning diverse behaviors for accomplishing a task can directly lead to behavior that generalizes to varying environments, without needing to perform explicit perturbations during training. By identifying multiple solutions for the task in a single environment during training, our approach can generalize to new situations by abandoning solutions that are no longer effective and adopting those that are. We theoretically characterize a robustness set of environments that arises from our algorithm and empirically find that our diversity-driven approach can extrapolate to various changes in the environment and task.

We thank the reviewers for their interest in our work and their helpful comments. Please find our response below. DDPG and TD3, by keeping an exploration strategy which does not decay to zero. Gradient methods to bridge the gap between DPO and GAC. Reviewer 3: Thank you for pointing out some confusing explanations, we will make sure to clarify them in the paper.

We used popular ResNet models viz. ResNet18 and ResNet50 models and MobileNetV2 as well as their skeptical variants to evaluate the efficacy of proposed hybrid distillation scheme. For the ResNet models we added the auxiliary classifiers (ACs) enhancements after the basic block layer number 2 and 3. For the MobileNetV2 variant these ACs are placed after stage 4 and stage 6 where a stage is a combination of linear bottleneck layers as defined by [1]. It is noteworthy that the skeptical models are more parameter-heavy due to the added parameter cost for the ACs.

Knowledge distillation (KD) has recently been identified as a method that can unintentionally leak private information regarding the details of a teacher model to an unauthorized student. Recent research in developing undistillable nasty teachers that can protect model confidentiality has gained significant attention. However, the level of protection these nasty models offer has been largely untested. In this paper, we show that transferring knowledge to a shallow sub-section of a student can largely reduce a teacher's influence. By exploring the depth of the shallow subsection, we then present a distillation technique that enables a skeptical student model to learn even from a nasty teacher. To evaluate the efficacy of our skeptical students, we conducted experiments with several models with KD under both training data-available and data-free scenarios for various datasets. While distilling from nasty teachers, compared to the normal student models, skeptical students consistently provide superior classification performance of up to 59.5%. Moreover, similar to normal students, skeptical students maintain high classification accuracy when distilled from a normal teacher, showing their efficacy irrespective of the teacher being nasty or not. We believe the ability of skeptical students to largely diminish the KD-immunity of a potentially nasty teacher will motivate the research community to create more robust mechanisms for model confidentiality.