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.
Cornell University(康奈尔大学);University of Connecticut(康涅狄格大学)
Inverse reinforcement learning (IRL) aims to estimate the reward function of optimizing agents by observing their response (estimates or actions). This paper considers IRL when noisy estimates of the gradient of a reward function generated by multiple stochastic gradient agents are observed. We present a generalized Langevin dynamics algorithm to estimate the reward function $R(θ)$; specifically, the resulting Langevin algorithm asymptotically generates samples from the distribution proportional to $\exp(R(θ))$. The proposed IRL algorithms use kernel-based passive learning schemes. We also con…
Algorithms that tackle deep exploration -- an important challenge in reinforcement learning -- have relied on epistemic uncertainty representation through ensembles or other hypermodels, exploration bonuses, or visitation count distributions. An open question is whether deep exploration can be achieved by an incremental reinforcement learning algorithm that tracks a single point estimate, without additional complexity required to account for epistemic uncertainty. We answer this question in the affirmative. In particular, we develop Langevin DQN, a variation of DQN that differs only in perturb…
Explicit engineering of reward functions for given environments has been a major hindrance to reinforcement learning methods. While Inverse Reinforcement Learning (IRL) is a solution to recover reward functions from demonstrations only, these learned rewards are generally heavily \textit{entangled} with the dynamics of the environment and therefore not portable or \emph{robust} to changing environments. Modern adversarial methods have yielded some success in reducing reward entanglement in the IRL setting. In this work, we leverage one such method, Adversarial Inverse Reinforcement Learning (A…
Reinforcement learning agents are prone to undesired behaviors due to reward mis-specification. Finding a set of reward functions to properly guide agent behaviors is particularly challenging in multi-agent scenarios. Inverse reinforcement learning provides a framework to automatically acquire suitable reward functions from expert demonstrations. Its extension to multi-agent settings, however, is difficult due to the more complex notions of rational behaviors. In this paper, we propose MA-AIRL, a new framework for multi-agent inverse reinforcement learning, which is effective and scalable for …
In the past few years, deep reinforcement learning has been proven to solve problems which have complex states like video games or board games. The next step of intelligent agents would be able to generalize between tasks, and using prior experience to pick up new skills more quickly. However, most reinforcement learning algorithms for now are often suffering from catastrophic forgetting even when facing a very similar target task. Our approach enables the agents to generalize knowledge from a single source task, and boost the learning progress with a semisupervised learning method when facing…
Adversarial examples are firstly investigated in the area of computer vision: by adding some carefully designed ''noise'' to the original input image, the perturbed image that cannot be distinguished from the original one by human, can fool a well-trained classifier easily. In recent years, researchers also demonstrated that adversarial examples can mislead deep reinforcement learning (DRL) agents on playing video games using image inputs with similar methods. However, although DRL has been more and more popular in the area of intelligent transportation systems, there is little research invest…
UCLA(加州大学洛杉矶分校);MIT(麻省理工学院);NVIDIA(英伟达);UIUC(伊利诺伊大学厄巴纳-香槟分校);University of Michigan(密歇根大学)
A deep reinforcement learning (DRL) agent observes its states through observations, which may contain natural measurement errors or adversarial noises. Since the observations deviate from the true states, they can mislead the agent into making suboptimal actions. Several works have shown this vulnerability via adversarial attacks, but existing approaches on improving the robustness of DRL under this setting have limited success and lack for theoretical principles. We show that naively applying existing techniques on improving robustness for classification tasks, like adversarial training, is i…
Provable and Practical: Efficient Exploration in Reinforcement Learning via Langevin Monte Carlo
Mila, McGill University(米拉研究所,麦吉尔大学);University of Alberta, Amii(阿尔伯塔大学,阿尔伯塔创新机器学习研究所);Duke University(杜克大学);CIFAR AI Chair, Amii(加拿大高级研究所人工智能主席职位,阿尔伯塔创新机器学习研究所);Google DeepMind(谷歌DeepMind);California Institute of Technology, Nvidia(加州理工学院,英伟达);Nvidia(英伟达)
To improve efficiency and reduce failures in autonomous vehicles, research has focused on developing robust and safe learning methods that take into account disturbances in the environment. Existing literature in robust reinforcement learning poses the learning problem as a two player game between the autonomous system and disturbances. This paper examines two different algorithms to solve the game, Robust Adversarial Reinforcement Learning and Neural Fictitious Self Play, and compares performance on an autonomous driving scenario. We extend the game formulation to a semi-competitive setting a…
In deep reinforcement learning (RL), adversarial attacks can trick an agent into unwanted states and disrupt training. We propose a system called Robust Student-DQN (RS-DQN), which permits online robustness training alongside Q networks, while preserving competitive performance. We show that RS-DQN can be combined with (i) state-of-the-art adversarial training and (ii) provably robust training to obtain an agent that is resilient to strong attacks during training and evaluation.
Switching costs, which capture the costs for changing policies, are regarded as a critical metric in reinforcement learning (RL), in addition to the standard metric of losses (or rewards). However, existing studies on switching costs (with a coefficient $β$ that is strictly positive and is independent of $T$) have mainly focused on static RL, where the loss distribution is assumed to be fixed during the learning process, and thus practical scenarios where the loss distribution could be non-stationary or even adversarial are not considered. While adversarial RL better models this type of practi…
Iowa State University(爱荷华州立大学);Amity University Uttar Pradesh(阿米提大学北方邦分校)
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 sy…
The use of deep neural networks as function approximators has led to striking progress for reinforcement learning algorithms and applications. Yet the knowledge we have on decision boundary geometry and the loss landscape of neural policies is still quite limited. In this paper we propose a framework to investigate the decision boundary and loss landscape similarities across states and across MDPs. We conduct experiments in various games from Arcade Learning Environment, and discover that high sensitivity directions for neural policies are correlated across MDPs. We argue that these high sensi…
Recently, many cooperative distributed multi-agent reinforcement learning (MARL) algorithms have been proposed in the literature. In this work, we study the effect of adversarial attacks on a network that employs a consensus-based MARL algorithm. We show that an adversarial agent can persuade all the other agents in the network to implement policies that optimize an objective that it desires. In this sense, the standard consensus-based MARL algorithms are fragile to attacks.
Reinforcement learning has seen great advancements in the past five years. The successful introduction of deep learning in place of more traditional methods allowed reinforcement learning to scale to very complex domains achieving super-human performance in environments like the game of Go or numerous video games. Despite great successes in multiple domains, these new methods suffer from their own issues that make them often inapplicable to the real world problems. Extreme lack of data efficiency, together with huge variance and difficulty in enforcing safety constraints, is one of the three m…
Radboud University(拉德堡德大学);University of Antwerp(安特卫普大学)
Deep Reinforcement Learning (RL) agents are susceptible to adversarial noise in their observations that can mislead their policies and decrease their performance. However, an adversary may be interested not only in decreasing the reward, but also in modifying specific temporal logic properties of the policy. This paper presents a metric that measures the exact impact of adversarial attacks against such properties. We use this metric to craft optimal adversarial attacks. Furthermore, we introduce a model checking method that allows us to verify the robustness of RL policies against adversarial …
Adversarial Imitation Learning (AIL) is a class of algorithms in Reinforcement learning (RL), which tries to imitate an expert without taking any reward from the environment and does not provide expert behavior directly to the policy training. Rather, an agent learns a policy distribution that minimizes the difference from expert behavior in an adversarial setting. Adversarial Inverse Reinforcement Learning (AIRL) leverages the idea of AIL, integrates a reward function approximation along with learning the policy, and shows the utility of IRL in the transfer learning setting. But the reward fu…
Tsinghua University(清华大学);University of Virginia(弗吉尼亚大学);Stony Brook University(石溪大学)
Reinforcement learning is well suited for optimizing policies of recommender systems. Current solutions mostly focus on model-free approaches, which require frequent interactions with the real environment, and thus are expensive in model learning. Offline evaluation methods, such as importance sampling, can alleviate such limitations, but usually request a large amount of logged data and do not work well when the action space is large. In this work, we propose a model-based reinforcement learning solution which models user-agent interaction for offline policy learning via a generative adversar…
Deep reinforcement learning (RL) policies are known to be vulnerable to adversarial perturbations to their observations, similar to adversarial examples for classifiers. However, an attacker is not usually able to directly modify another agent's observations. This might lead one to wonder: is it possible to attack an RL agent simply by choosing an adversarial policy acting in a multi-agent environment so as to create natural observations that are adversarial? We demonstrate the existence of adversarial policies in zero-sum games between simulated humanoid robots with proprioceptive observation…
There are great interests as well as many challenges in applying reinforcement learning (RL) to recommendation systems. In this setting, an online user is the environment; neither the reward function nor the environment dynamics are clearly defined, making the application of RL challenging. In this paper, we propose a novel model-based reinforcement learning framework for recommendation systems, where we develop a generative adversarial network to imitate user behavior dynamics and learn her reward function. Using this user model as the simulation environment, we develop a novel Cascading DQN …
Adversarial training has become the primary method to defend against adversarial samples. However, it is hard to practically apply due to many shortcomings. One of the shortcomings of adversarial training is that it will reduce the recognition accuracy of normal samples. Adaptive perturbation adversarial training is proposed to alleviate this problem. It uses marginal adversarial samples that are close to the decision boundary but does not cross the decision boundary for adversarial training, which improves the accuracy of model recognition while maintaining the robustness of the model. Howeve…
Reinforcement learning provides a powerful and general framework for decision making and control, but its application in practice is often hindered by the need for extensive feature and reward engineering. Deep reinforcement learning methods can remove the need for explicit engineering of policy or value features, but still require a manually specified reward function. Inverse reinforcement learning holds the promise of automatic reward acquisition, but has proven exceptionally difficult to apply to large, high-dimensional problems with unknown dynamics. In this work, we propose adverserial in…
Learning from raw high dimensional data via interaction with a given environment has been effectively achieved through the utilization of deep neural networks. Yet the observed degradation in policy performance caused by imperceptible worst-case policy dependent translations along high sensitivity directions (i.e. adversarial perturbations) raises concerns on the robustness of deep reinforcement learning policies. In our paper, we show that these high sensitivity directions do not lie only along particular worst-case directions, but rather are more abundant in the deep neural policy landscape …
Complex autonomous control systems are subjected to sensor failures, cyber-attacks, sensor noise, communication channel failures, etc. that introduce errors in the measurements. The corrupted information, if used for making decisions, can lead to degraded performance. We develop a framework for using adversarial deep reinforcement learning to design observer strategies that are robust to adversarial errors in information channels. We further show through simulation studies that the learned observation strategies perform remarkably well when the adversary's injected errors are bounded in some s…
The University of Melbourne(墨尔本大学);Defence Science and Technology Group, Australian Department of Defence(澳大利亚国防部国防科技集团)
Recent studies have demonstrated that reinforcement learning (RL) agents are susceptible to adversarial manipulation, similar to vulnerabilities previously demonstrated in the supervised learning setting. While most existing work studies the problem in the context of computer vision or console games, this paper focuses on reinforcement learning in autonomous cyber defence under partial observability. We demonstrate that under the black-box setting, where the attacker has no direct access to the target RL model, causative attacks---attacks that target the training process---can poison RL agents…
Despite considerable advances in deep reinforcement learning, it has been shown to be highly vulnerable to adversarial perturbations to state observations. Recent efforts that have attempted to improve adversarial robustness of reinforcement learning can nevertheless tolerate only very small perturbations, and remain fragile as perturbation size increases. We propose Bootstrapped Opportunistic Adversarial Curriculum Learning (BCL), a novel flexible adversarial curriculum learning framework for robust reinforcement learning. Our framework combines two ideas: conservatively bootstrapping each cu…
Westlake University(西湖大学);Westlake Institute for Advanced Study(西湖高等研究院);Nanyang Technological University(南洋理工大学)
Meta Reinforcement Learning (MRL) enables an agent to learn from a limited number of past trajectories and extrapolate to a new task. In this paper, we attempt to improve the robustness of MRL. We build upon model-agnostic meta-learning (MAML) and propose a novel method to generate adversarial samples for MRL by using Generative Adversarial Network (GAN). That allows us to enhance the robustness of MRL to adversal attacks by leveraging these attacks during meta training process.
Georgia Institute of Technology(佐治亚理工学院);IBM Research(IBM研究院);Preferred Network America(美国首选网络公司);Columbia University(哥伦比亚大学)
Recent deep neural networks based techniques, especially those equipped with the ability of self-adaptation in the system level such as deep reinforcement learning (DRL), are shown to possess many advantages of optimizing robot learning systems (e.g., autonomous navigation and continuous robot arm control.) However, the learning-based systems and the associated models may be threatened by the risks of intentionally adaptive (e.g., noisy sensor confusion) and adversarial perturbations from real-world scenarios. In this paper, we introduce timing-based adversarial strategies against a DRL-based …
Google Research(谷歌研究院);Mila, Québec Artificial Intelligence Institute(Mila,魁北克人工智能研究所);Université de Montréal(蒙特利尔大学);CIFAR(加拿大高等研究院);IVADO(IVADO数据价值研究所)
Advancements in reinforcement learning (RL) have been remarkable in recent years. However, the limitations of traditional training methods have become increasingly evident, particularly in meta-RL settings where agents face new, unseen tasks. Conventional training approaches are susceptible to failure in such situations as they need more robustness to adversity. Our proposed adversarial training regime for Multi-Task Reinforcement Learning (MT-RL) addresses the limitations of conventional training methods in RL, especially in meta-RL environments where the agent faces new tasks. The adversaria…
Recent studies have shown that deep reinforcement learning agents are vulnerable to small adversarial perturbations on the agent's inputs, which raises concerns about deploying such agents in the real world. To address this issue, we propose RADIAL-RL, a principled framework to train reinforcement learning agents with improved robustness against $l_p$-norm bounded adversarial attacks. Our framework is compatible with popular deep reinforcement learning algorithms and we demonstrate its performance with deep Q-learning, A3C and PPO. We experiment on three deep RL benchmarks (Atari, MuJoCo and P…
Generative Adversarial Networks (GANs) have experienced a recent surge in popularity, performing competitively in a variety of tasks, especially in computer vision. However, GAN training has shown limited success in natural language processing. This is largely because sequences of text are discrete, and thus gradients cannot propagate from the discriminator to the generator. Recent solutions use reinforcement learning to propagate approximate gradients to the generator, but this is inefficient to train. We propose to utilize an autoencoder to learn a low-dimensional representation of sentences…
The University of Texas at Austin(得克萨斯大学奥斯汀分校);US Army Research Laboratory(美国陆军研究实验室);Sony AI(索尼人工智能)
While Adversarial Imitation Learning (AIL) algorithms have recently led to state-of-the-art results on various imitation learning benchmarks, it is unclear as to what impact various design decisions have on performance. To this end, we present here an organizing, modular framework called Reinforcement-learning-based Adversarial Imitation Learning (RAIL) that encompasses and generalizes a popular subclass of existing AIL approaches. Using the view espoused by RAIL, we create two new IfO (Imitation from Observation) algorithms, which we term SAIfO: SAC-based Adversarial Imitation from Observatio…
We introduce two tactics to attack agents trained by deep reinforcement learning algorithms using adversarial examples, namely the strategically-timed attack and the enchanting attack. In the strategically-timed attack, the adversary aims at minimizing the agent's reward by only attacking the agent at a small subset of time steps in an episode. Limiting the attack activity to this subset helps prevent detection of the attack by the agent. We propose a novel method to determine when an adversarial example should be crafted and applied. In the enchanting attack, the adversary aims at luring the …
Massachusetts Institute of Technology(麻省理工学院);MIT-IBM Watson AI Lab(MIT-IBM沃森人工智能实验室);Ludwig-Maximilians-Universität München(慕尼黑路德维希-马克西米利安大学);IBM Research(IBM研究院);University of Cambridge(剑桥大学);Alan Turing Institute(艾伦·图灵研究所)
We introduce a framework for dynamic adversarial discovery of information (DADI), motivated by a scenario where information (a feature set) is used by third parties with unknown objectives. We train a reinforcement learning agent to sequentially acquire a subset of the information while balancing accuracy and fairness of predictors downstream. Based on the set of already acquired features, the agent decides dynamically to either collect more information from the set of available features or to stop and predict using the information that is currently available. Building on previous work explori…
Cornell University(康奈尔大学);Lockheed Martin Advanced Technology Laboratories(洛克希德·马丁先进技术实验室)
Inverse reinforcement learning (IRL) deals with estimating an agent's utility function from its actions. In this paper, we consider how an agent can hide its strategy and mitigate an adversarial IRL attack; we call this inverse IRL (I-IRL). How should the decision maker choose its response to ensure a poor reconstruction of its strategy by an adversary performing IRL to estimate the agent's strategy? This paper comprises four results: First, we present an adversarial IRL algorithm that estimates the agent's strategy while controlling the agent's utility function. Our second result for I-IRL re…
University of California San Diego(加利福尼亚大学圣地亚哥分校);Georgia Institute of Technology(佐治亚理工学院)
We consider a problem of learning the reward and policy from expert examples under unknown dynamics. Our proposed method builds on the framework of generative adversarial networks and introduces the empowerment-regularized maximum-entropy inverse reinforcement learning to learn near-optimal rewards and policies. Empowerment-based regularization prevents the policy from overfitting to expert demonstrations, which advantageously leads to more generalized behaviors that result in learning near-optimal rewards. Our method simultaneously learns empowerment through variational information maximizati…
In this paper, we implement three state-of-art continuous reinforcement learning algorithms, Deep Deterministic Policy Gradient (DDPG), Proximal Policy Optimization (PPO) and Policy Gradient (PG)in portfolio management. All of them are widely-used in game playing and robot control. What's more, PPO has appealing theoretical propeties which is hopefully potential in portfolio management. We present the performances of them under different settings, including different learning rates, objective functions, feature combinations, in order to provide insights for parameters tuning, features selectio…
Deep reinforcement learning models are vulnerable to adversarial attacks that can decrease a victim's cumulative expected reward by manipulating the victim's observations. Despite the efficiency of previous optimization-based methods for generating adversarial noise in supervised learning, such methods might not be able to achieve the lowest cumulative reward since they do not explore the environmental dynamics in general. In this paper, we provide a framework to better understand the existing methods by reformulating the problem of adversarial attacks on reinforcement learning in the function…
Beijing Institute of Technology(北京理工大学);University of Electronic Science and Technology(电子科技大学);Shanghai University of Science and Technology(上海科技大学)
Partial domain adaptation aims to transfer knowledge from a label-rich source domain to a label-scarce target domain which relaxes the fully shared label space assumption across different domains. In this more general and practical scenario, a major challenge is how to select source instances in the shared classes across different domains for positive transfer. To address this issue, we propose a Domain Adversarial Reinforcement Learning (DARL) framework to automatically select source instances in the shared classes for circumventing negative transfer as well as to simultaneously learn transfe…
School of Computer Science, McGill University(麦吉尔大学计算机科学学院);Department of Electrical, Computer, and Software Engineering, McGill University(麦吉尔大学电气、计算机与软件工程系)
Reinforcement learning has shown promise in learning policies that can solve complex problems. However, manually specifying a good reward function can be difficult, especially for intricate tasks. Inverse reinforcement learning offers a useful paradigm to learn the underlying reward function directly from expert demonstrations. Yet in reality, the corpus of demonstrations may contain trajectories arising from a diverse set of underlying reward functions rather than a single one. Thus, in inverse reinforcement learning, it is useful to consider such a decomposition. The options framework in rei…
The vulnerability of the high-performance machine learning models implies a security risk in applications with real-world consequences. Research on adversarial attacks is beneficial in guiding the development of machine learning models on the one hand and finding targeted defenses on the other. However, most of the adversarial attacks today leverage the gradient or logit information from the models to generate adversarial perturbation. Works in the more realistic domain: decision-based attacks, which generate adversarial perturbation solely based on observing the output label of the targeted m…
Deep Neural Network-based systems are now the state-of-the-art in many robotics tasks, but their application in safety-critical domains remains dangerous without formal guarantees on network robustness. Small perturbations to sensor inputs (from noise or adversarial examples) are often enough to change network-based decisions, which was recently shown to cause an autonomous vehicle to swerve into another lane. In light of these dangers, numerous algorithms have been developed as defensive mechanisms from these adversarial inputs, some of which provide formal robustness guarantees or certificat…
Deep reinforcement learning (DRL) has recently been used to perform efficient resource allocation in wireless communications. In this paper, the vulnerabilities of such DRL agents to adversarial attacks is studied. In particular, we consider multiple DRL agents that perform both dynamic channel access and power control in wireless interference channels. For these victim DRL agents, we design a jammer, which is also a DRL agent. We propose an adversarial jamming attack scheme that utilizes a listening phase and significantly degrades the users' sum rate. Subsequently, we develop an ensemble pol…
We consider the problem of generalization in reinforcement learning where visual aspects of the observations might differ, e.g. when there are different backgrounds or change in contrast, brightness, etc. We assume that our agent has access to only a few of the MDPs from the MDP distribution during training. The performance of the agent is then reported on new unknown test domains drawn from the distribution (e.g. unseen backgrounds). For this "zero-shot RL" task, we enforce invariance of the learned representations to visual domains via a domain adversarial optimization process. We empiricall…
The generalization gap in reinforcement learning (RL) has been a significant obstacle that prevents the RL agent from learning general skills and adapting to varying environments. Increasing the generalization capacity of the RL systems can significantly improve their performance on real-world working environments. In this work, we propose a novel policy-aware adversarial data augmentation method to augment the standard policy learning method with automatically generated trajectory data. Different from the commonly used observation transformation based data augmentations, our proposed method a…
University of Illinois at Urbana-Champaign(伊利诺伊大学厄巴纳-香槟分校)
This paper proposes adversarial attacks for Reinforcement Learning (RL) and then improves the robustness of Deep Reinforcement Learning algorithms (DRL) to parameter uncertainties with the help of these attacks. We show that even a naively engineered attack successfully degrades the performance of DRL algorithm. We further improve the attack using gradient information of an engineered loss function which leads to further degradation in performance. These attacks are then leveraged during training to improve the robustness of RL within robust control framework. We show that this adversarial tra…
Monash University(莫纳什大学);South China University of Technology(华南理工大学)
Deep reinforcement learning has made significant progress in the field of continuous control, such as physical control and autonomous driving. However, it is challenging for a reinforcement model to learn a policy for each task sequentially due to catastrophic forgetting. Specifically, the model would forget knowledge it learned in the past when trained on a new task. We consider this challenge from two perspectives: i) acquiring task-specific skills is difficult since task information and rewards are not highly related; ii) learning knowledge from previous experience is difficult in continuou…
We show that adversarial reinforcement learning (ARL) can be used to produce market marking agents that are robust to adversarial and adaptively-chosen market conditions. To apply ARL, we turn the well-studied single-agent model of Avellaneda and Stoikov [2008] into a discrete-time zero-sum game between a market maker and adversary. The adversary acts as a proxy for other market participants that would like to profit at the market maker's expense. We empirically compare two conventional single-agent RL agents with ARL, and show that our ARL approach leads to: 1) the emergence of risk-averse be…
University of California, Berkeley(加州大学伯克利分校);Google Research(谷歌研究院)
Learning from demonstrations has made great progress over the past few years. However, it is generally data hungry and task specific. In other words, it requires a large amount of data to train a decent model on a particular task, and the model often fails to generalize to new tasks that have a different distribution. In practice, demonstrations from new tasks will be continuously observed and the data might be unlabeled or only partially labeled. Therefore, it is desirable for the trained model to adapt to new tasks that have limited data samples available. In this work, we build an adaptable…
University of New South Wales(新南威尔士大学);University of Technology Sydney(悉尼科技大学);University of Adelaide(阿德莱德大学)
Adversarial attacks pose significant challenges for detecting adversarial attacks at an early stage. We propose attack-agnostic detection on reinforcement learning-based interactive recommendation systems. We first craft adversarial examples to show their diverse distributions and then augment recommendation systems by detecting potential attacks with a deep learning-based classifier based on the crafted data. Finally, we study the attack strength and frequency of adversarial examples and evaluate our model on standard datasets with multiple crafting methods. Our extensive experiments show tha…