Robust Outlier Arm Identification

We study the problem of Robust Outlier Arm Identification (ROAI), where the goal is to identify arms whose expected rewards deviate substantially from the majority, by adaptively sampling from their reward distributions. We compute the outlier threshold using the median and median absolute deviation of the expected rewards. This is a robust choice for the threshold compared to using the mean and standard deviation, since it can identify outlier arms even in the presence of extreme outlier values. Our setting is different from existing pure exploration problems where the threshold is pre-specified as a given value or rank. This is useful in applications where the goal is to identify the set of promising items but the cardinality of this set is unknown, such as finding promising drugs for a new disease or identifying items favored by a population. We propose two $\delta$-PAC algorithms for ROAI, which includes the first UCB-style algorithm for outlier detection, and derive upper bounds on their sample complexity. We also prove a matching, up to logarithmic factors, worst case lower bound for the problem, indicating that our upper bounds are generally unimprovable. Experimental results show that our algorithms are both robust and about $5$x sample efficient compared to state-of-the-art.

On Regret with Multiple Best Arms

We study regret minimization problem with the existence of multiple best/near-optimal arms in the multi-armed bandit setting. We consider the case where the number of arms/actions is comparable or much larger than the time horizon, and make no assumptions about the structure of the bandit instance. Our goal is to design algorithms that can automatically adapt to the unknown hardness of the problem, i.e., the number of best arms. Our setting captures many modern applications of bandit algorithms where the action space is enormous and the information about the underlying instance/structure is unavailable. We first propose an adaptive algorithm that is agnostic to the hardness level and theoretically derive its regret bound. We then prove a lower bound for our problem setting, which indicates: (1) no algorithm can be optimal simultaneously over all hardness levels; and (2) our algorithm achieves an adaptive rate function that is Pareto optimal. With additional knowledge of the expected reward of the best arm, we propose another adaptive algorithm that is minimax optimal, up to polylog factors, over all hardness levels. Experimental results confirm our theoretical guarantees and show advantages of our algorithms over the previous state-of-the-art.

ReabsNet: Detecting and Revising Adversarial Examples

Though deep neural network has hit a huge success in recent studies and applica- tions, it still remains vulnerable to adversarial perturbations which are imperceptible to humans. To address this problem, we propose a novel network called ReabsNet to achieve high classification accuracy in the face of various attacks. The approach is to augment an existing classification network with a guardian network to detect if a sample is natural or has been adversarially perturbed. Critically, instead of simply rejecting adversarial examples, we revise them to get their true labels. We exploit the observation that a sample containing adversarial perturbations has a possibility of returning to its true class after revision. We demonstrate that our ReabsNet outperforms the state-of-the-art defense method under various adversarial attacks.