The fidelity bandits problem is a variant of the $K$-armed bandit problem in which the reward of each arm is augmented by a fidelity reward that provides the player with an additional payoff depending on how ‘loyal’ the player has been to that arm in the past. We propose two models for fidelity. In the loyalty-points model the amount of extra reward depends on the number of times the arm has previously been played. In the subscription model the additional reward depends on the current number of consecutive draws of the arm. We consider both stochastic and adversarial problems. Since single-arm strategies are not always optimal in stochastic problems, the notion of regret in the adversarial setting needs careful adjustment. We introduce three possible notions of regret and investigate which can be bounded sublinearly. We study in detail the special cases of increasing, decreasing and coupon (where the player gets an additional reward after every $m$ plays of an arm) fidelity rewards. For the models which do not necessarily enjoy sublinear regret, we provide a worst case lower bound. For those models which exhibit sublinear regret, we provide algorithms and bound their regret.

Deep Convolutional Neural Networks (DCNNs) achieve invariance to domain transformations (deformations) by using multiple `max-pooling' (MP) layers. In this work we show that alternative methods of modeling deformations can improve the accuracy and efficiency of DCNNs. First, we introduce epitomic convolution as an alternative to the common convolution-MP cascade of DCNNs, that comes with the same computational cost but favorable learning properties. Second, we introduce a Multiple Instance Learning algorithm to accommodate global translation and scaling in image classification, yielding an efficient algorithm that trains and tests a DCNN in a consistent manner. Third we develop a DCNN sliding window detector that explicitly, but efficiently, searches over the object's position, scale, and aspect ratio. We provide competitive image classification and localization results on the ImageNet dataset and object detection results on Pascal VOC2007.

The problem of detecting correlations from samples of a high-dimensional Gaussian vector has recently received a lot of attention. In most existing work, detection procedures are provided with a full sample. However, following common wisdom in experimental design, the experimenter may have the capacity to make targeted measurements in an on-line and adaptive manner. In this paper, we investigate such adaptive sensing procedures for detecting positive correlations. It is shown that, using the same number of measurements, adaptive procedures are able to detect significantly weaker correlations than their nonadaptive counterparts. We also establish minimax lower bounds that show the limitations of any procedure.