We consider a batch active learning scenario where the learner adaptively issues batches of points to a labeling oracle. Sampling labels in batches is highly desirable in practice due to the smaller number of interactive rounds with the labeling oracle (often human beings). However, batch active learning typically pays the price of a reduced adaptivity, leading to suboptimal results. In this paper we propose a solution which requires a careful trade off between the informativeness of the queried points and their diversity. We theoretically investigate batch active learning in the practically relevant scenario where the unlabeled pool of data is available beforehand (pool-based active learning). We analyze a novel stage-wise greedy algorithm and show that, as a function of the label complexity, the excess risk of this algorithm matches the known minimax rates in a standard statistical learning setting with linear function spaces. Our results also exhibit a mild dependence on the batch size. These initial results are then extended to hold for general function spaces with similar algorithmics. These are the first theoretical results that employ careful trade offs between informativeness and diversity to rigorously quantify the statistical performance of batch active learning in the pool-based scenario.

We consider a batch active learning scenario where the learner adaptively issues batches of points to a labeling oracle. Sampling labels in batches is highly desirable in practice due to the smaller number of interactive rounds with the labeling oracle (often human beings). However, batch active learning typically pays the price of a reduced adaptivity, leading to suboptimal results. In this paper we propose a solution which requires a careful trade off between the informativeness of the queried points and their diversity. We theoretically investigate batch active learning in the practically relevant scenario where the unlabeled pool of data is available beforehand (pool-based active learning). We analyze a novel stage-wise greedy algorithm and show that, as a function of the label complexity, the excess risk of this algorithm %operating in the realizable setting for which we prove matches the known minimax rates in standard statistical learning settings. Our results also exhibit a mild dependence on the batch size. These are the first theoretical results that employ careful trade offs between informativeness and diversity to rigorously quantify the statistical performance of batch active learning in the pool-based scenario.

We investigate the problem of active learning in the streaming setting in non-parametric regimes, where the labels are stochastically generated from a class of functions on which we make no assumptions whatsoever. We rely on recently proposed Neural Tangent Kernel (NTK) approximation tools to construct a suitable neural embedding that determines the feature space the algorithm operates on and the learned model computed atop. Since the shape of the label requesting threshold is tightly related to the complexity of the function to be learned, which is a-priori unknown, we also derive a version of the algorithm which is agnostic to any prior knowledge. This algorithm relies on a regret balancing scheme to solve the resulting online model selection problem, and is computationally efficient. We prove joint guarantees on the cumulative regret and number of requested labels which depend on the complexity of the labeling function at hand. In the linear case, these guarantees recover known minimax results of the generalization error as a function of the label complexity in a standard statistical learning setting.

This work addresses the classic machine learning problem of online prediction with expert advice. We consider the finite-horizon version of this zero-sum, two-person game. Using verification arguments from optimal control theory, we view the task of finding better lower and upper bounds on the value of the game (regret) as the problem of finding better sub- and supersolutions of certain partial differential equations (PDEs). These sub- and supersolutions serve as the potentials for player and adversary strategies, which lead to the corresponding bounds. To get explicit bounds, we use closed-form solutions of specific PDEs. Our bounds hold for any given number of experts and horizon; in certain regimes (which we identify) they improve upon the previous state of the art. For two and three experts, our bounds provide the optimal leading order term.

We propose an active learning-based grasp method for accurate industrial manipulation that combines the high accuracy of geometrically driven grasp methods and the generalization ability of data-driven grasp methods. Our grasp sequence consists of pregrasp stage and grasp stage which integrates the active perception and manipulation. In pregrasp stage, the manipulator actively moves and perceives the object. At each step, given the perception image, a motion is chosen so that the manipulator can adjust to a proper pose to grasp the object. We train a convolutional neural network to estimate the motion and combine the network with a closed-loop control so that the end effector can move to the pregrasp state. In grasp stage, the manipulator executes a fixed motion to complete the grasp task. The fixed motion can be acquired from the demonstration with nonexpert conveniently. Our proposed method does not require the prior knowledge of camera intrinsic parameters, hand-eye transformation, or manually designed feature of objects. Instead, the training data sets containing prior knowledge are collected through interactive perception. The method can be easily transferred to new tasks with a few human interventions and is able to complete high accuracy grasp task with a certain robustness to partial observation condition. In our circuit board grasping tests, we could achieve a grasp accuracy of 0.8 mm and 0.6°.