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We present a new active learning algorithm that adaptively partitions the input space into a finite number of regions, and subsequently seeks a distinct predictor for each region, both phases actively requesting labels. We prove theoretical guarantees for both the generalization error and the label complexity of our algorithm, and analyze the number of regions defined by the algorithm under some mild assumptions. We also report the results of an extensive suite of experiments on several real-world datasets demonstrating substantial empirical benefits over existing single-region and non-adaptive region-based active learning baselines.
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We introduce the technique of adaptive discretization to design an efficient model-based episodic reinforcement learning algorithm in large (potentially continuous) state-action spaces. Our algorithm is based on optimistic one-step value iteration extended to maintain an adaptive discretization of the space. From a theoretical perspective we provide worst-case regret bounds for our algorithm which are competitive compared to the state-of-the-art model-based algorithms. Moreover, our bounds are obtained via a modular proof technique which can potentially extend to incorporate additional structure on the problem. From an implementation standpoint, our algorithm has much lower storage and computational requirements due to maintaining a more efficient partition of the state and action spaces. We illustrate this via experiments on several canonical control problems, which shows that our algorithm empirically performs significantly better than fixed discretization in terms of both faster convergence and lower memory usage. Interestingly, we observe empirically that while fixed-discretization model-based algorithms vastly outperform their model-free counterparts, the two achieve comparable performance with adaptive discretization.
A primary motivation for the development and implementation of structural health monitoring systems, is the prospect of gaining the ability to make informed decisions regarding the operation and maintenance of structures and infrastructure. Unfortunately, descriptive labels for measured data corresponding to health-state information for the structure of interest are seldom available prior to the implementation of a monitoring system. This issue limits the applicability of the traditional supervised and unsupervised approaches to machine learning in the development of statistical classifiers for decision-supporting SHM systems. The current paper presents a risk-based formulation of active learning, in which the querying of class-label information is guided by the expected value of said information for each incipient data point. When applied to structural health monitoring, the querying of class labels can be mapped onto the inspection of a structure of interest in order to determine its health state. In the current paper, the risk-based active learning process is explained and visualised via a representative numerical example and subsequently applied to the Z24 Bridge benchmark. The results of the case studies indicate that a decision-makers performance can be improved via the risk-based active learning of a statistical classifier, such that the decision process itself is taken into account.
We propose a new batch mode active learning algorithm designed for neural networks and large query batch sizes. The method, Discriminative Active Learning (DAL), poses active learning as a binary classification task, attempting to choose examples to label in such a way as to make the labeled set and the unlabeled pool indistinguishable. Experimenting on image classification tasks, we empirically show our method to be on par with state of the art methods in medium and large query batch sizes, while being simple to implement and also extend to other domains besides classification tasks. Our experiments also show that none of the state of the art methods of today are clearly better than uncertainty sampling when the batch size is relatively large, negating some of the reported results in the recent literature.
In this work we consider active local learning: given a query point $x$, and active access to an unlabeled training set $S$, output the prediction $h(x)$ of a near-optimal $h in H$ using significantly fewer labels than would be needed to actually learn $h$ fully. In particular, the number of label queries should be independent of the complexity of $H$, and the function $h$ should be well-defined, independent of $x$. This immediately also implies an algorithm for distance estimation: estimating the value $opt(H)$ from many fewer labels than needed to actually learn a near-optimal $h in H$, by running local learning on a few random query points and computing the average error. For the hypothesis class consisting of functions supported on the interval $[0,1]$ with Lipschitz constant bounded by $L$, we present an algorithm that makes $O(({1 / epsilon^6}) log(1/epsilon))$ label queries from an unlabeled pool of $O(({L / epsilon^4})log(1/epsilon))$ samples. It estimates the distance to the best hypothesis in the class to an additive error of $epsilon$ for an arbitrary underlying distribution. We further generalize our algorithm to more than one dimensions. We emphasize that the number of labels used is independent of the complexity of the hypothesis class which depends on $L$. Furthermore, we give an algorithm to locally estimate the values of a near-optimal function at a few query points of interest with number of labels independent of $L$. We also consider the related problem of approximating the minimum error that can be achieved by the Nadaraya-Watson estimator under a linear diagonal transformation with eigenvalues coming from a small range. For a $d$-dimensional pointset of size $N$, our algorithm achieves an additive approximation of $epsilon$, makes $tilde{O}({d}/{epsilon^2})$ queries and runs in $tilde{O}({d^2}/{epsilon^{d+4}}+{dN}/{epsilon^2})$ time.
Data-efficient learning algorithms are essential in many practical applications where data collection is expensive, e.g., in robotics due to the wear and tear. To address this problem, meta-learning algorithms use prior experience about tasks to learn new, related tasks efficiently. Typically, a set of training tasks is assumed given or randomly chosen. However, this setting does not take into account the sequential nature that naturally arises when training a model from scratch in real-life: how do we collect a set of training tasks in a data-efficient manner? In this work, we introduce task selection based on prior experience into a meta-learning algorithm by conceptualizing the learner and the active meta-learning setting using a probabilistic latent variable model. We provide empirical evidence that our approach improves data-efficiency when compared to strong baselines on simulated robotic experiments.
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