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Register a new userAdaptive Learning with Robust Generalization Guarantees
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Added by
Zhiwei Steven Wu
Publication date
2016
fields
Informatics Engineering
and research's language is
English
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The traditional notion of generalization---i.e., learning a hypothesis whose empirical error is close to its true error---is surprisingly brittle. As has recently been noted in [DFH+15b], even if several algorithms have this guarantee in isolation, the guarantee need not hold if the algorithms are composed adaptively. In this paper, we study three notions of generalization---increasing in strength---that are robust to postprocessing and amenable to adaptive composition, and examine the relationships between them. We call the weakest such notion Robust Generalization. A second, intermediate, notion is the stability guarantee known as differential privacy. The strongest guarantee we consider we call Perfect Generalization. We prove that every hypothesis class that is PAC learnable is also PAC learnable in a robustly generalizing fashion, with almost the same sample complexity. It was previously known that differentially private algorithms satisfy robust generalization. In this paper, we show that robust generalization is a strictly weaker concept, and that there is a learning task that can be carried out subject to robust generalization guarantees, yet cannot be carried out subject to differential privacy. We also show that perfect generalization is a strictly stronger guarantee than differential privacy, but that, nevertheless, many learning tasks can be carried out subject to the guarantees of perfect generalization.
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Control policies from imitation learning can often fail to generalize to novel environments due to imperfect demonstrations or the inability of imitation learning algorithms to accurately infer the experts policies. In this paper, we present rigorous generalization guarantees for imitation learning by leveraging the Probably Approximately Correct (PAC)-Bayes framework to provide upper bounds on the expected cost of policies in novel environments. We propose a two-stage training method where a latent policy distribution is first embedded with multi-modal expert behavior using a conditional variational autoencoder, and then fine-tuned in new training environments to explicitly optimize the generalization bound. We demonstrate strong generalization bounds and their tightness relative to empirical performance in simulation for (i) grasping diverse mugs, (ii) planar pushing with visual feedback, and (iii) vision-based indoor navigation, as well as through hardware experiments for the two manipulation tasks.
The combination of machine learning with control offers many opportunities, in particular for robust control. However, due to strong safety and reliability requirements in many real-world applications, providing rigorous statistical and control-theoretic guarantees is of utmost importance, yet difficult to achieve for learning-based control schemes. We present a general framework for learning-enhanced robust control that allows for systematic integration of prior engineering knowledge, is fully compatible with modern robust control and still comes with rigorous and practically meaningful guarantees. Building on the established Linear Fractional Representation and Integral Quadratic Constraints framework, we integrate Gaussian Process Regression as a learning component and state-of-the-art robust controller synthesis. In a concrete robust control example, our approach is demonstrated to yield improved performance with more data, while guarantees are maintained throughout.
We resolve one of the major outstanding problems in robust statistics. In particular, if $X$ is an evenly weighted mixture of two arbitrary $d$-dimensional Gaussians, we devise a polynomial time algorithm that given access to samples from $X$ an $eps$-fraction of which have been adversarially corrupted, learns $X$ to error $poly(eps)$ in total variation distance.
The fragility of deep neural networks to adversarially-chosen inputs has motivated the need to revisit deep learning algorithms. Including adversarial examples during training is a popular defense mechanism against adversarial attacks. This mechanism can be formulated as a min-max optimization problem, where the adversary seeks to maximize the loss function using an iterative first-order algorithm while the learner attempts to minimize it. However, finding adversarial examples in this way causes excessive computational overhead during training. By interpreting the min-max problem as an optimal control problem, it has recently been shown that one can exploit the compositional structure of neural networks in the optimization problem to improve the training time significantly. In this paper, we provide the first convergence analysis of this adversarial training algorithm by combining techniques from robust optimal control and inexact oracle methods in optimization. Our analysis sheds light on how the hyperparameters of the algorithm affect the its stability and convergence. We support our insights with experiments on a robust classification problem.
Algorithms typically come with tunable parameters that have a considerable impact on the computational resources they consume. Too often, practitioners must hand-tune the parameters, a tedious and error-prone task. A recent line of research provides algorithms that return nearly-optimal parameters from within a finite set. These algorithms can be used when the parameter space is infinite by providing as input a random sample of parameters. This data-independent discretization, however, might miss pockets of nearly-optimal parameters: prior research has presented scenarios where the only viable parameters lie within an arbitrarily small region. We provide an algorithm that learns a finite set of promising parameters from within an infinite set. Our algorithm can help compile a configuration portfolio, or it can be used to select the input to a configuration algorithm for finite parameter spaces. Our approach applies to any configuration problem that satisfies a simple yet ubiquitous structure: the algorithms performance is a piecewise constant function of its parameters. Prior research has exhibited this structure in domains from integer programming to clustering.
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