30,889 research outputs found
Improved Generalization Bounds for Robust Learning
We consider a model of robust learning in an adversarial environment. The
learner gets uncorrupted training data with access to possible corruptions that
may be affected by the adversary during testing. The learner's goal is to build
a robust classifier that would be tested on future adversarial examples. We use
a zero-sum game between the learner and the adversary as our game theoretic
framework. The adversary is limited to possible corruptions for each input.
Our model is closely related to the adversarial examples model of Schmidt et
al. (2018); Madry et al. (2017).
Our main results consist of generalization bounds for the binary and
multi-class classification, as well as the real-valued case (regression). For
the binary classification setting, we both tighten the generalization bound of
Feige, Mansour, and Schapire (2015), and also are able to handle an infinite
hypothesis class . The sample complexity is improved from
to
. Additionally, we
extend the algorithm and generalization bound from the binary to the multiclass
and real-valued cases. Along the way, we obtain results on fat-shattering
dimension and Rademacher complexity of -fold maxima over function classes;
these may be of independent interest.
For binary classification, the algorithm of Feige et al. (2015) uses a regret
minimization algorithm and an ERM oracle as a blackbox; we adapt it for the
multi-class and regression settings. The algorithm provides us with
near-optimal policies for the players on a given training sample.Comment: Appearing at the 30th International Conference on Algorithmic
Learning Theory (ALT 2019
Robust Regression for Safe Exploration in Control
We study the problem of safe learning and exploration in sequential control problems. The goal is to safely collect data samples from an operating environment to learn an optimal controller. A central challenge in this setting is how to quantify uncertainty in order to choose provably-safe actions that allow us to collect useful data and reduce uncertainty, thereby achieving both improved safety and optimality. To address this challenge, we present a deep robust regression model that is trained to directly predict the uncertainty bounds for safe exploration. We then show how to integrate our robust regression approach with model-based control methods by learning a dynamic model with robustness bounds. We derive generalization bounds under domain shifts for learning and connect them with safety and stability bounds in control. We demonstrate empirically that our robust regression approach can outperform conventional Gaussian process (GP) based safe exploration in settings where it is difficult to specify a good GP prior
Robust Regression for Safe Exploration in Control
We study the problem of safe learning and exploration in sequential control problems. The goal is to safely collect data samples from an operating environment to learn an optimal controller. A central challenge in this setting is how to quantify uncertainty in order to choose provably-safe actions that allow us to collect useful data and reduce uncertainty, thereby achieving both improved safety and optimality. To address this challenge, we present a deep robust regression model that is trained to directly predict the uncertainty bounds for safe exploration. We then show how to integrate our robust regression approach with model-based control methods by learning a dynamic model with robustness bounds. We derive generalization bounds under domain shifts for learning and connect them with safety and stability bounds in control. We demonstrate empirically that our robust regression approach can outperform conventional Gaussian process (GP) based safe exploration in settings where it is difficult to specify a good GP prior
Robust Regression for Safe Exploration in Control
We study the problem of safe learning and exploration in sequential control problems. The goal is to safely collect data samples from an operating environment to learn an optimal controller. A central challenge in this setting is how to quantify uncertainty in order to choose provably-safe actions that allow us to collect useful data and reduce uncertainty, thereby achieving both improved safety and optimality. To address this challenge, we present a deep robust regression model that is trained to directly predict the uncertainty bounds for safe exploration. We then show how to integrate our robust regression approach with model-based control methods by learning a dynamic model with robustness bounds. We derive generalization bounds under domain shifts for learning and connect them with safety and stability bounds in control. We demonstrate empirically that our robust regression approach can outperform conventional Gaussian process (GP) based safe exploration in settings where it is difficult to specify a good GP prior
Interval Bound Propagation\unicode{x2013}aided Few\unicode{x002d}shot Learning
Few-shot learning aims to transfer the knowledge acquired from training on a
diverse set of tasks, from a given task distribution, to generalize to unseen
tasks, from the same distribution, with a limited amount of labeled data. The
underlying requirement for effective few-shot generalization is to learn a good
representation of the task manifold. One way to encourage this is to preserve
local neighborhoods in the feature space learned by the few-shot learner. To
this end, we introduce the notion of interval bounds from the provably robust
training literature to few-shot learning. The interval bounds are used to
characterize neighborhoods around the training tasks. These neighborhoods can
then be preserved by minimizing the distance between a task and its respective
bounds. We further introduce a novel strategy to artificially form new tasks
for training by interpolating between the available tasks and their respective
interval bounds, to aid in cases with a scarcity of tasks. We apply our
framework to both model-agnostic meta-learning as well as prototype-based
metric-learning paradigms. The efficacy of our proposed approach is evident
from the improved performance on several datasets from diverse domains in
comparison to a sizable number of recent competitors
Hedging Complexity in Generalization via a Parametric Distributionally Robust Optimization Framework
Empirical risk minimization (ERM) and distributionally robust optimization
(DRO) are popular approaches for solving stochastic optimization problems that
appear in operations management and machine learning. Existing generalization
error bounds for these methods depend on either the complexity of the cost
function or dimension of the random perturbations. Consequently, the
performance of these methods can be poor for high-dimensional problems with
complex objective functions. We propose a simple approach in which the
distribution of random perturbations is approximated using a parametric family
of distributions. This mitigates both sources of complexity; however, it
introduces a model misspecification error. We show that this new source of
error can be controlled by suitable DRO formulations. Our proposed parametric
DRO approach has significantly improved generalization bounds over existing ERM
and DRO methods and parametric ERM for a wide variety of settings. Our method
is particularly effective under distribution shifts and works broadly in
contextual optimization. We also illustrate the superior performance of our
approach on both synthetic and real-data portfolio optimization and regression
tasks.Comment: Preliminary version appeared in AISTATS 202
Generalization Error in Deep Learning
Deep learning models have lately shown great performance in various fields
such as computer vision, speech recognition, speech translation, and natural
language processing. However, alongside their state-of-the-art performance, it
is still generally unclear what is the source of their generalization ability.
Thus, an important question is what makes deep neural networks able to
generalize well from the training set to new data. In this article, we provide
an overview of the existing theory and bounds for the characterization of the
generalization error of deep neural networks, combining both classical and more
recent theoretical and empirical results
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