Related papers: Understanding the Eluder Dimension
We consider linear stochastic bandits where the set of actions is an ellipsoid. We provide the first known minimax optimal algorithm for this problem. We first derive a novel information-theoretic lower bound on the regret of any algorithm,…
We propose an algorithmic framework, that employs active subspace techniques, for scalable global optimization of functions with low effective dimension (also referred to as low-rank functions). This proposal replaces the original…
We propose an algorithmic framework, Offline Estimation to Decisions (OE2D), that reduces contextual bandit learning with general reward function approximation to offline regression. The framework allows near-optimal regret for contextual…
A central problem in online learning and decision making -- from bandits to reinforcement learning -- is to understand what modeling assumptions lead to sample-efficient learning guarantees. We consider a general adversarial decision making…
The exploding and vanishing gradient problem has been the major conceptual principle behind most architecture and training improvements in recurrent neural networks (RNNs) during the last decade. In this paper, we argue that this principle,…
We consider the problem of multiclass transductive online learning when the number of labels can be unbounded. Previous works by Ben-David et al. [1997] and Hanneke et al. [2023b] only consider the case of binary and finite label spaces,…
We study gapped scale-sensitive dimensions of a function class in both sequential and non-sequential settings. We demonstrate that covering numbers for any uniformly bounded class are controlled above by these gapped dimensions,…
Many real networks are embedded in space, where in some of them the links length decay as a power law distribution with distance. Indications that such systems can be characterized by the concept of dimension were found recently. Here, we…
For infinite action contextual bandits, smoothed regret and reduction to regression results in state-of-the-art online performance with computational cost independent of the action set: unfortunately, the resulting data exhaust does not…
We study the problem of online learning with dynamics, where a learner interacts with a stateful environment over multiple rounds. In each round of the interaction, the learner selects a policy to deploy and incurs a cost that depends on…
We introduce exploration potential, a quantity that measures how much a reinforcement learning agent has explored its environment class. In contrast to information gain, exploration potential takes the problem's reward structure into…
In this paper, we consider regression models with a Hilbert-space-valued predictor and a scalar response, where the response depends on the predictor only through a finite number of projections. The linear subspace spanned by these…
In the incentivized exploration model, a principal aims to explore and learn over time by interacting with a sequence of self-interested agents. It has been recently understood that the main challenge in designing incentive-compatible…
The paper briefy reviews several recent results on hierarchical architectures for learning from examples, that may formally explain the conditions under which Deep Convolutional Neural Networks perform much better in function approximation…
In this paper, we initiate a rigorous study of the phenomenon of low-dimensional adversarial perturbations (LDAPs) in classification. Unlike the classical setting, these perturbations are limited to a subspace of dimension $k$ which is much…
In the classical multi-armed bandit problem, instance-dependent algorithms attain improved performance on "easy" problems with a gap between the best and second-best arm. Are similar guarantees possible for contextual bandits? While…
We present a framework for analyzing the exact dynamics of a class of online learning algorithms in the high-dimensional scaling limit. Our results are applied to two concrete examples: online regularized linear regression and principal…
We propose a simple model selection approach for algorithms in stochastic bandit and reinforcement learning problems. As opposed to prior work that (implicitly) assumes knowledge of the optimal regret, we only require that each base…
We consider ReLU networks with random weights, in which the dimension decreases at each layer. We show that for most such networks, most examples $x$ admit an adversarial perturbation at an Euclidean distance of…
The number of free parameters, or dimension, of a model is a straightforward way to measure its complexity: a model with more parameters can encode more information. However, this is not an accurate measure of complexity: models capable of…