Related papers: Time-Space Tradeoffs for Learning from Small Test …
Motivated by problems arising in random sampling of trigonometric polynomials, we derive exponential inequalities for the operator norm of the difference between the sample second moment matrix $n^{-1}U^*U$ and its expectation where $U$ is…
In this work, we show, for the well-studied problem of learning parity under noise, where a learner tries to learn $x=(x_1,\ldots,x_n) \in \{0,1\}^n$ from a stream of random linear equations over $\mathrm{F}_2$ that are correct with…
How can we enable machines to make sense of the world, and become better at learning? To approach this goal, I believe viewing intelligence in terms of many integral aspects, and also a universal two-term tradeoff between task performance…
Reinforcement learning with function approximation has recently achieved tremendous results in applications with large state spaces. This empirical success has motivated a growing body of theoretical work proposing necessary and sufficient…
We say that a classifier is \emph{adversarially robust} to perturbations of norm $r$ if, with high probability over a point $x$ drawn from the input distribution, there is no point within distance $\le r$ from $x$ that is classified…
We establish a time-stepping learning algorithm and apply it to predict the solution of the partial differential equation of motion in micromagnetism as a dynamical system depending on the external field as parameter. The data-driven…
Finding global optima in high-dimensional optimization problems is extremely challenging since the number of function evaluations required to sufficiently explore the search space increases exponentially with its dimensionality.…
Learning problems in the text processing domain often map the text to a space whose dimensions are the measured features of the text, e.g., its words. Three characteristic properties of this domain are (a) very high dimensionality, (b) both…
Many machine learning tasks, such as learning with invariance and policy evaluation in reinforcement learning, can be characterized as problems of learning from conditional distributions. In such problems, each sample $x$ itself is…
We propose an automata-theoretic approach for reinforcement learning (RL) under complex spatio-temporal constraints with time windows. The problem is formulated using a Markov decision process under a bounded temporal logic constraint.…
We study the problem of learning general (i.e., not necessarily homogeneous) halfspaces with Random Classification Noise under the Gaussian distribution. We establish nearly-matching algorithmic and Statistical Query (SQ) lower bound…
Deep learning algorithms can fare poorly when the training dataset suffers from heavy class-imbalance but the testing criterion requires good generalization on less frequent classes. We design two novel methods to improve performance in…
We consider episodic reinforcement learning in reward-mixing Markov decision processes (RMMDPs): at the beginning of every episode nature randomly picks a latent reward model among $M$ candidates and an agent interacts with the MDP…
Neural networks have achieved tremendous success in a large variety of applications. However, their memory footprint and computational demand can render them impractical in application settings with limited hardware or energy resources. In…
Learning from Demonstration is increasingly used for transferring operator manipulation skills to robots. In practice, it is important to cater for limited data and imperfect human demonstrations, as well as underlying safety constraints.…
We prove the hardness of weakly learning halfspaces in the presence of adversarial noise using polynomial threshold functions (PTFs). In particular, we prove that for any constants $d \in \mathbb{Z}^+$ and $\varepsilon > 0$, it is NP-hard…
We provide lower error bounds for randomized algorithms that approximate integrals of functions depending on an unrestricted or even infinite number of variables. More precisely, we consider the infinite-dimensional integration problem on…
In most real-world scenarios, labeled training datasets are highly class-imbalanced, where deep neural networks suffer from generalizing to a balanced testing criterion. In this paper, we explore a novel yet simple way to alleviate this…
In this paper, we study first-order methods on a large variety of low-rank matrix optimization problems, whose solutions only live in a low dimensional eigenspace. Traditional first-order methods depend on the eigenvalue decomposition at…
The increased availability of data in recent years has led several authors to ask whether it is possible to use data as a {\em computational} resource. That is, if more data is available, beyond the sample complexity limit, is it possible…