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We apply the PAC-Bayes theory to the setting of learning-to-optimize. To the best of our knowledge, we present the first framework to learn optimization algorithms with provable generalization guarantees (PAC-bounds) and explicit trade-off…

We study contrastive learning under the PAC learning framework. While a series of recent works have shown statistical results for learning under contrastive loss, based either on the VC-dimension or Rademacher complexity, their algorithms…

We study the problem of PAC learning $\gamma$-margin halfspaces with Random Classification Noise. We establish an information-computation tradeoff suggesting an inherent gap between the sample complexity of the problem and the sample…

We study the optimal scale at which real-valued function classes exhibit uniform convergence and learnability. Our main result establishes a scale-sensitive generalization of the fundamental theorem of PAC learning: for every bounded…

Multi-distribution learning generalizes the classic PAC learning to handle data coming from multiple distributions. Given a set of $k$ data distributions and a hypothesis class of VC dimension $d$, the goal is to learn a hypothesis that…

In this paper, we find a sample complexity bound for learning a simplex from noisy samples. Assume a dataset of size $n$ is given which includes i.i.d. samples drawn from a uniform distribution over an unknown simplex in $\mathbb{R}^K$,…

We establish new hardness results for decision tree optimization problems, adding to a line of work that dates back to Hyafil and Rivest in 1976. We prove, under randomized ETH, superpolynomial lower bounds for two basic problems: given an…

In 1984, Valiant [ 7 ] introduced the Probably Approximately Correct (PAC) learning framework for boolean function classes. Blumer et al. [ 2] extended this model in 1989 by introducing the VC dimension as a tool to characterize the…

We study the sample complexity of learning an $\epsilon$-optimal policy in the Stochastic Shortest Path (SSP) problem. We first derive sample complexity bounds when the learner has access to a generative model. We show that there exists a…

Due to the costliness of labelled data in real-world applications, semi-supervised object detectors, underpinned by pseudo labelling, are appealing. However, handling confusing samples is nontrivial: discarding valuable confusing samples…

While it is commonly observed in practice that pruning networks to a certain level of sparsity can improve the quality of the features, a theoretical explanation of this phenomenon remains elusive. In this work, we investigate this by…

We study the sample complexity of semi-supervised learning (SSL) and introduce new assumptions based on the mismatch between a mixture model learned from unlabeled data and the true mixture model induced by the (unknown) class conditional…

In reinforcement learning, the classic objectives of maximizing discounted and finite-horizon cumulative rewards are PAC-learnable: There are algorithms that learn a near-optimal policy with high probability using a finite amount of samples…

The ultimate performance of machine learning algorithms for classification tasks is usually measured in terms of the empirical error probability (or accuracy) based on a testing dataset. Whereas, these algorithms are optimized through the…

We use the PAC-Bayesian theory for the setting of learning-to-optimize. To the best of our knowledge, we present the first framework to learn optimization algorithms with provable generalization guarantees (PAC-Bayesian bounds) and explicit…

We investigate the feasibility of sample average approximation (SAA) for general stochastic optimization problems, including two-stage stochastic programming without the relatively complete recourse assumption. Instead of analyzing problems…

We study binary classification algorithms for which the prediction on any point is not too sensitive to individual examples in the dataset. Specifically, we consider the notions of uniform stability (Bousquet and Elisseeff, 2001) and…

We conduct a non asymptotic study of the Cross Validation (CV) estimate of the generalization risk for learning algorithms dedicated to extreme regions of the covariates space. In this Extreme Value Analysis context, the risk function…

A standard approach in pattern classification is to estimate the distributions of the label classes, and then to apply the Bayes classifier to the estimates of the distributions in order to classify unlabeled examples. As one might expect,…

We consider the problem of probably approximately correct (PAC) ranking $n$ items by adaptively eliciting subset-wise preference feedback. At each round, the learner chooses a subset of $k$ items and observes stochastic feedback indicating…