Related papers: On Learning for Ambiguous Chance Constrained Probl…
In this paper, Bayesian quickest change detection problems with sampling right constraints are considered. Specifically, there is a sequence of random variables whose probability density function will change at an unknown time. The goal is…
In the "correlated sampling" problem, two players are given probability distributions $P$ and $Q$, respectively, over the same finite set, with access to shared randomness. Without any communication, the two players are each required to…
We consider the problem of learning a discrete distribution in the presence of an $\epsilon$ fraction of malicious data sources. Specifically, we consider the setting where there is some underlying distribution, $p$, and each data source…
This article aims to introduce the paradigm of distributional robustness from the field of convex optimization to tackle optimal design problems under uncertainty. We consider realistic situations where the physical model, and thereby the…
Distribution testing is a fundamental statistical task with many applications, but we are interested in a variety of problems where systematic mislabelings of the sample prevent us from applying the existing theory. To apply distribution…
We consider the problem of choosing design parameters to minimize the probability of an undesired rare event that is described through the average of $n$ iid random variables. Since the probability of interest for near optimal design…
Distributionally robust control is a well-studied framework for optimal decision making under uncertainty, with the objective of minimizing an expected cost function over control actions, assuming the most adverse probability distribution…
We study stochastic optimization problems with chance and risk constraints, where in the latter, risk is quantified in terms of the conditional value-at-risk (CVaR). We consider the distributionally robust versions of these problems, where…
We study the fundamental problems of agnostically learning halfspaces and ReLUs under Gaussian marginals. In the former problem, given labeled examples $(\mathbf{x}, y)$ from an unknown distribution on $\mathbb{R}^d \times \{ \pm 1\}$,…
We investigate a class of chance-constrained combinatorial optimization problems. Given a pre-specified risk level $\epsilon \in [0,1]$, the chance-constrained program aims to find the minimum cost selection of a vector of binary decisions…
Given samples from an unknown distribution $p$, is it possible to distinguish whether $p$ belongs to some class of distributions $\mathcal{C}$ versus $p$ being far from every distribution in $\mathcal{C}$? This fundamental question has…
In distributionally robust optimization the probability distribution of the uncertain problem parameters is itself uncertain, and a fictitious adversary, e.g., nature, chooses the worst distribution from within a known ambiguity set. A…
The empirical risk minimization approach to data-driven decision making requires access to training data drawn under the same conditions as those that will be faced when the decision rule is deployed. However, in a number of settings, we…
We revisit the problem of distribution learning within the framework of learning-augmented algorithms. In this setting, we explore the scenario where a probability distribution is provided as potentially inaccurate advice on the true,…
We consider the problem of testing a null hypothesis defined by equality and inequality constraints on a statistical parameter. Testing such hypotheses can be challenging because the number of relevant constraints may be on the same order…
Stochastic programs where the uncertainty distribution must be inferred from noisy data samples are considered. The stochastic programs are approximated with distributionally-robust optimizations that minimize the worst-case expected cost…
Anomaly detection is an important problem in many application areas, such as network security. Many deep learning methods for unsupervised anomaly detection produce good empirical performance but lack theoretical guarantees. By casting…
We propose a novel distribution-free scheme to solve optimization problems where the goal is to minimize the expected value of a cost function subject to probabilistic constraints. Unlike standard sampling-based methods, our idea consists…
We propose a fast and scalable optimization method to solve chance or probabilistic constrained optimization problems governed by partial differential equations (PDEs) with high-dimensional random parameters. To address the critical…
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…