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We propose a deep learning algorithm for high dimensional optimal stopping problems. Our method is inspired by the penalty method for solving free boundary PDEs. Within our approach, the penalized PDE is approximated using the Deep BSDE…

In this work, we investigate black-box optimization from the perspective of frequentist kernel methods. We propose a novel batch optimization algorithm, which jointly maximizes the acquisition function and select points from a whole batch…

A crucial task in predictive maintenance is estimating the remaining useful life of physical systems. In the last decade, deep learning has improved considerably upon traditional model-based and statistical approaches in terms of predictive…

We consider a periodic-review, fixed-lifetime perishable inventory control problem where demand is a general stochastic process. The optimal solution for this problem is intractable due to "curse of dimensionality". In this paper, we first…

A plethora of recent research has focused on improving the memory footprint and inference speed of deep networks by reducing the complexity of (i) numerical representations (for example, by deterministic or stochastic quantization) and (ii)…

This paper considers an optimization problem for a dynamical system whose evolution depends on a collection of binary decision variables. We develop scalable approximation algorithms with provable suboptimality bounds to provide…

Real-world data typically contain repeated and periodic patterns. This suggests that they can be effectively represented and compressed using only a few coefficients of an appropriate basis (e.g., Fourier, Wavelets, etc.). However, distance…

The development of randomized algorithms for numerical linear algebra, e.g. for computing approximate QR and SVD factorizations, has recently become an intense area of research. This paper studies one of the most frequently discussed…

The need to recognise long-term dependencies in sequential data such as video streams has made Long Short-Term Memory (LSTM) networks a prominent Artificial Intelligence model for many emerging applications. However, the high computational…

The recent rising popularity of ultra-fast delivery services on retail platforms fuels the increasing use of urban warehouses, whose proximity to customers makes fast deliveries viable. The space limit in urban warehouses poses a problem…

We consider the problem of automatically proving resource bounds. That is, we study how to prove that an integer-valued resource variable is bounded by a given program expression. Automatic resource-bound analysis has recently received…

We address the problem of learning an unknown smooth function and its derivatives from noisy pointwise evaluations under the supremum norm. While classical nonparametric regression provides a strong theoretical foundation, traditional…

We present a fast and memory-efficient algorithm for transient, space-time-domain, and elastodynamic boundary-integral analysis. Associated data-sparse approximations and operations are named fast domain partitioning hierarchical matrices…

In recent years we have witnessed an increase on the development of methods for submodular optimization, which have been motivated by the wide applicability of submodular functions in real-world data-science problems. In this paper, we…

We study the fixed design segmented regression problem: Given noisy samples from a piecewise linear function $f$, we want to recover $f$ up to a desired accuracy in mean-squared error. Previous rigorous approaches for this problem rely on…

Network design problems involve constructing edges in a transportation or supply chain network to minimize construction and daily operational costs. We study a stochastic version where operational costs are uncertain due to fluctuating…

Stochastic gradient descent (SGD) is a powerful method for large-scale optimization problems in the area of machine learning, especially for a finite-sum formulation with numerous variables. In recent years, mini-batch SGD gains great…

In this paper, we introduce a method for approximating the solution to inference and optimization tasks in uncertain and deterministic reasoning. Such tasks are in general intractable for exact algorithms because of the large number of…

We present a novel approach to Bayesian inference and general Bayesian computation that is defined through a sequential decision loop. Our method defines a recursive partitioning of the sample space. It neither relies on gradients nor…

Bayesian method is capable of capturing real world uncertainties/incompleteness and properly addressing the over-fitting issue faced by deep neural networks. In recent years, Bayesian Neural Networks (BNNs) have drawn tremendous attentions…