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Estimating the density of a distribution from samples is a fundamental problem in statistics. In many practical settings, the Wasserstein distance is an appropriate error metric for density estimation. For example, when estimating…
We prove new upper and lower bounds for sample complexity of finding an $\epsilon$-optimal policy of an infinite-horizon average-reward Markov decision process (MDP) given access to a generative model. When the mixing time of the…
We study several questions related to diversifying search results. We give improved approximation algorithms in each of the following problems, together with some lower bounds. - We give a polynomial-time approximation scheme (PTAS) for a…
In the optimization of dynamical systems, the variables typically have constraints. Such problems can be modeled as a constrained Markov Decision Process (CMDP). This paper considers a model-free approach to the problem, where the…
This paper proposes a computationally tractable algorithm for learning infinite-horizon average-reward linear mixture Markov decision processes (MDPs) under the Bellman optimality condition. Our algorithm for linear mixture MDPs achieves a…
In the predict-then-optimize framework, the objective is to train a predictive model, mapping from environment features to parameters of an optimization problem, which maximizes decision quality when the optimization is subsequently solved.…
We develop a novel, general and computationally efficient framework, called Divide and Conquer Dynamic Programming (DCDP), for localizing change points in time series data with high-dimensional features. DCDP deploys a class of greedy…
The Multidimensional Assignment Problem (MAP or s-AP in the case of s dimensions) is an extension of the well-known assignment problem. The most studied case of MAP is 3-AP, though the problems with larger values of s have also a number of…
Given a set of strings over a specified alphabet, identifying a median or consensus string that minimizes the total distance to all input strings is a fundamental data aggregation problem. When the Hamming distance is considered as the…
We explore the problems of classification of composite object (images, speech signals) with low number of models per class. We study the question of improving recognition performance for medium-sized database (thousands of classes). The key…
A semidefinite program (SDP) is a particular kind of convex optimization problem with applications in operations research, combinatorial optimization, quantum information science, and beyond. In this work, we propose variational quantum…
Covariance matrix estimation is an important problem in multivariate data analysis, both from theoretical as well as applied points of view. Many simple and popular covariance matrix estimators are known to be severely affected by model…
Much effort has been directed at algorithms for obtaining the highest probability configuration in a probabilistic random field model known as the maximum a posteriori (MAP) inference problem. In many situations, one could benefit from…
Several high-throughput distributed data-processing applications require multi-hop processing of streams of data. These applications include continual processing on data streams originating from a network of sensors, composing a multimedia…
Partial differential equations (PDEs) are often computationally challenging to solve, and in many settings many related PDEs must be be solved either at every timestep or for a variety of candidate boundary conditions, parameters, or…
In this paper, we propose a fast algorithm for element selection, a multiplication-free form of dimension reduction that produces a dimension-reduced vector by simply selecting a subset of elements from the input. Dimension reduction is a…
Metric Differential Privacy (mDP) extends the concept of Differential Privacy (DP) to serve as a new paradigm of data perturbation. It is designed to protect secret data represented in general metric space, such as text data encoded as word…
We give polynomial time algorithms for quantitative (and qualitative) reachability analysis for Branching Markov Decision Processes (BMDPs). Specifically, given a BMDP, and given an initial population, where the objective of the controller…
The maximum-entropy sampling problem is a fundamental and challenging combinatorial-optimization problem, with application in spatial statistics. It asks to find a maximum-determinant order-$s$ principal submatrix of an order-$n$ covariance…
Approximate dynamic programming is a popular method for solving large Markov decision processes. This paper describes a new class of approximate dynamic programming (ADP) methods- distributionally robust ADP-that address the curse of…