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In this work, we give efficient algorithms for privately estimating a Gaussian distribution in both pure and approximate differential privacy (DP) models with optimal dependence on the dimension in the sample complexity. In the pure DP…
The issue of determining not only an adequate dose but also a dosing frequency of a drug arises frequently in Phase II clinical trials. This results in the comparison of models which have some parameters in common. Planning such studies…
Determining the causal structure of a set of variables is critical for both scientific inquiry and decision-making. However, this is often challenging in practice due to limited interventional data. Given that randomized experiments are…
Motion planning under differential constraints is a classic problem in robotics. To date, the state of the art is represented by sampling-based techniques, with the Rapidly-exploring Random Tree algorithm as a leading example. Yet, the…
A crucial task in system identification problems is the selection of the most appropriate model class, and is classically addressed resorting to cross-validation or using asymptotic arguments. As recently suggested in the literature, this…
The Laplacian matrix and its pseudo-inverse for a strongly connected directed graph is fundamental in computing many properties of a directed graph. Examples include random-walk centrality and betweenness measures, average hitting and…
We show that the $A$-optimal design optimization problem over $m$ design points in $\mathbb{R}^n$ is equivalent to minimizing a quadratic function plus a group lasso sparsity inducing term over $n\times m$ real matrices. This observation…
This paper presents a new exact method to calculate worst-case parameter realizations in two-stage robust optimization problems with categorical or binary-valued uncertain data. Traditional exact algorithms for these problems, notably…
Matrix Lie groups are an important class of manifolds commonly used in control and robotics, and optimizing control policies on these manifolds is a fundamental problem. In this work, we propose a novel computationally efficient approach…
The first-order optimality conditions for a generic nonlinear optimization problem are generated as part of the terminal transversality conditions of an optimal control problem. It is shown that the Lagrangian of the optimization problem is…
In this paper, we propose novel algorithms for inferring the Maximum a Posteriori (MAP) solution of discrete pairwise random field models under multiple constraints. We show how this constrained discrete optimization problem can be…
Optimal experiment design for parameter estimation is a research topic that has been in the interest of various studies. A key problem in optimal input design is that the optimal input depends on some unknown system parameters that are to…
The ability to differentiate through optimization problems has unlocked numerous applications, from optimization-based layers in machine learning models to complex design problems formulated as bilevel programs. It has been shown that…
We develop an efficient method for solving non-convex constrained optimization problems that are pervasive in economics. The optimal solution to these problems often involves randomization. We employ a Lagrangian framework and prove that…
We consider a linear regression model with complex-valued response and predictors from a compact and connected Lie group. The regression model is formulated in terms of eigenfunctions of the Laplace-Beltrami operator on the Lie group. We…
The determination of an optimal design for a given regression problem is an intricate optimization problem, especially for models with multivariate predictors. Design admissibility and invariance are main tools to reduce the complexity of…
One fundamental problem in decentralized multi-agent optimization is the trade-off between gradient/sampling complexity and communication complexity. We propose new algorithms whose gradient and sampling complexities are graph topology…
We consider the problem of designing deterministic graph algorithms for the model of Massively Parallel Computation (MPC) that improve with the sparsity of the input graph, as measured by the notion of arboricity. For the problems of…
This paper studies an infinite horizon optimal control problem for discrete-time linear system and quadratic criteria, both with random parameters which are independent and identically distributed with respect to time. In this general…
Decentralized optimization is widely used in large scale and privacy preserving machine learning and various distributed control and sensing systems. It is assumed that every agent in the network possesses a local objective function, and…