Related papers: Randomized Douglas-Rachford methods for linear sys…
The Kaczmarz method is an algorithm for finding the solution to an overdetermined consistent system of linear equations Ax=b by iteratively projecting onto the solution spaces. The randomized version put forth by Strohmer and Vershynin…
Nonlinear parametric inverse problems appear in many applications. Here, we focus on diffuse optical tomography (DOT) in medical imaging to recover unknown images of interest, such as cancerous tissue in a given medium, using a mathematical…
In practice, it is quite common to face combinatorial optimization problems which contain uncertainty along with non-determinism and dynamicity. These three properties call for appropriate algorithms; reinforcement learning (RL) is dealing…
Sampling-based motion planning algorithms are widely used in robotics because they are very effective in high-dimensional spaces. However, the success rate and quality of the solutions are determined by an adequate selection of their…
Rapidly Exploring Random Trees (RRT) is one of the most widely used algorithms for motion planning in the field of robotics. To reduce the exploration time, RRT-Connect was introduced where two trees are simultaneously formed and eventually…
This article extends the optimal covariance steering (CS) problem for discrete time linear stochastic systems modeled using moment-based ambiguity sets. To hedge against the uncertainty in the state distributions while performing covariance…
Simultaneously performing variable selection and inference in high-dimensional regression models is an open challenge in statistics and machine learning. The increasing availability of vast amounts of variables requires the adoption of…
Regularization schemes for regression have been widely studied in learning theory and inverse problems. In this paper, we study distribution regression (DR) which involves two stages of sampling, and aims at regressing from probability…
We develop and analyze algorithms for distributionally robust optimization (DRO) of convex losses. In particular, we consider group-structured and bounded $f$-divergence uncertainty sets. Our approach relies on an accelerated method that…
This paper investigates the problems large-scale distributed composite convex optimization, with motivations from a broad range of applications, including multi-agent systems, federated learning, smart grids, wireless sensor networks,…
Aiming to provide a faster and convenient truncated SVD algorithm for large sparse matrices from real applications (i.e. for computing a few of largest singular values and the corresponding singular vectors), a dynamically shifted power…
Distributionally robust optimization (DRO) is an effective framework for controlling real-world systems with various uncertainties, typically modeled using distributional uncertainty balls. However, DRO problems often involve infinitely…
In recommendation systems (RS), user behavior data is observational rather than experimental, resulting in widespread bias in the data. Consequently, tackling bias has emerged as a major challenge in the field of recommendation systems.…
Random Projection (RP) technique has been widely applied in many scenarios because it can reduce high-dimensional features into low-dimensional space within short time and meet the need of real-time analysis of massive data. There is an…
Among recent developments centered around Randomized Kaczmarz (RK), a row-sampling iterative projection method for large-scale linear systems, several adaptions to the method have inspired faster convergence. Focusing solely on…
Randomized coordinate descent (RCD) methods are state-of-the-art algorithms for training linear predictors via minimizing regularized empirical risk. When the number of examples ($n$) is much larger than the number of features ($d$), a…
The averaged alternating modified reflections (AAMR) method is a projection algorithm for finding the closest point in the intersection of convex sets to any arbitrary point in a Hilbert space. This method can be seen as an adequate…
With the growth of data, it is more important than ever to develop an efficient and robust method for solving the consistent matrix equation AXB=C. The randomized Kaczmarz (RK) method has received a lot of attention because of its…
In order to accelerate the Douglas--Rachford method we recently developed the circumcentered--reflection method, which provides the closest iterate to the solution among all points relying on successive reflections, for the best…
We consider finite Markov decision processes (MDPs) with convex constraints and known dynamics. In principle, this problem is amenable to off-the-shelf convex optimization solvers, but typically this approach suffers from poor scalability.…