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Distributionally robust optimization (DRO) problems are increasingly seen as a viable method to train machine learning models for improved model generalization. These min-max formulations, however, are more difficult to solve. We therefore…
The disparity information provided by stereo cameras has enabled advanced driver assistance systems to estimate road area more accurately and effectively. In this paper, a novel disparity transformation algorithm is proposed to extract road…
We present a novel algorithm for online, real-time orientation estimation. Our algorithm integrates gyroscope data and corrects the resulting orientation estimate for integration drift using accelerometer and magnetometer data. This…
In our work, we propose a novel yet simple approach to obtain an adaptive learning rate for gradient-based descent methods on classification tasks. Instead of the traditional approach of selecting adaptive learning rates via the decayed…
Seeking to improve model generalization, we consider a new approach based on distributionally robust learning (DRL) that applies stochastic gradient descent to the outer minimization problem. Our algorithm efficiently estimates the gradient…
Low-rank tensor models are widely used in statistics. However, most existing methods rely heavily on the assumption that data follows a sub-Gaussian distribution. To address the challenges associated with heavy-tailed distributions…
Stochastic coordinate descent algorithms are efficient methods in which each iterate is obtained by fixing most coordinates at their values from the current iteration, and approximately minimizing the objective with respect to the remaining…
We propose accelerated randomized coordinate descent algorithms for stochastic optimization and online learning. Our algorithms have significantly less per-iteration complexity than the known accelerated gradient algorithms. The proposed…
We introduce data structures for solving robust regression through stochastic gradient descent (SGD) by sampling gradients with probability proportional to their norm, i.e., importance sampling. Although SGD is widely used for large scale…
The paper considers the problem of network-based computation of global minima in smooth nonconvex optimization problems. It is known that distributed gradient-descent-type algorithms can achieve convergence to the set of global minima by…
Many core problems in robotics can be framed as constrained optimization problems. Often on these problems, the robotic system has uncertainty, or it would be advantageous to identify multiple high quality feasible solutions. To enable…
This paper investigates the problem of tracking solutions of stochastic optimization problems with time-varying costs that depend on random variables with decision-dependent distributions. In this context, we propose the use of an online…
We propose an approach to construction of robust non-Euclidean iterative algorithms for convex composite stochastic optimization based on truncation of stochastic gradients. For such algorithms, we establish sub-Gaussian confidence bounds…
Rotation estimation plays a fundamental role in computer vision and robot tasks, and extremely robust rotation estimation is significantly useful for safety-critical applications. Typically, estimating a rotation is considered a non-linear…
In a variety of problems originating in supervised, unsupervised, and reinforcement learning, the loss function is defined by an expectation over a collection of random variables, which might be part of a probabilistic model or the external…
Under mild conditions on the noise level of the measurements, rotation averaging satisfies strong duality, which enables global solutions to be obtained via semidefinite programming (SDP) relaxation. However, generic solvers for SDP are…
This paper presents a novel stochastic gradient descent algorithm for constrained optimization. The proposed algorithm randomly samples constraints and components of the finite sum objective function and relies on a relaxed logarithmic…
We present a stochastic descent algorithm for unconstrained optimization that is particularly efficient when the objective function is slow to evaluate and gradients are not easily obtained, as in some PDE-constrained optimization and…
In this paper we present a novel randomized block coordinate descent method for the minimization of a convex composite objective function. The method uses (approximate) partial second-order (curvature) information, so that the algorithm…
In this article, we extend our previous work (Applicable Analysis, 2024, pp. 1-25) on the steepest descent method for uncertain multiobjective optimization problems. While that study established local convergence, it did not address global…