Related papers: An Optimal Linear Time Algorithm for Quasi-Monoton…
Stochastic optimization is a widely used approach for optimization under uncertainty, where uncertain input parameters are modeled by random variables. Exact or approximation algorithms have been obtained for several fundamental problems in…
We give a new general approach for designing exact exponential-time algorithms for subset problems. In a subset problem the input implicitly describes a family of sets over a universe of size n and the task is to determine whether the…
We present linear-time algorithms for partitioning a path or a tree with weights on the vertices by removing $k$ edges to maximize the minimum-weight component. We also use the same framework to partition a path with weight on the vertices,…
We investigate the calibration of estimations to increase performance with an optimal monotone transform on the estimator outputs. We start by studying the traditional square error setting with its weighted variant and show that the optimal…
In this work, we study the problem of finding the maximum value of a non-negative submodular function subject to a limit on the number of items selected, a ubiquitous problem that appears in many applications, such as data summarization and…
We consider the problem of minimizing a sum of several convex non-smooth functions. We introduce a new algorithm called the selective linearization method, which iteratively linearizes all but one of the functions and employs simple…
Matrix-monotonic optimization exploits the monotonic nature of positive semi-definite matrices to derive optimal diagonalizable structures for the matrix variables of matrix-variable optimization problems. Based on the optimal structures…
In this paper, to remedy this deficiency, we propose a Linear Attention Mechanism which is approximate to dot-product attention with much less memory and computational costs. The efficient design makes the incorporation between attention…
Time Optimal Path Parametrization is the problem of minimizing the time interval during which an actuation constrained agent can traverse a given path. Recently, an efficient linear-time algorithm for solving this problem was proposed.…
It has been found that stochastic algorithms often find good solutions much more rapidly than inherently-batch approaches. Indeed, a very useful rule of thumb is that often, when solving a machine learning problem, an iterative technique…
Inspired by the successes of stochastic algorithms in the training of deep neural networks and the simulation of interacting particle systems, we propose and analyze a framework for randomized time-splitting in linear-quadratic optimal…
A simple yet efficient computational algorithm for computing the continuous optimal experimental design for linear models is proposed. An alternative proof the monotonic convergence for $D$-optimal criterion on continuous design spaces are…
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…
This paper introduces a novel, fast atomic-snapshot protocol for asynchronous message-passing systems. In the process of defining what ``fast'' means exactly, we spot a few interesting issues that arise when conventional time metrics are…
For many tasks of data analysis, we may only have the information of the explanatory variable and the evaluation of the response values are quite expensive. While it is impractical or too costly to obtain the responses of all units, a…
Many combinatorial optimization problems can be formulated as the search for a subgraph that satisfies certain properties and minimizes the total weight. We assume here that the vertices correspond to points in a metric space and can take…
We study the problem of multiway number partition optimization, which has a myriad of applications in the decision, learning and optimization literature. Even though the original multiway partitioning problem is NP-hard and requires…
Many signal processing problems can be solved by maximizing the fitness of a segmented model over all possible partitions of the data interval. This letter describes a simple but powerful algorithm that searches the exponentially large…
We present a complexity reduction algorithm for a family of parameter-dependent linear systems when the system parameters belong to a compact semi-algebraic set. This algorithm potentially describes the underlying dynamical system with…
This paper presents a trajectory generation method that optimizes a quadratic cost functional with respect to linear system dynamics and to linear input and state constraints. The method is based on continuous-time flatness-based trajectory…