Related papers: From Dynamic Programs to Greedy Algorithms
Monotone submodular maximization with a knapsack constraint is NP-hard. Various approximation algorithms have been devised to address this optimization problem. In this paper, we revisit the widely known modified greedy algorithm. First, we…
A number of scientific fields rely on placing permanent magnets in order to produce a desired magnetic field. We have shown in recent work that the placement process can be formulated as sparse regression. However, binary, grid-aligned…
When developing robust preconditioners for multiphysics problems, fractional functions of the Laplace operator often arise and need to be inverted. Rational approximation in the uniform norm can be used to convert inverting those fractional…
We study sparse approximate solutions to convex optimization problems. It is known that in many engineering applications researchers are interested in an approximate solution of an optimization problem as a linear combination of elements…
Motivated by recent work on stochastic gradient descent methods, we develop two stochastic variants of greedy algorithms for possibly non-convex optimization problems with sparsity constraints. We prove linear convergence in expectation to…
We consider dynamic programming problems with finite, discrete-time horizons and prohibitively high-dimensional, discrete state-spaces for direct computation of the value function from the Bellman equation. For the case that the value…
The Long Term Evolution (LTE) as a mobile broadband technology supports a wide domain of communication services with different requirements. Therefore, scheduling of all flows from various applications in overload states in which the…
In this paper, we will develop a systematic approach to deriving guaranteed bounds for approximate dynamic programming (ADP) schemes in optimal control problems. Our approach is inspired by our recent results on bounding the performance of…
The greedy strategy is an approximation algorithm to solve optimization problems arising in decision making with multiple actions. How good is the greedy strategy compared to the optimal solution? In this survey, we mainly consider two…
The problem of column subset selection has recently attracted a large body of research, with feature selection serving as one obvious and important application. Among the techniques that have been applied to solve this problem, the greedy…
The classical problem of maximizing a submodular function under a matroid constraint is considered. Defining a new measure for the increments made by the greedy algorithm at each step, called the discriminant, improved approximation ratio…
Greedy algorithms have been successfully analyzed and applied in training neural networks for solving variational problems, ensuring guaranteed convergence orders. In this paper, we extend the analysis of the orthogonal greedy algorithm…
We study a pair of budget- and performance-constrained weak-submodular maximization problems. For computational efficiency, we explore the use of stochastic greedy algorithms which limit the search space via random sampling instead of the…
Multimodal learning considers learning from multi-modality data, aiming to fuse heterogeneous sources of information. However, it is not always feasible to leverage all available modalities due to memory constraints. Further, training on…
We connect high-dimensional subset selection and submodular maximization. Our results extend the work of Das and Kempe (2011) from the setting of linear regression to arbitrary objective functions. For greedy feature selection, this…
We describe an approximate dynamic programming approach to compute lower bounds on the optimal value function for a discrete time, continuous space, infinite horizon setting. The approach iteratively constructs a family of lower bounding…
This letter studies the problem of minimizing increasing set functions, or equivalently, maximizing decreasing set functions, over the base of a matroid. This setting has received great interest, since it generalizes several applied…
We consider stochastic dynamic programming problems with high-dimensional, discrete state-spaces and finite, discrete-time horizons that prohibit direct computation of the value function from a given Bellman equation for all states and time…
We study a fundamental problem in Bayesian learning, where the goal is to select a set of data sources with minimum cost while achieving a certain learning performance based on the data streams provided by the selected data sources. First,…
In this paper, we study the problem of maximizing $k$-submodular functions subject to a knapsack constraint. For monotone objective functions, we present a $\frac{1}{2}(1-e^{-2})\approx 0.432$ greedy approximation algorithm. For the…