The Experts below are selected from a list of 21918 Experts worldwide ranked by ideXlab platform
Feng Chen - One of the best experts on this subject based on the ideXlab platform.
-
Rank-Based Multi-task Learning for Fair Regression
2019 IEEE International Conference on Data Mining (ICDM), 2019Co-Authors: Chen Zhao, Feng ChenAbstract:In this work, we develop a novel fairness learning approach for multi-task regression models based on a biased training dataset, using a popular rank-based non-parametric independence test, i.e., Mann Whitney U statistic, for measuring the dependency between target variable and protected variables. To solve this learning problem efficiently, we first reformulate the problem as a new non-Convex optimization problem, in which a non-Convex Constraint is defined based on group-wise ranking functions of individual objects. We then develop an efficient model-training algorithm based on the framework of non-Convex alternating direction method of multipliers (NC-ADMM), in which one of the main challenges is to implement an efficient projection oracle to the preceding non-Convex set defined based on ranking functions. Through the extensive experiments on both synthetic and real-world datasets, we validated the out-performance of our new approach against several state-of-the-art competitive methods on several popular metrics relevant to fairness learning.
Peng Lin - One of the best experts on this subject based on the ideXlab platform.
-
distributed continuous time and discrete time optimization with nonuniform unbounded Convex Constraint sets and nonuniform stepsizes
IEEE Transactions on Automatic Control, 2019Co-Authors: Peng Lin, Wei Ren, Chunhua Yang, Weihua GuiAbstract:This paper is devoted to distributed continuous-time and discrete-time optimization problems with nonuniform Convex Constraint sets and nonuniform stepsizes for general differentiable Convex objective functions. The communication graphs are not required to be strongly connected at any time, the gradients of the local objective functions are not required to be bounded when their independent variables tend to infinity, and the Constraint sets are not required to be bounded. For continuous-time multiagent systems, a distributed continuous algorithm is first introduced where the stepsizes and the Convex Constraint sets are both nonuniform. It is shown that all agents reach a consensus while minimizing the team objective function even when the Constraint sets are unbounded. After that, the obtained results are extended to discrete-time multiagent systems and then the case where each agent remains in a corresponding Convex Constraint set is studied. To ensure all agents to remain in a bounded region, a switching mechanism is introduced in the algorithms. It is shown that the distributed optimization problems can be solved, even though the discretization of the algorithms might deviate the convergence of the agents from the minimum of the objective functions.
-
distributed continuous time optimization nonuniform gradient gains finite time convergence and Convex Constraint set
IEEE Transactions on Automatic Control, 2017Co-Authors: Peng Lin, Wei Ren, Jay A FarrellAbstract:In this paper, a distributed optimization problem with general differentiable Convex objective functions is studied for continuous-time multi-agent systems with single-integrator dynamics. The objective is for multiple agents to cooperatively optimize a team objective function formed by a sum of local objective functions with only local interaction and information while explicitly taking into account nonuniform gradient gains, finite-time convergence, and a common Convex Constraint set. First, a distributed nonsmooth algorithm is introduced for a special class of Convex objective functions that have a quadratic-like form. It is shown that all agents reach a consensus in finite time while minimizing the team objective function asymptotically. Second, a distributed algorithm is presented for general differentiable Convex objective functions, in which the interaction gains of each agent can be self-adjusted based on local states. A corresponding condition is then given to guarantee that all agents reach a consensus in finite time while minimizing the team objective function asymptotically. Third, a distributed optimization algorithm with state-dependent gradient gains is given for general differentiable Convex objective functions. It is shown that the distributed continuous-time optimization problem can be solved even though the gradient gains are not identical. Fourth, a distributed tracking algorithm combined with a distributed estimation algorithm is given for general differentiable Convex objective functions. It is shown that all agents reach a consensus while minimizing the team objective function in finite time. Fifth, as an extension of the previous results, a distributed constrained optimization algorithm with nonuniform gradient gains and a distributed constrained finite-time optimization algorithm are given. It is shown that both algorithms can be used to solve a distributed continuous-time optimization problem with a common Convex Constraint set. Numerical examples are included to illustrate the obtained theoretical results.
-
distributed optimization with nonuniform unbounded Convex Constraint sets and nonuniform step sizes
2017Co-Authors: Peng Lin, Wei RenAbstract:This paper is devoted to distributed continuous-time and discrete-time optimization problems with nonuniform Convex Constraint sets and nonuniform stepsizes for general differentiable Convex objective functions. The communication graphs are not required to be strongly connected at any time, the gradients of the local objective functions are not required to be bounded when their independent variables tend to infinity, and the Constraint sets are not required to be bounded. For continuous-time multi-agent systems, a distributed continuous algorithm is first introduced where the stepsizes and the Convex Constraint sets are both nonuniform. It is shown that all agents reach a consensus while minimizing the team objective function even when the Constraint sets are unbounded. After that, the obtained results are extended to discrete-time multi-agent systems and then the case where each agent remains in a corresponding Convex Constraint set is studied. To ensure all agents to remain in a bounded region, a switching mechanism is introduced in the algorithms. It is shown that the distributed optimization problems can be solved, even though the discretization of the algorithms might deviate the convergence of the agents from the minimum of the objective functions. Finally, numerical examples are included to show the obtained theoretical results.
-
distributed continuous time and discrete time optimization with nonuniform unbounded Convex Constraint sets and nonuniform stepsizes
arXiv: Optimization and Control, 2017Co-Authors: Peng Lin, Wei Ren, Chunhua Yang, Weihua GuiAbstract:This paper is devoted to distributed continuous-time and discrete-time optimization problems with nonuniform Convex Constraint sets and nonuniform stepsizes for general differentiable Convex objective functions. The communication graphs are not required to be strongly connected at any time, the gradients of the local objective functions are not required to be bounded when their independent variables tend to infinity, and the Constraint sets are not required to be bounded. For continuous-time multi-agent systems, a distributed continuous algorithm is first introduced where the stepsizes and the Convex Constraint sets are both nonuniform. It is shown that all agents reach a consensus while minimizing the team objective function even when the Constraint sets are unbounded. After that, the obtained results are extended to discrete-time multi-agent systems and then the case where each agent remains in a corresponding Convex Constraint set is studied. To ensure all agents to remain in a bounded region, a switching mechanism is introduced in the algorithms. It is shown that the distributed optimization problems can be solved, even though the discretization of the algorithms might deviate the convergence of the agents from the minimum of the objective functions. Finally, numerical examples are included to show the obtained theoretical results.
Andrew R Teel - One of the best experts on this subject based on the ideXlab platform.
-
examples when nonlinear model predictive control is nonrobust
Automatica, 2004Co-Authors: G Grimm, M J Messina, S E Tuna, Andrew R TeelAbstract:We consider nominal robustness of model predictive control for discrete-time nonlinear systems. We show, by examples, that when the optimization problem involves state Constraints, or terminal Constraints coupled with short optimization horizons, the asymptotic stability of the closed loop may have absolutely no robustness. That is to say, it is possible for arbitrarily small disturbances to keep the closed loop strictly inside the interior of the feasibility region of the optimization problem and, at the same time, far from the desired set point. This phenomenon does not occur when using model predictive control for linear systems with Convex Constraint sets. We emphasize that a necessary condition for the absence of nominal robustness in nonlinear model predictive control is that the value function and feedback law are discontinuous at some point(s) in the interior of the feasibility region.
Martin J Wainwright - One of the best experts on this subject based on the ideXlab platform.
-
iterative hessian sketch fast and accurate solution approximation for constrained least squares
Journal of Machine Learning Research, 2016Co-Authors: Mert Pilanci, Martin J WainwrightAbstract:We study randomized sketching methods for approximately solving least-squares problem with a general Convex Constraint. The quality of a least-squares approximation can be assessed in different ways: either in terms of the value of the quadratic objective function (cost approximation), or in terms of some distance measure between the approximate minimizer and the true minimizer (solution approximation). Focusing on the latter criterion, our first main result provides a general lower bound on any randomized method that sketches both the data matrix and vector in a least-squares problem; as a surprising consequence, the most widely used least-squares sketch is sub-optimal for solution approximation. We then present a new method known as the iterative Hessian sketch, and show that it can be used to obtain approximations to the original least-squares problem using a projection dimension proportional to the statistical complexity of the least-squares minimizer, and a logarithmic number of iterations. We illustrate our general theory with simulations for both unconstrained and constrained versions of least-squares, including l1-regularization and nuclear norm Constraints. We also numerically demonstrate the practicality of our approach in a real face expression classification experiment.
-
iterative hessian sketch fast and accurate solution approximation for constrained least squares
arXiv: Optimization and Control, 2014Co-Authors: Mert Pilanci, Martin J WainwrightAbstract:We study randomized sketching methods for approximately solving least-squares problem with a general Convex Constraint. The quality of a least-squares approximation can be assessed in different ways: either in terms of the value of the quadratic objective function (cost approximation), or in terms of some distance measure between the approximate minimizer and the true minimizer (solution approximation). Focusing on the latter criterion, our first main result provides a general lower bound on any randomized method that sketches both the data matrix and vector in a least-squares problem; as a surprising consequence, the most widely used least-squares sketch is sub-optimal for solution approximation. We then present a new method known as the iterative Hessian sketch, and show that it can be used to obtain approximations to the original least-squares problem using a projection dimension proportional to the statistical complexity of the least-squares minimizer, and a logarithmic number of iterations. We illustrate our general theory with simulations for both unconstrained and constrained versions of least-squares, including $\ell_1$-regularization and nuclear norm Constraints. We also numerically demonstrate the practicality of our approach in a real face expression classification experiment.
D.a. Boas - One of the best experts on this subject based on the ideXlab platform.
-
A multi-resolution admissible solution approach for diffuse optical tomography
Proceedings IEEE International Symposium on Biomedical Imaging, 2002Co-Authors: Yiheng Zhang, D.h. Brooks, D.a. BoasAbstract:We address the use of diffuse light to characterize the space-varying absorption coefficient in tissue, posed as an inverse problem, ill-posed due to the physics and limitations on source-detector location. Accurate reliable solutions require a priori Constraints. We extend our previously utilized admissible solution approach, with Convex Constraint functions defining admissibility conditions, by using the deep-cut ellipsoid algorithm, iteratively choosing the most important Constraint value, and introducing a multi-resolution grid method to decrease the computational burden. Simulations in representative 2-D scenarios indicate that we successfully reconstruct relatively deep anomalies while reducing the computational time more than 95%.