The Experts below are selected from a list of 294 Experts worldwide ranked by ideXlab platform
Soummya Kar - One of the best experts on this subject based on the ideXlab platform.
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distributed gradient descent Nonconvergence to saddle points and the stable manifold theorem
Allerton Conference on Communication Control and Computing, 2019Co-Authors: Brian Swenson, Ryan Murray, Vincent H Poor, Soummya KarAbstract:The paper studies continuous-time distributed gradient descent (DGD) and considers the problem of showing that in nonconvex optimization problems, DGD typically converges to local minima rather than saddle points. In centralized settings, the problem of demonstrating Nonconvergence to saddle points is typically handled by way of the stable-manifold theorem from classical dynamical systems theory. However, the classical stable-manifold theorem is not applicable in the distributed setting. The paper develops an appropriate stable-manifold theorem for DGD. This shows that convergence to saddle points may only occur from a low-dimensional stable manifold. Under appropriate assumptions (e.g., coercivity), the result implies that DGD almost always converges to local minima.
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Allerton - Distributed Gradient Descent: Nonconvergence to Saddle Points and the Stable-Manifold Theorem
2019 57th Annual Allerton Conference on Communication Control and Computing (Allerton), 2019Co-Authors: Brian Swenson, Ryan Murray, H. Vincent Poor, Soummya KarAbstract:The paper studies continuous-time distributed gradient descent (DGD) and considers the problem of showing that in nonconvex optimization problems, DGD typically converges to local minima rather than saddle points. In centralized settings, the problem of demonstrating Nonconvergence to saddle points is typically handled by way of the stable-manifold theorem from classical dynamical systems theory. However, the classical stable-manifold theorem is not applicable in the distributed setting. The paper develops an appropriate stable-manifold theorem for DGD. This shows that convergence to saddle points may only occur from a low-dimensional stable manifold. Under appropriate assumptions (e.g., coercivity), the result implies that DGD almost always converges to local minima.
Brian Swenson - One of the best experts on this subject based on the ideXlab platform.
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distributed gradient descent Nonconvergence to saddle points and the stable manifold theorem
Allerton Conference on Communication Control and Computing, 2019Co-Authors: Brian Swenson, Ryan Murray, Vincent H Poor, Soummya KarAbstract:The paper studies continuous-time distributed gradient descent (DGD) and considers the problem of showing that in nonconvex optimization problems, DGD typically converges to local minima rather than saddle points. In centralized settings, the problem of demonstrating Nonconvergence to saddle points is typically handled by way of the stable-manifold theorem from classical dynamical systems theory. However, the classical stable-manifold theorem is not applicable in the distributed setting. The paper develops an appropriate stable-manifold theorem for DGD. This shows that convergence to saddle points may only occur from a low-dimensional stable manifold. Under appropriate assumptions (e.g., coercivity), the result implies that DGD almost always converges to local minima.
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Allerton - Distributed Gradient Descent: Nonconvergence to Saddle Points and the Stable-Manifold Theorem
2019 57th Annual Allerton Conference on Communication Control and Computing (Allerton), 2019Co-Authors: Brian Swenson, Ryan Murray, H. Vincent Poor, Soummya KarAbstract:The paper studies continuous-time distributed gradient descent (DGD) and considers the problem of showing that in nonconvex optimization problems, DGD typically converges to local minima rather than saddle points. In centralized settings, the problem of demonstrating Nonconvergence to saddle points is typically handled by way of the stable-manifold theorem from classical dynamical systems theory. However, the classical stable-manifold theorem is not applicable in the distributed setting. The paper develops an appropriate stable-manifold theorem for DGD. This shows that convergence to saddle points may only occur from a low-dimensional stable manifold. Under appropriate assumptions (e.g., coercivity), the result implies that DGD almost always converges to local minima.
Stanley L Winer - One of the best experts on this subject based on the ideXlab platform.
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political competition and convergence to fundamentals with application to the political business cycle and the size of government
2006Co-Authors: Stephen J Ferris, Soobin Park, Stanley L WinerAbstract:We address the problem of how to investigate whether economics, or politics, or both, matter in the explanation of public policy. The problem is first posed in a particular context by uncovering a political business cycle (using Canadian data for 130 years) and by taking up the challenge to make this fact meaningful by finding a transmission mechanism through actual public choices. Since the cycle is in real growth, and it is reasonable to suppose that public expenditure would be involved, the central task then is to investigate the role of (partisan and opportunistic) political factors, as opposed to economic fundamentals, in the evolution of government size. We proceed by asking whether the data allow us to distinguish between the convergence and the Nonconvergence hypotheses. Convergence means that political competition forces public spending to converge in the long run to a level dictated by endowments, tastes and technology. Nonconvergence is taken to mean that political factors other than the degree of political competition prevent convergence to that long run. The general idea here, one that may be applied in any situation where the key issue is the role of economics versus politics over time, is that an overtly political factor can be said to play a distinct role in the evolution of public choices if it can be shown to lead to departures from a dynamic path defined by the evolution of economic fundamentals in a competitive political system.
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political competition and convergence to fundamentals with application to the political business cycle and the size of the public sector
Social Science Research Network, 2005Co-Authors: Stephen J Ferris, Soobin Park, Stanley L WinerAbstract:We address the problem of how to investigate whether economics, or politics, or both, matter in the explanation of public policy. We first pose the problem in a particular context by uncovering a political business cycle (using Canadian data covering 130 years), and by taking up the challenge to make this fact meaningful by finding a transmission mechanism through actual public choices. Since the cycle is in real growth and it is reasonable to suppose that public expenditure would be involved, we then focus on empirical investigation of the role of (partisan and opportunistic) political factors, as opposed to economics, in the evolution of government size. We ask whether the data allow us to distinguish between the convergence and the Nonconvergence hypotheses. Convergence means that political competition forces public spending to converge in the longer run to a level dictated by endowments, tastes and technology. Nonconvergence is taken to mean that political factors other than the degree of political competition prevent convergence to that long run. The general idea is that a political factor can clearly be said to play a role in the evolution of public choices if it can be shown to lead to departures from a dynamic path defined by economic fundamentals in a competitive political system. The results of applying cointegration and error correction modeling to implement this idea show that public expenditure cannot serve as the required transmission mechanism. Of the political factors considered, only variation in the degree of political competition leads to substantial departures of public expenditure from its long run path defined by economic fundamentals. We conclude with some general implications of the analysis for future research.
Ryan Murray - One of the best experts on this subject based on the ideXlab platform.
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distributed gradient descent Nonconvergence to saddle points and the stable manifold theorem
Allerton Conference on Communication Control and Computing, 2019Co-Authors: Brian Swenson, Ryan Murray, Vincent H Poor, Soummya KarAbstract:The paper studies continuous-time distributed gradient descent (DGD) and considers the problem of showing that in nonconvex optimization problems, DGD typically converges to local minima rather than saddle points. In centralized settings, the problem of demonstrating Nonconvergence to saddle points is typically handled by way of the stable-manifold theorem from classical dynamical systems theory. However, the classical stable-manifold theorem is not applicable in the distributed setting. The paper develops an appropriate stable-manifold theorem for DGD. This shows that convergence to saddle points may only occur from a low-dimensional stable manifold. Under appropriate assumptions (e.g., coercivity), the result implies that DGD almost always converges to local minima.
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Allerton - Distributed Gradient Descent: Nonconvergence to Saddle Points and the Stable-Manifold Theorem
2019 57th Annual Allerton Conference on Communication Control and Computing (Allerton), 2019Co-Authors: Brian Swenson, Ryan Murray, H. Vincent Poor, Soummya KarAbstract:The paper studies continuous-time distributed gradient descent (DGD) and considers the problem of showing that in nonconvex optimization problems, DGD typically converges to local minima rather than saddle points. In centralized settings, the problem of demonstrating Nonconvergence to saddle points is typically handled by way of the stable-manifold theorem from classical dynamical systems theory. However, the classical stable-manifold theorem is not applicable in the distributed setting. The paper develops an appropriate stable-manifold theorem for DGD. This shows that convergence to saddle points may only occur from a low-dimensional stable manifold. Under appropriate assumptions (e.g., coercivity), the result implies that DGD almost always converges to local minima.
Lin Zhou - One of the best experts on this subject based on the ideXlab platform.
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Nonconvergence of the Mas-Colell and Zhou bargaining sets
Econometrica, 1997Co-Authors: Robert M. Anderson, Walter Trockel, Lin ZhouAbstract:In an nontransferable utility (NTU) exchange economy with a continuum of agents, the Mas- Colell bargaining set coincides with the set of Walrasian equilibria. In this paper, we show that the Mas-Colell bargaining set, as well as a smaller bargaining set due to Zhou, may fail to converge to competitive outcomes in large finite NTU exchange economies. (This abstract was borrowed from another version of this item.) (This abstract was borrowed from another version of this item.)
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Nonconvergence of the Mas-Colell and Zhou Bargaining Sets
Game Theory and Information, 1994Co-Authors: Robert M. Anderson, Walter Tockel, Lin ZhouAbstract:In an nontransferable utility (NTU) exchange economy with a continuum of agents, the Mas- Colell bargaining set coincides with the set of Walrasian equilibria. In this paper, we show that the Mas-Colell bargaining set, as well as a smaller bargaining set due to Zhou, may fail to converge to competitive outcomes in large finite NTU exchange economies.