Stochastic Dual Averaging for Decentralized Online Optimization on Time-Varying Communication Graphs
We consider a decentralized online convex optimization problem in a network of agents, where each agent controls only a coordinate (or a part) of the global decision vector. For such a problem, we propose two decentralized stochastic variants (<inline-formula><tex-math notation="LaTeX&...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Lee, Soomin [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2017 |
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| Schlagwörter: |
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| Übergeordnetes Werk: |
Enthalten in: IEEE transactions on automatic control - New York, NY : Inst., 1963, 62(2017), 12, Seite 6407-6414 |
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| Übergeordnetes Werk: |
volume:62 ; year:2017 ; number:12 ; pages:6407-6414 |
| Links: |
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| DOI / URN: |
10.1109/TAC.2017.2650563 |
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| Katalog-ID: |
OLC1998666131 |
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| 520 | |a We consider a decentralized online convex optimization problem in a network of agents, where each agent controls only a coordinate (or a part) of the global decision vector. For such a problem, we propose two decentralized stochastic variants (<inline-formula><tex-math notation="LaTeX">\mathsf{SODA}\hbox{-}\mathsf{C}</tex-math> </inline-formula> and <inline-formula><tex-math notation="LaTeX">\mathsf{SODA}\hbox{-}\mathsf{PS}</tex-math> </inline-formula>) of Nesterov's dual averaging method <inline-formula><tex-math notation="LaTeX">(\mathsf{DA}) </tex-math></inline-formula>, where each agent only uses a coordinate of the noise-corrupted gradient in the dual-averaging step. We show that the expected regret bounds for both algorithms have sublinear growth of <inline-formula><tex-math notation="LaTeX">O(\sqrt{T})</tex-math></inline-formula>, with the time horizon <inline-formula><tex-math notation="LaTeX">T</tex-math></inline-formula>, in scenarios when the underlying communication topology is time-varying. The sublinear regret can be obtained when the stepsize is of the form <inline-formula><tex-math notation="LaTeX">1/\sqrt{t}</tex-math></inline-formula> and the objective functions are Lipschitz-continuous convex functions with Lipschitz gradients, and the variance of the noisy gradients is bounded. We also provide simulation results of the proposed algorithms on sensor networks to complement our theoretical analysis. | ||
| 650 | 4 | |a Convex functions | |
| 650 | 4 | |a Stochastic processes | |
| 650 | 4 | |a Decentralized optimization | |
| 650 | 4 | |a Resource management | |
| 650 | 4 | |a Signal processing algorithms | |
| 650 | 4 | |a Linear programming | |
| 650 | 4 | |a Algorithm design and analysis | |
| 650 | 4 | |a pseudo-regret | |
| 650 | 4 | |a online optimization | |
| 650 | 4 | |a Optimization | |
| 650 | 4 | |a stochastic dual-averaging method | |
| 700 | 1 | |a Nedic, Angelia |4 oth | |
| 700 | 1 | |a Raginsky, Maxim |4 oth | |
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10.1109/TAC.2017.2650563 doi PQ20171228 (DE-627)OLC1998666131 (DE-599)GBVOLC1998666131 (PRQ)c1067-b08b816e9097e30a84e5547743d2dd5924283aa297e5e45ee527280e64ff97430 (KEY)0005057120170000062001206407stochasticdualaveragingfordecentralizedonlineoptim DE-627 ger DE-627 rakwb eng 620 DNB Lee, Soomin verfasserin aut Stochastic Dual Averaging for Decentralized Online Optimization on Time-Varying Communication Graphs 2017 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier We consider a decentralized online convex optimization problem in a network of agents, where each agent controls only a coordinate (or a part) of the global decision vector. For such a problem, we propose two decentralized stochastic variants (<inline-formula><tex-math notation="LaTeX">\mathsf{SODA}\hbox{-}\mathsf{C}</tex-math> </inline-formula> and <inline-formula><tex-math notation="LaTeX">\mathsf{SODA}\hbox{-}\mathsf{PS}</tex-math> </inline-formula>) of Nesterov's dual averaging method <inline-formula><tex-math notation="LaTeX">(\mathsf{DA}) </tex-math></inline-formula>, where each agent only uses a coordinate of the noise-corrupted gradient in the dual-averaging step. We show that the expected regret bounds for both algorithms have sublinear growth of <inline-formula><tex-math notation="LaTeX">O(\sqrt{T})</tex-math></inline-formula>, with the time horizon <inline-formula><tex-math notation="LaTeX">T</tex-math></inline-formula>, in scenarios when the underlying communication topology is time-varying. The sublinear regret can be obtained when the stepsize is of the form <inline-formula><tex-math notation="LaTeX">1/\sqrt{t}</tex-math></inline-formula> and the objective functions are Lipschitz-continuous convex functions with Lipschitz gradients, and the variance of the noisy gradients is bounded. We also provide simulation results of the proposed algorithms on sensor networks to complement our theoretical analysis. Convex functions Stochastic processes Decentralized optimization Resource management Signal processing algorithms Linear programming Algorithm design and analysis pseudo-regret online optimization Optimization stochastic dual-averaging method Nedic, Angelia oth Raginsky, Maxim oth Enthalten in IEEE transactions on automatic control New York, NY : Inst., 1963 62(2017), 12, Seite 6407-6414 (DE-627)129601705 (DE-600)241443-0 (DE-576)015095320 0018-9286 nnns volume:62 year:2017 number:12 pages:6407-6414 http://dx.doi.org/10.1109/TAC.2017.2650563 Volltext http://ieeexplore.ieee.org/document/7811275 GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-MAT GBV_ILN_11 GBV_ILN_70 GBV_ILN_120 GBV_ILN_193 GBV_ILN_2014 GBV_ILN_2016 GBV_ILN_2333 GBV_ILN_4193 AR 62 2017 12 6407-6414 |
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10.1109/TAC.2017.2650563 doi PQ20171228 (DE-627)OLC1998666131 (DE-599)GBVOLC1998666131 (PRQ)c1067-b08b816e9097e30a84e5547743d2dd5924283aa297e5e45ee527280e64ff97430 (KEY)0005057120170000062001206407stochasticdualaveragingfordecentralizedonlineoptim DE-627 ger DE-627 rakwb eng 620 DNB Lee, Soomin verfasserin aut Stochastic Dual Averaging for Decentralized Online Optimization on Time-Varying Communication Graphs 2017 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier We consider a decentralized online convex optimization problem in a network of agents, where each agent controls only a coordinate (or a part) of the global decision vector. For such a problem, we propose two decentralized stochastic variants (<inline-formula><tex-math notation="LaTeX">\mathsf{SODA}\hbox{-}\mathsf{C}</tex-math> </inline-formula> and <inline-formula><tex-math notation="LaTeX">\mathsf{SODA}\hbox{-}\mathsf{PS}</tex-math> </inline-formula>) of Nesterov's dual averaging method <inline-formula><tex-math notation="LaTeX">(\mathsf{DA}) </tex-math></inline-formula>, where each agent only uses a coordinate of the noise-corrupted gradient in the dual-averaging step. We show that the expected regret bounds for both algorithms have sublinear growth of <inline-formula><tex-math notation="LaTeX">O(\sqrt{T})</tex-math></inline-formula>, with the time horizon <inline-formula><tex-math notation="LaTeX">T</tex-math></inline-formula>, in scenarios when the underlying communication topology is time-varying. The sublinear regret can be obtained when the stepsize is of the form <inline-formula><tex-math notation="LaTeX">1/\sqrt{t}</tex-math></inline-formula> and the objective functions are Lipschitz-continuous convex functions with Lipschitz gradients, and the variance of the noisy gradients is bounded. We also provide simulation results of the proposed algorithms on sensor networks to complement our theoretical analysis. Convex functions Stochastic processes Decentralized optimization Resource management Signal processing algorithms Linear programming Algorithm design and analysis pseudo-regret online optimization Optimization stochastic dual-averaging method Nedic, Angelia oth Raginsky, Maxim oth Enthalten in IEEE transactions on automatic control New York, NY : Inst., 1963 62(2017), 12, Seite 6407-6414 (DE-627)129601705 (DE-600)241443-0 (DE-576)015095320 0018-9286 nnns volume:62 year:2017 number:12 pages:6407-6414 http://dx.doi.org/10.1109/TAC.2017.2650563 Volltext http://ieeexplore.ieee.org/document/7811275 GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-MAT GBV_ILN_11 GBV_ILN_70 GBV_ILN_120 GBV_ILN_193 GBV_ILN_2014 GBV_ILN_2016 GBV_ILN_2333 GBV_ILN_4193 AR 62 2017 12 6407-6414 |
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10.1109/TAC.2017.2650563 doi PQ20171228 (DE-627)OLC1998666131 (DE-599)GBVOLC1998666131 (PRQ)c1067-b08b816e9097e30a84e5547743d2dd5924283aa297e5e45ee527280e64ff97430 (KEY)0005057120170000062001206407stochasticdualaveragingfordecentralizedonlineoptim DE-627 ger DE-627 rakwb eng 620 DNB Lee, Soomin verfasserin aut Stochastic Dual Averaging for Decentralized Online Optimization on Time-Varying Communication Graphs 2017 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier We consider a decentralized online convex optimization problem in a network of agents, where each agent controls only a coordinate (or a part) of the global decision vector. For such a problem, we propose two decentralized stochastic variants (<inline-formula><tex-math notation="LaTeX">\mathsf{SODA}\hbox{-}\mathsf{C}</tex-math> </inline-formula> and <inline-formula><tex-math notation="LaTeX">\mathsf{SODA}\hbox{-}\mathsf{PS}</tex-math> </inline-formula>) of Nesterov's dual averaging method <inline-formula><tex-math notation="LaTeX">(\mathsf{DA}) </tex-math></inline-formula>, where each agent only uses a coordinate of the noise-corrupted gradient in the dual-averaging step. We show that the expected regret bounds for both algorithms have sublinear growth of <inline-formula><tex-math notation="LaTeX">O(\sqrt{T})</tex-math></inline-formula>, with the time horizon <inline-formula><tex-math notation="LaTeX">T</tex-math></inline-formula>, in scenarios when the underlying communication topology is time-varying. The sublinear regret can be obtained when the stepsize is of the form <inline-formula><tex-math notation="LaTeX">1/\sqrt{t}</tex-math></inline-formula> and the objective functions are Lipschitz-continuous convex functions with Lipschitz gradients, and the variance of the noisy gradients is bounded. We also provide simulation results of the proposed algorithms on sensor networks to complement our theoretical analysis. Convex functions Stochastic processes Decentralized optimization Resource management Signal processing algorithms Linear programming Algorithm design and analysis pseudo-regret online optimization Optimization stochastic dual-averaging method Nedic, Angelia oth Raginsky, Maxim oth Enthalten in IEEE transactions on automatic control New York, NY : Inst., 1963 62(2017), 12, Seite 6407-6414 (DE-627)129601705 (DE-600)241443-0 (DE-576)015095320 0018-9286 nnns volume:62 year:2017 number:12 pages:6407-6414 http://dx.doi.org/10.1109/TAC.2017.2650563 Volltext http://ieeexplore.ieee.org/document/7811275 GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-MAT GBV_ILN_11 GBV_ILN_70 GBV_ILN_120 GBV_ILN_193 GBV_ILN_2014 GBV_ILN_2016 GBV_ILN_2333 GBV_ILN_4193 AR 62 2017 12 6407-6414 |
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10.1109/TAC.2017.2650563 doi PQ20171228 (DE-627)OLC1998666131 (DE-599)GBVOLC1998666131 (PRQ)c1067-b08b816e9097e30a84e5547743d2dd5924283aa297e5e45ee527280e64ff97430 (KEY)0005057120170000062001206407stochasticdualaveragingfordecentralizedonlineoptim DE-627 ger DE-627 rakwb eng 620 DNB Lee, Soomin verfasserin aut Stochastic Dual Averaging for Decentralized Online Optimization on Time-Varying Communication Graphs 2017 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier We consider a decentralized online convex optimization problem in a network of agents, where each agent controls only a coordinate (or a part) of the global decision vector. For such a problem, we propose two decentralized stochastic variants (<inline-formula><tex-math notation="LaTeX">\mathsf{SODA}\hbox{-}\mathsf{C}</tex-math> </inline-formula> and <inline-formula><tex-math notation="LaTeX">\mathsf{SODA}\hbox{-}\mathsf{PS}</tex-math> </inline-formula>) of Nesterov's dual averaging method <inline-formula><tex-math notation="LaTeX">(\mathsf{DA}) </tex-math></inline-formula>, where each agent only uses a coordinate of the noise-corrupted gradient in the dual-averaging step. We show that the expected regret bounds for both algorithms have sublinear growth of <inline-formula><tex-math notation="LaTeX">O(\sqrt{T})</tex-math></inline-formula>, with the time horizon <inline-formula><tex-math notation="LaTeX">T</tex-math></inline-formula>, in scenarios when the underlying communication topology is time-varying. The sublinear regret can be obtained when the stepsize is of the form <inline-formula><tex-math notation="LaTeX">1/\sqrt{t}</tex-math></inline-formula> and the objective functions are Lipschitz-continuous convex functions with Lipschitz gradients, and the variance of the noisy gradients is bounded. We also provide simulation results of the proposed algorithms on sensor networks to complement our theoretical analysis. Convex functions Stochastic processes Decentralized optimization Resource management Signal processing algorithms Linear programming Algorithm design and analysis pseudo-regret online optimization Optimization stochastic dual-averaging method Nedic, Angelia oth Raginsky, Maxim oth Enthalten in IEEE transactions on automatic control New York, NY : Inst., 1963 62(2017), 12, Seite 6407-6414 (DE-627)129601705 (DE-600)241443-0 (DE-576)015095320 0018-9286 nnns volume:62 year:2017 number:12 pages:6407-6414 http://dx.doi.org/10.1109/TAC.2017.2650563 Volltext http://ieeexplore.ieee.org/document/7811275 GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-MAT GBV_ILN_11 GBV_ILN_70 GBV_ILN_120 GBV_ILN_193 GBV_ILN_2014 GBV_ILN_2016 GBV_ILN_2333 GBV_ILN_4193 AR 62 2017 12 6407-6414 |
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10.1109/TAC.2017.2650563 doi PQ20171228 (DE-627)OLC1998666131 (DE-599)GBVOLC1998666131 (PRQ)c1067-b08b816e9097e30a84e5547743d2dd5924283aa297e5e45ee527280e64ff97430 (KEY)0005057120170000062001206407stochasticdualaveragingfordecentralizedonlineoptim DE-627 ger DE-627 rakwb eng 620 DNB Lee, Soomin verfasserin aut Stochastic Dual Averaging for Decentralized Online Optimization on Time-Varying Communication Graphs 2017 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier We consider a decentralized online convex optimization problem in a network of agents, where each agent controls only a coordinate (or a part) of the global decision vector. For such a problem, we propose two decentralized stochastic variants (<inline-formula><tex-math notation="LaTeX">\mathsf{SODA}\hbox{-}\mathsf{C}</tex-math> </inline-formula> and <inline-formula><tex-math notation="LaTeX">\mathsf{SODA}\hbox{-}\mathsf{PS}</tex-math> </inline-formula>) of Nesterov's dual averaging method <inline-formula><tex-math notation="LaTeX">(\mathsf{DA}) </tex-math></inline-formula>, where each agent only uses a coordinate of the noise-corrupted gradient in the dual-averaging step. We show that the expected regret bounds for both algorithms have sublinear growth of <inline-formula><tex-math notation="LaTeX">O(\sqrt{T})</tex-math></inline-formula>, with the time horizon <inline-formula><tex-math notation="LaTeX">T</tex-math></inline-formula>, in scenarios when the underlying communication topology is time-varying. The sublinear regret can be obtained when the stepsize is of the form <inline-formula><tex-math notation="LaTeX">1/\sqrt{t}</tex-math></inline-formula> and the objective functions are Lipschitz-continuous convex functions with Lipschitz gradients, and the variance of the noisy gradients is bounded. We also provide simulation results of the proposed algorithms on sensor networks to complement our theoretical analysis. Convex functions Stochastic processes Decentralized optimization Resource management Signal processing algorithms Linear programming Algorithm design and analysis pseudo-regret online optimization Optimization stochastic dual-averaging method Nedic, Angelia oth Raginsky, Maxim oth Enthalten in IEEE transactions on automatic control New York, NY : Inst., 1963 62(2017), 12, Seite 6407-6414 (DE-627)129601705 (DE-600)241443-0 (DE-576)015095320 0018-9286 nnns volume:62 year:2017 number:12 pages:6407-6414 http://dx.doi.org/10.1109/TAC.2017.2650563 Volltext http://ieeexplore.ieee.org/document/7811275 GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-MAT GBV_ILN_11 GBV_ILN_70 GBV_ILN_120 GBV_ILN_193 GBV_ILN_2014 GBV_ILN_2016 GBV_ILN_2333 GBV_ILN_4193 AR 62 2017 12 6407-6414 |
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Enthalten in IEEE transactions on automatic control 62(2017), 12, Seite 6407-6414 volume:62 year:2017 number:12 pages:6407-6414 |
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Enthalten in IEEE transactions on automatic control 62(2017), 12, Seite 6407-6414 volume:62 year:2017 number:12 pages:6407-6414 |
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Lee, Soomin @@aut@@ Nedic, Angelia @@oth@@ Raginsky, Maxim @@oth@@ |
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stochastic dual averaging for decentralized online optimization on time-varying communication graphs |
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Stochastic Dual Averaging for Decentralized Online Optimization on Time-Varying Communication Graphs |
| abstract |
We consider a decentralized online convex optimization problem in a network of agents, where each agent controls only a coordinate (or a part) of the global decision vector. For such a problem, we propose two decentralized stochastic variants (<inline-formula><tex-math notation="LaTeX">\mathsf{SODA}\hbox{-}\mathsf{C}</tex-math> </inline-formula> and <inline-formula><tex-math notation="LaTeX">\mathsf{SODA}\hbox{-}\mathsf{PS}</tex-math> </inline-formula>) of Nesterov's dual averaging method <inline-formula><tex-math notation="LaTeX">(\mathsf{DA}) </tex-math></inline-formula>, where each agent only uses a coordinate of the noise-corrupted gradient in the dual-averaging step. We show that the expected regret bounds for both algorithms have sublinear growth of <inline-formula><tex-math notation="LaTeX">O(\sqrt{T})</tex-math></inline-formula>, with the time horizon <inline-formula><tex-math notation="LaTeX">T</tex-math></inline-formula>, in scenarios when the underlying communication topology is time-varying. The sublinear regret can be obtained when the stepsize is of the form <inline-formula><tex-math notation="LaTeX">1/\sqrt{t}</tex-math></inline-formula> and the objective functions are Lipschitz-continuous convex functions with Lipschitz gradients, and the variance of the noisy gradients is bounded. We also provide simulation results of the proposed algorithms on sensor networks to complement our theoretical analysis. |
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We consider a decentralized online convex optimization problem in a network of agents, where each agent controls only a coordinate (or a part) of the global decision vector. For such a problem, we propose two decentralized stochastic variants (<inline-formula><tex-math notation="LaTeX">\mathsf{SODA}\hbox{-}\mathsf{C}</tex-math> </inline-formula> and <inline-formula><tex-math notation="LaTeX">\mathsf{SODA}\hbox{-}\mathsf{PS}</tex-math> </inline-formula>) of Nesterov's dual averaging method <inline-formula><tex-math notation="LaTeX">(\mathsf{DA}) </tex-math></inline-formula>, where each agent only uses a coordinate of the noise-corrupted gradient in the dual-averaging step. We show that the expected regret bounds for both algorithms have sublinear growth of <inline-formula><tex-math notation="LaTeX">O(\sqrt{T})</tex-math></inline-formula>, with the time horizon <inline-formula><tex-math notation="LaTeX">T</tex-math></inline-formula>, in scenarios when the underlying communication topology is time-varying. The sublinear regret can be obtained when the stepsize is of the form <inline-formula><tex-math notation="LaTeX">1/\sqrt{t}</tex-math></inline-formula> and the objective functions are Lipschitz-continuous convex functions with Lipschitz gradients, and the variance of the noisy gradients is bounded. We also provide simulation results of the proposed algorithms on sensor networks to complement our theoretical analysis. |
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We consider a decentralized online convex optimization problem in a network of agents, where each agent controls only a coordinate (or a part) of the global decision vector. For such a problem, we propose two decentralized stochastic variants (<inline-formula><tex-math notation="LaTeX">\mathsf{SODA}\hbox{-}\mathsf{C}</tex-math> </inline-formula> and <inline-formula><tex-math notation="LaTeX">\mathsf{SODA}\hbox{-}\mathsf{PS}</tex-math> </inline-formula>) of Nesterov's dual averaging method <inline-formula><tex-math notation="LaTeX">(\mathsf{DA}) </tex-math></inline-formula>, where each agent only uses a coordinate of the noise-corrupted gradient in the dual-averaging step. We show that the expected regret bounds for both algorithms have sublinear growth of <inline-formula><tex-math notation="LaTeX">O(\sqrt{T})</tex-math></inline-formula>, with the time horizon <inline-formula><tex-math notation="LaTeX">T</tex-math></inline-formula>, in scenarios when the underlying communication topology is time-varying. The sublinear regret can be obtained when the stepsize is of the form <inline-formula><tex-math notation="LaTeX">1/\sqrt{t}</tex-math></inline-formula> and the objective functions are Lipschitz-continuous convex functions with Lipschitz gradients, and the variance of the noisy gradients is bounded. We also provide simulation results of the proposed algorithms on sensor networks to complement our theoretical analysis. |
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Stochastic Dual Averaging for Decentralized Online Optimization on Time-Varying Communication Graphs |
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