TY - JOUR
T1 - A virtual-queue-based algorithm for constrained online convex optimization with applications to data center resource allocation
AU - Cao, Xuanyu
AU - Zhang, Junshan
AU - Poor, H. Vincent
N1 - Funding Information:
Manuscript received September 30, 2017; revised February 27, 2018; accepted March 26, 2018. Date of publication April 16, 2018; date of current version July 27, 2018. This work was supported by the U.S. Army Research Office under Grant W911NF-16-1-0448. The guest editor coordinating the review of this manuscript and approving it for publication was Prof. Deepa Kundur. (Corresponding author: Xuanyu Cao.) X. Cao and H. Vincent Poor are with the Department of Electrical Engineering, Princeton University, Princeton, NJ 08544 USA (e-mail:, x.cao@ princeton.edu; poor@princeton.edu).
Publisher Copyright:
© 2018 IEEE.
PY - 2018/8
Y1 - 2018/8
N2 - In this paper, online convex optimization (OCO) problems with time-varying objective and constraint functions are studied from the perspective of an agent who takes actions in real time. Information about the current objective and constraint functions is revealed only after the corresponding action is already chosen. Inspired by a fast converging algorithm for time-invariant optimization in the very recent work [1], we develop a novel online algorithm based on virtual queues for constrained OCO. Optimal points of the dynamic optimization problems with full knowledge of the current objective and constraint functions are used as a dynamic benchmark sequence. Upper bounds on the regrets with respect to the dynamic benchmark and the constraint violations are derived for the presented algorithm in terms of the temporal variations of the underlying dynamic optimization problems. It is observed that the proposed algorithm possesses sublinear regret and sublinear constraint violations, as long as the temporal variations of the optimization problems are sublinear, i.e., the objective and constraint functions do not vary too drastically across time. The performance bounds of the proposed algorithm are superior to those of the state-of-the-art OCO method in most scenarios. Besides, different from the saddle point methods widely used in constrained OCO, the stepsize of the proposed algorithm does not rely on the total time horizon, which may be unknown in practice. Finally, the algorithm is applied to a dynamic resource allocation problem in data center networks. Numerical experiments are conducted to corroborate the merit of the developed algorithm and its advantage over the state-of-the-art.
AB - In this paper, online convex optimization (OCO) problems with time-varying objective and constraint functions are studied from the perspective of an agent who takes actions in real time. Information about the current objective and constraint functions is revealed only after the corresponding action is already chosen. Inspired by a fast converging algorithm for time-invariant optimization in the very recent work [1], we develop a novel online algorithm based on virtual queues for constrained OCO. Optimal points of the dynamic optimization problems with full knowledge of the current objective and constraint functions are used as a dynamic benchmark sequence. Upper bounds on the regrets with respect to the dynamic benchmark and the constraint violations are derived for the presented algorithm in terms of the temporal variations of the underlying dynamic optimization problems. It is observed that the proposed algorithm possesses sublinear regret and sublinear constraint violations, as long as the temporal variations of the optimization problems are sublinear, i.e., the objective and constraint functions do not vary too drastically across time. The performance bounds of the proposed algorithm are superior to those of the state-of-the-art OCO method in most scenarios. Besides, different from the saddle point methods widely used in constrained OCO, the stepsize of the proposed algorithm does not rely on the total time horizon, which may be unknown in practice. Finally, the algorithm is applied to a dynamic resource allocation problem in data center networks. Numerical experiments are conducted to corroborate the merit of the developed algorithm and its advantage over the state-of-the-art.
KW - Online convex optimization
KW - constrained optimization
KW - data centers
KW - dynamic resource allocation
KW - sequential decision making
KW - virtual queues
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U2 - 10.1109/JSTSP.2018.2827302
DO - 10.1109/JSTSP.2018.2827302
M3 - Article
AN - SCOPUS:85045674683
SN - 1932-4553
VL - 12
SP - 703
EP - 716
JO - IEEE Journal on Selected Topics in Signal Processing
JF - IEEE Journal on Selected Topics in Signal Processing
IS - 4
M1 - 8338087
ER -