Distributed Online Optimization With Long-Term Constraints

In this article, we consider distributed online convex optimization problems, where the distributed system consists of various computing units connected through a time-varying communication graph. In each time step, each computing unit selects a constrained vector, experiences a loss equal to an arb...

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Vydané v:IEEE transactions on automatic control Ročník 67; číslo 3; s. 1089 - 1104
Hlavní autori: Yuan, Deming, Proutiere, Alexandre, Shi, Guodong
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: New York IEEE 01.03.2022
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Predmet:
Absolute constraint violation
Algorithms
Communication graphs
Computational geometry
Computer networks
Constraint violation
Constraints
Convex functions
Convex optimization
Convexity
Cumulative constraints
Decentralized algorithms
Distributed algorithms
Distributed computer systems
Distributed database systems
Distributed online convex optimization
distributed online convex optimization (DOCO)
Distributed systems
Functions
long-term constraints
longterm constraints
one-point bandit feedback
Online convex optimizations
Online optimization
Optimization
regret
Robots
State-of-the-art algorithms
Time-varying systems
Unsolicited e-mail
Upper bound
Upper bounds
ISSN:0018-9286, 1558-2523, 1558-2523
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Shrnutí:In this article, we consider distributed online convex optimization problems, where the distributed system consists of various computing units connected through a time-varying communication graph. In each time step, each computing unit selects a constrained vector, experiences a loss equal to an arbitrary convex function evaluated at this vector, and may communicate to its neighbors in the graph. The objective is to minimize the system-wide loss accumulated over time. We propose a decentralized algorithm with regret and cumulative constraint violation in <inline-formula><tex-math notation="LaTeX">{\mathcal O}(T^{\max \lbrace c,1-c\rbrace })</tex-math></inline-formula> and <inline-formula><tex-math notation="LaTeX">{\mathcal O}(T^{1-c/2})</tex-math></inline-formula>, respectively, for any <inline-formula><tex-math notation="LaTeX">c\in (0,1)</tex-math></inline-formula>, where <inline-formula><tex-math notation="LaTeX">T</tex-math></inline-formula> is the time horizon. When the loss functions are strongly convex, we establish improved regret and constraint violation upper bounds in <inline-formula><tex-math notation="LaTeX">{\mathcal O}(\log (T))</tex-math></inline-formula> and <inline-formula><tex-math notation="LaTeX">{\mathcal O}(\sqrt{T\log (T)})</tex-math></inline-formula>. These regret scalings match those obtained by state-of-the-art algorithms and fundamental limits in the corresponding centralized online optimization problem (for both convex and strongly convex loss functions). In the case of bandit feedback, the proposed algorithms achieve a regret and constraint violation in <inline-formula><tex-math notation="LaTeX">{\mathcal O}(T^{\max \lbrace c,1-c/3 \rbrace })</tex-math></inline-formula> and <inline-formula><tex-math notation="LaTeX">{\mathcal O}(T^{1-c/2})</tex-math></inline-formula> for any <inline-formula><tex-math notation="LaTeX">c\in (0,1)</tex-math></inline-formula>. We numerically illustrate the performance of our algorithms for the particular case of distributed online regularized linear regression problems on synthetic and real data.
Bibliografia:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:0018-9286
1558-2523
1558-2523
DOI:10.1109/TAC.2021.3057601