A saddle point algorithm for networked online convex optimization

Koppel, Alec; Jakubiec, Felicia Y.; Ribeiro, Alejandro

doi:10.1109/icassp.2014.6855218

Cited by 48 publications

(116 citation statements)

References 7 publications

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“…The primal gradient step of the classical saddlepoint approach in [11], [13], [14] is tantamount to minimizing a first-order approximation of L t−1 (x, λ t ) at x = x t−1 plus a proximal term x − x t−1 2 /(2α). We call the primal-dual recursion (8) and (9) as a modified online saddle-point approach, since the primal update (8) is not an exact gradient step when the constraint g t (x) is nonlinear w.r.t.…”

Section: Remarkmentioning

confidence: 99%

“…x. However, when g t (x) is linear, (8) and (9) reduce to the approach in [11], [13], [14]. Similar to the primal update of OCO with long-term but timeinvariant constraints in [12], the minimization in (8) penalizes the exact constraint violation g t (x) instead of its first-order approximation, which improves control of constraint violations and facilitates performance analysis of MOSP.…”

Section: Remarkmentioning

confidence: 99%

“…To ensure feasibility of online decisions, the notion of dynamic fit is introduced to measure the accumulated violation of constraints; under time-invariant long-term constraints [11], [12], [14] or under time-varying constraints [13]. It is defined as…”

Section: B Performance and Feasibility Metricsmentioning

confidence: 99%

“…The regret bounds in [11] have been improved in [12] and [13]. Decentralized optimization with consensus constraints, as a special case of having longterm but time-invariant constraints, has been studied in [14]- [16]. Nevertheless, [11]- [16] do not deal with OCO under timevarying adversarial constraints.…”

Section: Introductionmentioning

confidence: 99%

“…To demonstrate the impact of these results, we further apply the proposed MOSP approach to a dynamic network resource arXiv:1701.03974v2 [cs.SY] 27 Jan 2017 [4] Static No No [5], [8], [17] Dynamic No No [6], [7] Dynamic No No [9], [10] Dynamic No No [11], [12], [14], [15] Static Yes No [16] Dynamic Yes No This work Dynamic Yes Yes allocation task, where online management of resources is sought without knowing future network states. Existing algorithms include first-and second-order methods in the dual domain [18]- [23], which are tailored for time-invariant deterministic formulations.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

An Online Convex Optimization Approach to Proactive Network Resource Allocation

Chen

Ling

Giannakis

2017

IEEE Trans. Signal Process.

202

212

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Abstract-Existing approaches to online convex optimization (OCO) make sequential one-slot-ahead decisions, which lead to (possibly adversarial) losses that drive subsequent decision iterates. Their performance is evaluated by the so-called regret that measures the difference of losses between the online solution and the best yet fixed overall solution in hindsight. The present paper deals with online convex optimization involving adversarial loss functions and adversarial constraints, where the constraints are revealed after making decisions, and can be tolerable to instantaneous violations but must be satisfied in the long term. Performance of an online algorithm in this setting is assessed by: i) the difference of its losses relative to the best dynamic solution with one-slot-ahead information of the loss function and the constraint (that is here termed dynamic regret); and, ii) the accumulated amount of constraint violations (that is here termed dynamic fit). In this context, a modified online saddle-point (MOSP) scheme is developed, and proved to simultaneously yield sub-linear dynamic regret and fit, provided that the accumulated variations of perslot minimizers and constraints are sub-linearly growing with time. MOSP is also applied to the dynamic network resource allocation task, and it is compared with the well-known stochastic dual gradient method. Under various scenarios, numerical experiments demonstrate the performance gain of MOSP relative to the stateof-the-art.

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Section: Remarkmentioning

confidence: 99%

Section: Remarkmentioning

confidence: 99%

Section: B Performance and Feasibility Metricsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

An Online Convex Optimization Approach to Proactive Network Resource Allocation

Chen

Ling

Giannakis

2017

IEEE Trans. Signal Process.

202

212

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Exploiting problem structure in optimization under uncertainty via online convex optimization

Ho-Nguyen

Kılınç-Karzan

2018

Math. Program.

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In this paper, we consider two paradigms that are developed to account for uncertainty in optimization models: robust optimization (RO) and joint estimation-optimization (JEO). We examine recent developments on efficient and scalable iterative first-order methods for these problems, and show that these iterative methods can be viewed through the lens of online convex optimization (OCO). The standard OCO framework has seen much success for its ability to handle decision-making in dynamic, uncertain, and even adversarial environments. Nevertheless, our applications of interest present further flexibility in OCO via three simple modifications to standard OCO assumptions: we introduce two new concepts of weighted regret and online saddle point problems and study the possibility of making lookahead (anticipatory) decisions. Our analyses demonstrate that these flexibilities introduced into the OCO framework have significant consequences whenever they are applicable. For example, in the strongly convex case, minimizing unweighted regret has a proven optimal bound of O(log(T )/T ), whereas we show that a bound of O(1/T ) is possible when we consider weighted regret. Similarly, for the smooth case, considering 1-lookahead decisions results in a O(1/T ) bound, compared to O(1/ √ T ) in the standard OCO setting. Consequently, these OCO tools are instrumental in exploiting structural properties of functions and results in improved convergence rates for RO and JEO. In certain cases, our results for RO and JEO match the best known or optimal rates in the corresponding problem classes without data uncertainty.

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Online Learning over a Decentralized Network Through ADMM

Ling

Ribeiro

2015

J. Oper. Res. Soc. China

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A saddle point algorithm for networked online convex optimization

Cited by 48 publications

References 7 publications

An Online Convex Optimization Approach to Proactive Network Resource Allocation

An Online Convex Optimization Approach to Proactive Network Resource Allocation

Exploiting problem structure in optimization under uncertainty via online convex optimization

Online Learning over a Decentralized Network Through ADMM

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