This paper is concerned with an online distributed convex-constrained optimization prob-lem over a multi-agent network, where the limited network bandwidth and potential feed-back delay caused by network communication...
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This paper is concerned with an online distributed convex-constrained optimization prob-lem over a multi-agent network, where the limited network bandwidth and potential feed-back delay caused by network communication are considered. To cope with the limited network bandwidth, an event-triggered communication scheme is introduced in informa-tion exchange. Then, based on the delayed (i.e., single-point and two-point) bandit feed-back, two event-triggered distributed online convex optimization algorithms are developed by utilizing the Bregman divergence in the projection step. Meanwhile, the convergence of the two developed algorithms is analyzed according to the provided static regret bounds achieved by the algorithm. The obtained results show that a sublinear static regret with respect to the time horizon T can be ensured if the triggering threshold gradually ap-proaches zero. In this case, the corresponding order of the regret bounds is also deter-mined by choosing suitable triggering thresholds. Finally, a distributed online regularized linear regression problem is provided as an example to illustrate the effectiveness of the proposed two algorithms. (c) 2023 Elsevier Inc. All rights reserved.
This paper is concerned with the constrained distributed multi-agent convex optimization problem over a timevarying *** assume that the bit rate of the considered communication is limited,such that a uniform quantizer...
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This paper is concerned with the constrained distributed multi-agent convex optimization problem over a timevarying *** assume that the bit rate of the considered communication is limited,such that a uniform quantizer is applied in the process of exchanging information over the multi-agent *** a quantizer-based distributed mirrordescent（QDMD） algorithm,which utilizes the Bregman divergence as the distance-measuring function,is developed for such optimization *** convergence result of the developed algorithm is also *** choosing the iteration step-size ■ and quantization interval v_t/t=λ/t with a prescribed parameter A,it is shown that the convergence rate of the QDMD algorithm can achieve ■,where T is the number of iterations.
This paper aims to present improvable and computable approximation approaches for solving the two-stage robust optimization problem, which arises from various applications such as optimal energy management and product...
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This paper aims to present improvable and computable approximation approaches for solving the two-stage robust optimization problem, which arises from various applications such as optimal energy management and production planning. Based on sampling finite number scenarios of uncertainty, we can obtain a lower bound approximation and show that the corresponding solution is at least -level feasible. Moreover, piecewise linear decision rules (PLDRs) are also introduced to improve the upper bound that obtained by the widely-used linear decision rule. Furthermore, we show that both the lower bound and upper bound approximation problems can be reformulated into solvable saddle point problems and consequently be solved by the mirrordescent method.
Stochastic optimization is a fundamental problem that finds applications in many areas including biological and cognitive sciences. The classical stochastic approximation algorithm for iterative stochastic optimizatio...
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ISBN:
(纸本)9781510601123
Stochastic optimization is a fundamental problem that finds applications in many areas including biological and cognitive sciences. The classical stochastic approximation algorithm for iterative stochastic optimization requires gradient information of the sample object function that is typically difficult to obtain in practice. Recently there has been renewed interests in derivative free approaches to stochastic optimization. In this paper, we examine the rates of convergence for the Kiefer-Wolfowitz algorithm and the mirror descent algorithm, under various updating schemes using finite differences as gradient approximations. The analysis is carried out under a general framework covering a wide range of updating scenarios. It is shown that the convergence of these algorithms can be accelerated by controlling the implementation of the finite differences.
We generalize stochastic subgradient descent methods to situations in which we do not receive independent samples from the distribution over which we optimize, instead receiving samples coupled over time. We show that...
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We generalize stochastic subgradient descent methods to situations in which we do not receive independent samples from the distribution over which we optimize, instead receiving samples coupled over time. We show that as long as the source of randomness is suitably ergodic it converges quickly enough to a stationary distribution-the method enjoys strong convergence guarantees, both in expectation and with high probability. This result has implications for stochastic optimization in high-dimensional spaces, peer-to-peer distributed optimization schemes, decision problems with dependent data, and stochastic optimization problems over combinatorial spaces.
The main goal of this paper is to develop accuracy estimates for stochastic programming problems by employing stochastic approximation (SA) type algorithms. To this end we show that while running a mirrordescent Stoc...
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The main goal of this paper is to develop accuracy estimates for stochastic programming problems by employing stochastic approximation (SA) type algorithms. To this end we show that while running a mirrordescent Stochastic Approximation procedure one can compute, with a small additional effort, lower and upper statistical bounds for the optimal objective value. We demonstrate that for a certain class of convex stochastic programs these bounds are comparable in quality with similar bounds computed by the sample average approximation method, while their computational cost is considerably smaller.
In this paper we consider optimization problems where the objective function is given in a form of the expectation. A basic difficulty of solving such stochastic optimization problems is that the involved multidimensi...
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In this paper we consider optimization problems where the objective function is given in a form of the expectation. A basic difficulty of solving such stochastic optimization problems is that the involved multidimensional integrals (expectations) cannot be computed with high accuracy. The aim of this paper is to compare two computational approaches based on Monte Carlo sampling techniques, namely, the stochastic approximation (SA) and the sample average approximation (SAA) methods. Both approaches, the SA and SAA methods, have a long history. Current opinion is that the SAA method can efficiently use a specific (say, linear) structure of the considered problem, while the SA approach is a crude subgradient method, which often performs poorly in practice. We intend to demonstrate that a properly modified SA approach can be competitive and even significantly outperform the SAA method for a certain class of convex stochastic problems. We extend the analysis to the case of convex-concave stochastic saddle point problems and present (in our opinion highly encouraging) results of numerical experiments.
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