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Stochastic programming

About: Stochastic programming is a research topic. Over the lifetime, 12343 publications have been published within this topic receiving 421049 citations.


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31 Jan 2014
TL;DR: The main idea presented here is that it is possible to decompose a complex decision making problem into a sequence of elementary decisions, where each decision of the sequence is solved using a (stochastic) multi-armed bandit (simple mathematical model for decision making in stochastic environments).
Abstract: This work covers several aspects of the optimism in the face of uncertainty principle applied to large scale optimization problems under finite numerical budget. The initial motivation for the research reported here originated from the empirical success of the so-called Monte-Carlo Tree Search method popularized in computer-go and further extended to many other games as well as optimization and planning problems. Our objective is to contribute to the development of theoretical foundations of the field by characterizing the complexity of the underlying optimization problems and designing efficient algorithms with performance guarantees. The main idea presented here is that it is possible to decompose a complex decision making problem (such as an optimization problem in a large search space) into a sequence of elementary decisions, where each decision of the sequence is solved using a (stochastic) multi-armed bandit (simple mathematical model for decision making in stochastic environments). This so-called hierarchical bandit approach (where the reward observed by a bandit in the hierarchy is itself the return of another bandit at a deeper level) possesses the nice feature of starting the exploration by a quasi-uniform sampling of the space and then focusing progressively on the most promising area, at different scales, according to the evaluations observed so far, and eventually performing a local search around the global optima of the function. The performance of the method is assessed in terms of the optimality of the returned solution as a function of the number of function evaluations. Our main contribution to the field of function optimization is a class of hierarchical optimistic algorithms designed for general search spaces (such as metric spaces, trees, graphs, Euclidean spaces, ...) with different algorithmic instantiations depending on whether the evaluations are noisy or noiseless and whether some measure of the ''smoothness'' of the function is known or unknown. The performance of the algorithms depend on the local behavior of the function around its global optima expressed in terms of the quantity of near-optimal states measured with some metric. If this local smoothness of the function is known then one can design very efficient optimization algorithms (with convergence rate independent of the space dimension), and when it is not known, we can build adaptive techniques that can, in some cases, perform almost as well as when it is known.

278 citations

Proceedings ArticleDOI
01 May 1998
TL;DR: It is shown that the fundamental problem of finding an optimal policy which maximizes the average performance level of a system, subject to a constraint on the power consumption, can be formulated as a stochastic optimization problem called policy optimization.
Abstract: Dynamic power management schemes (also called policies) can be used to control the power consumption levels of electronic systems, by setting their components in different states, each characterized by a performance level and a power consumption. In this paper, we describe power-managed systems using a finite-state, stochastic model. Furthermore, we show that the fundamental problem of finding an optimal policy which maximizes the average performance level of a system, subject to a constraint on the power consumption, can be formulated as a stochastic optimization problem called policy optimization. Policy optimization can be solved exactly in polynomial time (in the number of states of the model). We implemented a policy optimization tool and tested the quality of the optimal policies on a realistic case study.

278 citations

Journal ArticleDOI
01 Dec 1969-Tellus A
TL;DR: Stochastic dynamic prediction assumes the laws governing atmospheric behavior are entirely deterministic, but seeks solutions corresponding to probabilistic statements of the initial conditions, and assumes that the initial laws are deterministic as mentioned in this paper.
Abstract: Stochastic dynamic prediction assumes the laws governing atmospheric behavior are entirely deterministic, but seeks solutions corresponding to probabilistic statements of the initial conditions, th...

278 citations

Proceedings ArticleDOI
16 Jun 2012
TL;DR: The proposed method is the first to attempt and achieve the articulated motion tracking of two strongly interacting hands and employs Particle Swarm Optimization, an evolutionary, stochastic optimization method with the objective of finding the two-hands configuration that best explains observations provided by an RGB-D sensor.
Abstract: We propose a method that relies on markerless visual observations to track the full articulation of two hands that interact with each-other in a complex, unconstrained manner. We formulate this as an optimization problem whose 54-dimensional parameter space represents all possible configurations of two hands, each represented as a kinematic structure with 26 Degrees of Freedom (DoFs). To solve this problem, we employ Particle Swarm Optimization (PSO), an evolutionary, stochastic optimization method with the objective of finding the two-hands configuration that best explains observations provided by an RGB-D sensor. To the best of our knowledge, the proposed method is the first to attempt and achieve the articulated motion tracking of two strongly interacting hands. Extensive quantitative and qualitative experiments with simulated and real world image sequences demonstrate that an accurate and efficient solution of this problem is indeed feasible.

277 citations

Journal ArticleDOI
TL;DR: In this article, the authors proposed a distributionally robust optimization model for solving unit commitment (UC) problems considering volatile wind power generation, where the uncertainty of wind power is captured by an ambiguity set that defines a family of renewable power distributions, and the expected total cost under the worst-case distribution is minimized.
Abstract: This paper proposes a distributionally robust optimization model for solving unit commitment (UC) problems considering volatile wind power generation. The uncertainty of wind power is captured by an ambiguity set that defines a family of wind power distributions, and the expected total cost under the worst-case distribution is minimized. Compared with stochastic programming, this method may have less dependence on the data of exact probability distributions. It should also outperform the conventional robust optimization methods because some distribution information can be incorporated into the ambiguity sets to generate less conservative results. In this paper, the UC model is formulated based on the typical two-stage framework, where the UC decisions are determined in a here-and-now manner, and the economic dispatch decisions are assumed to be wait-and-see , made after the observation of wind power outcomes. For computational tractability, the wait-and-see decisions are addressed by linear decision rule approximation, assuming that the economic dispatch decisions affinely depend on uncertain parameters as well as auxiliary random variables introduced to describe distributional characteristics of wind power generation. It is shown in case studies that this decision rule model tends to provide a tight approximation to the original two-stage problem, and the performance of UC solutions may be greatly improved by incorporating information on wind power distributions into the robust model.

277 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
2023175
2022423
2021526
2020598
2019578
2018532