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99
Distributionally Robust Optimization under Moment Uncertainty with Application to DataDriven Problems
"... Stochastic programs can effectively describe the decisionmaking problem in an uncertain environment. Unfortunately, such programs are often computationally demanding to solve. In addition, their solutions can be misleading when there is ambiguity in the choice of a distribution for the random param ..."
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Cited by 53 (4 self)
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Stochastic programs can effectively describe the decisionmaking problem in an uncertain environment. Unfortunately, such programs are often computationally demanding to solve. In addition, their solutions can be misleading when there is ambiguity in the choice of a distribution for the random parameters. In this paper, we propose a model describing one’s uncertainty in both the distribution’s form (discrete, Gaussian, exponential, etc.) and moments (mean and covariance). We demonstrate that for a wide range of cost functions the associated distributionally robust stochastic program can be solved efficiently. Furthermore, by deriving new confidence regions for the mean and covariance of a random vector, we provide probabilistic arguments for using our model in problems that rely heavily on historical data. This is confirmed in a practical example of portfolio selection, where our framework leads to better performing policies on the “true” distribution underlying the daily return of assets.
Cuttingset methods for robust convex optimization with pessimizing oracles
 DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING, UNIVERSITY OF CALIFORNIA, SAN DIEGO. FROM
, 2011
"... We consider a general worstcase robust convex optimization problem, with arbitrary dependence on the uncertain parameters, which are assumed to lie in some given set of possible values. We describe a general method for solving such a problem, which alternates between optimization and worstcase ana ..."
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Cited by 17 (5 self)
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We consider a general worstcase robust convex optimization problem, with arbitrary dependence on the uncertain parameters, which are assumed to lie in some given set of possible values. We describe a general method for solving such a problem, which alternates between optimization and worstcase analysis. With exact worstcase analysis, the method is shown to converge to a robust optimal point. With approximate worstcase analysis, which is the best we can do in many practical cases, the method seems to work very well in practice, subject to the errors in our worstcase analysis. We give variations on the basic method that can give enhanced convergence, reduce data storage, or improve other algorithm properties. Numerical simulations suggest that the method finds a quite robust solution within a few tens of steps; using warmstart techniques in the optimization steps reduces the overall effort to a modest multiple of solving a nominal problem, ignoring the parameter variation. The method is illustrated with several application examples.
Robust power allocation for energyefficient locationaware networks
 IEEE/ACM Trans. Netw
"... Abstract—In wireless locationaware networks, mobile nodes (agents) typically obtain their positions using the range measurements to the nodes with known positions. Transmit power allocation not only affects network lifetime and throughput, but also determines localization accuracy. In this paper, ..."
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Cited by 11 (4 self)
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Abstract—In wireless locationaware networks, mobile nodes (agents) typically obtain their positions using the range measurements to the nodes with known positions. Transmit power allocation not only affects network lifetime and throughput, but also determines localization accuracy. In this paper, we present an optimization framework for robust power allocation in network localization with imperfect knowledge of network parameters. In particular, we formulate power allocation problems to minimize localization errors for a given power budget and show that such formulations can be solved via conic programming. Moreover, we design a distributed power allocation algorithm that allows parallel computation among agents. The simulation results show that the proposed schemes significantly outperform uniform power allocation, and the robust schemes outperform their nonrobust counterparts when the network parameters are subject to uncertainty. Index Terms—Localization, resource allocation, robust optimization, secondorder conic programming (SOCP), semidefinite programming (SDP), wireless networks. I.
On the Power of Robust Solutions in TwoStage Stochastic and Adaptive Optimization Problems
"... informs doi 10.1287/moor.1090.0440 ..."
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Power optimization for network localization
 IEEE/ACM Trans. on Networking
, 2014
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A Geometric Characterization of the Power of Finite Adaptability in Multistage Stochastic and Adaptive Optimization
"... In this paper, we show a significant role that geometric properties of uncertainty sets, such as symmetry, play in determining the power of robust and finitely adaptable solutions in multistage stochastic and adaptive optimization problems. We consider a fairly general class of multistage mixed in ..."
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Cited by 8 (5 self)
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In this paper, we show a significant role that geometric properties of uncertainty sets, such as symmetry, play in determining the power of robust and finitely adaptable solutions in multistage stochastic and adaptive optimization problems. We consider a fairly general class of multistage mixed integer stochastic and adaptive optimization problems and propose a good approximate solution policy with performance guarantees that depend on the geometric properties of the uncertainty sets. In particular, we show that a class of finitely adaptable solutions is a good approximation for both the multistage stochastic as well as the adaptive optimization problem. A finitely adaptable solution generalizes the notion of a static robust solution and specifies a small set of solutions for each stage and the solution policy implements the best solution from the given set depending on the realization of the uncertain parameters in past stages. Therefore, it is a tractable approximation to a fullyadaptable solution for the multistage problems. To the best of our knowledge, these are the first approximation results for the multistage problem in such generality. Moreover, the results and the proof techniques are quite general and also extend to include important constraints such as integrality and linear conic constraints.
Risk Sensitivity of Price of Anarchy under Uncertainty
, 2013
"... In algorithmic game theory, the price of anarchy framework studies efficiency loss in decentralized environments. In optimization and decision theory, the price of robustness framework explores the tradeoffs between optimality and robustness in the case of single agent decision making under uncertai ..."
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Cited by 6 (1 self)
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In algorithmic game theory, the price of anarchy framework studies efficiency loss in decentralized environments. In optimization and decision theory, the price of robustness framework explores the tradeoffs between optimality and robustness in the case of single agent decision making under uncertainty. We establish a connection between the two that provides a novel analytic framework for proving tight performance guarantees for distributed systems in uncertain environments. We present applications of this framework to novel variants of atomic congestion games with uncertain costs, for which we provide tight performance bounds under a wide range of risk attitudes. Our results establish that the individual’s attitude towards uncertainty has a critical effect on system performance and should therefore be a subject of close and systematic investigation.
Addressing Scalability and Robustness in Security Games with Multiple Boundedly Rational Adversaries
"... Abstract. Boundedly rational human adversaries pose a serious challenge to security because they deviate from the classical assumption of perfect rationality. An emerging trend in security game research addresses this challenge by using behavioral models such as quantal response (QR) and subjecti ..."
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Cited by 5 (2 self)
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Abstract. Boundedly rational human adversaries pose a serious challenge to security because they deviate from the classical assumption of perfect rationality. An emerging trend in security game research addresses this challenge by using behavioral models such as quantal response (QR) and subjective utility quantal response (SUQR). These models improve the quality of the defender’s strategy by more accurately modeling the decisions made by real human adversaries. Work on incorporating human behavioral models into security games has typically followed two threads. The first thread, scalability, seeks to develop efficient algorithms to design patrols for largescale domains that protect against a single adversary. However, this thread cannot handle the common situation of multiple adversary types with heterogeneous behavioral models. Having multiple adversary types introduces considerable uncertainty into the defender’s planning problem. The second thread, robustness, uses either Bayesian or maximin approaches to handle this uncertainty caused
Optimal stochastic coordinated beamforming with compressive CSI acquisition for CloudRAN (longer version with detailed proofs),” arXiv preprint arXiv:1312.0363
, 2013
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Tractable stochastic analysis in high dimensions via robust optimization
 MATH. PROGRAM., SER. B
, 2012
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