摘要 :
We extend the notion of globalized robustness to consider distributional information beyond the support of the ambiguous probability distribution. We propose the globalized distributionally robust counterpart that disallows any (r...
展开
We extend the notion of globalized robustness to consider distributional information beyond the support of the ambiguous probability distribution. We propose the globalized distributionally robust counterpart that disallows any (respectively, allows limited) constraint violation for distributions residing (respectively, not residing) in the ambiguity set. By varying its inputs, our proposal recovers several existing perceptions of parameter uncertainty. Focusing on the type 1 Wasserstein distance, we show that the globalized distributionally robust counterpart has an insightful interpretation in terms of shadow price of globalized robustness, and it can be seamlessly integrated with many popular optimization models under uncertainty without incurring any extra computational cost. Such computational attractiveness also holds for other ambiguity sets, including the ones based on probability metric, optimal transport, φ-divergences, or moment conditions, as well as the event-wise ambiguity set. Numerical studies on an adaptive network lot-sizing problem demonstrate the modeling flexibility of our proposal and its emphases on globalized robustness to constraint violation.
收起
摘要 :
The goal of robust optimization is to hedge against uncertainties: in most real-world applications, the specific problem instance depends on uncertain data and is hence not known beforehand. In this work we introduce a new two-sta...
展开
The goal of robust optimization is to hedge against uncertainties: in most real-world applications, the specific problem instance depends on uncertain data and is hence not known beforehand. In this work we introduce a new two-stage approach called recovery-to-optimality to handle uncertain optimization problems. Motivated by two-stage stochastic programming and in a similar spirit as the well-known approaches of adjustable robustness or recovery robustness, our new concept allows us to adapt a solution when the realized input scenario is revealed. Using a metric in the solution space measuring the recovery costs, we can evaluate the worst-case costs or the average costs of any solution. Our new concept recovery-to-optimality asks for a solution which can be recovered to an optimal solution with low recovery costs. We set up the robust counterpart (RecOpt) for this concept. However, our intention is to provide a practical approach that can easily be used to generate robust solutions for any application. Building on solution algorithms for the deterministic problem, and on algorithms from location theory, we propose a generic procedure which is able to generate solutions with low recovery costs. We point out properties of these solutions and analyze special cases in which the outcome of the procedure coincides with the optimal solutions to (RecOpt). In an experimental study, we apply our approach to linear programs, and to the problem of finding aperiodic train timetables. We compare it to other robustness concepts, and discuss their tradeoffs with respect to multiple evaluation criteria.
收起
摘要 :
This paper presents spatially robust far-field microphone beamformers and nullformers derived using the von Mises and von Mises-Fisher distributions to model the expected direction of arrival. Simple analytic expressions are prese...
展开
This paper presents spatially robust far-field microphone beamformers and nullformers derived using the von Mises and von Mises-Fisher distributions to model the expected direction of arrival. Simple analytic expressions are presented for 2D and 3D far-field correlation functions and used to design spatially robust beamformers and nullformers. It is demonstrated that the spatially robust beamformers show a modest improvement in tolerating uncertainty in the target direction of arrival without incurring a significant penalty in terms of SINR performance compared with the MVDR beamformer. In addition, the spatially robust formulation shows significantly improved numerical robustness, indicating improved ability in tolerating intrinsic array errors.
收起
摘要 :
In this paper we find verifiable regularity conditions to ensure that S-estimators of scale and regression and MM-estimators of regression are uniformly consistent and uniformly asymptotically normally distributed over contaminati...
展开
In this paper we find verifiable regularity conditions to ensure that S-estimators of scale and regression and MM-estimators of regression are uniformly consistent and uniformly asymptotically normally distributed over contamination neighbourhoods. Moreover, we show how to calculate the size of these neighbourhoods. In particular, we find that, for MM-estimators computed with Tukey's family of bisquare score functions, there is a trade-off between the size of these neighbourhoods and both the breakdown point of the S-estimators and the leverage of the contamination that is allowed in the neighbourhood. These results extend previous work of Salibian-Barrera and Zamar for location-scale to the linear regression model.
收起
摘要 :
In CT-RSA 2019, Geraud, Naccache and Rosie introduced the notion of robustness (ROB) for digital signature schemes to guarantee that the same signature and message pair cannot be valid under two different public keys. Their defini...
展开
In CT-RSA 2019, Geraud, Naccache and Rosie introduced the notion of robustness (ROB) for digital signature schemes to guarantee that the same signature and message pair cannot be valid under two different public keys. Their definition of complete ROB (CROB) can even support the ROB when the keys are malignantly generated. Motivated by the fact that the signature and the key could be illegally produced in some circumstances, we extended the ROB security one step further to guarantee that one valid signature cannot be modified to another valid signature under a different public key, which we call extreme robustness (EXROB). After analysing the relations between the EXROB security and existing ROB related definitions, we describe generic constructions to convert any digital signature scheme that is unforgeable into an EXROB secure one. Our hash-then-sign construction is very efficient, which only adds one hash calculation to the underlying digital signature scheme and does not increase the size of the signature generated by the underlying digital signature scheme. (C) 2020 Elsevier B.V. All rights reserved.
收起
摘要 :
This paper addresses the problem of analyzing and designing a robust controller for a missile (non-minimum phase plant). This study comprises three parts, namely, (ⅰ) designing the controller in the H~∞ mixed frame work (which s...
展开
This paper addresses the problem of analyzing and designing a robust controller for a missile (non-minimum phase plant). This study comprises three parts, namely, (ⅰ) designing the controller in the H~∞ mixed frame work (which satisfies the criteria of both robust performance and robust stability), (ⅱ) modification of the above controller design by making use of the theory of H~∞ parameter space method (which is a graphical interactive method), and (ⅲ) robust controller (which satisfies both time domain and frequency domain specifications in the controller parameter regon).
收起
摘要 :
In this paper, we propose a distribution-free model instead of considering a particular distribution for multiple objective games with incomplete information. We assume that each player does not know the exact value of the uncerta...
展开
In this paper, we propose a distribution-free model instead of considering a particular distribution for multiple objective games with incomplete information. We assume that each player does not know the exact value of the uncertain payoff parameters, but only knows that they belong to an uncertainty set. In our model, the players use a robust optimization approach for each of their objective to contend with payoff uncertainty. To formulate such a game, named "robust multiple objective games" here, we introduce three kinds of robust equilibrium under different preference structures. Then, by using a scalarization method and an existing result on the solutions for the generalized quasi-vector equilibrium problems, we obtain the existence of these robust equilibria. Finally, we give an example to illustrate our model and the existence theorems. Our results are new and fill the gap in the game theory literature.
收起
摘要 :
In this paper, the robust game model proposed by Aghassi and Bertsimas (Math Program Ser B 107:231-273,2006) for matrix games is extended to games with a broader class of payoff functions. This is a distribution-free model of inco...
展开
In this paper, the robust game model proposed by Aghassi and Bertsimas (Math Program Ser B 107:231-273,2006) for matrix games is extended to games with a broader class of payoff functions. This is a distribution-free model of incomplete information for finite games where players adopt a robust-optimization approach to contend with payoff uncertainty. They are called robust players and seek the maximum guaranteed payoff given the strategy of the others. Consistently with this decision criterion, a set of strategies is an equilibrium, robust-optimization equilibrium, if each player's strategy is a best response to the other player's strategies, under the worst-case scenarios. The aim of the paper is twofold. In the first part, we provide robust-optimization equilibrium's existence result for a quite general class of games and we prove that it exists a suitable value ∈ such that robust-optimization equilibria are a subset of ∈-Nash equilibria of the nominal version, i.e., without uncertainty, of the robust game. This provides a theoretical motivation for the robust approach, as it provides new insight and a rational agent motivation for ∈-Nash equilibrium. In the last part, we propose an application of the theory to a classical Cournot duopoly model which shows significant differences between the robust game and its nominal version.
收起
摘要 :
We consider the problem of robust performance analysis when some of the exogenous inputs acting on the system are assumed to be fixed and known, while others are unknown but bounded. In particular, we consider the case where perfo...
展开
We consider the problem of robust performance analysis when some of the exogenous inputs acting on the system are assumed to be fixed and known, while others are unknown but bounded. In particular, we consider the case where performance is measured by the l(oo) norm of the output signals, and the uncertainty on the nominal model is described by LTV perturbations of bounded l(oo)-induced norm. We first address the special case when all the exogenous inputs are fixed and known. We propose upper and lower bounds for the measure of robust performance. Two upper bounds are derived, which trade off accuracy versus computational expense. Both conditions are much less conservative than what one would obtain from assuming a worst-case exogenous input. We then generalize the conditions to the more general case, where both fixed and worst-case inputs act on the system. All these conditions are readily computable, and yield much less conservative results than one would obtain from applying standard worst-case analysis methods. Copyright paired right arrows 2005 John Wiley Sons, Ltd.
收起
摘要 :
Nearly all real-world engineering design optimisation problems have parameters with uncontrollable variations. Such variations can significantly degrade the performance of optimum design solutions in terms of their feasibility and...
展开
Nearly all real-world engineering design optimisation problems have parameters with uncontrollable variations. Such variations can significantly degrade the performance of optimum design solutions in terms of their feasibility and/or objective functions values, as obtained by multiobjective design optimisation methods. We present a deterministic feasibility and multiobjective optimisation approach, based on some worst case measures, for generating robustly non-dominated optimal solutions. Following this approach, for uncontrollable parameter variations, we can obtain a (1) feasibly robust design: for which no constraint is violated and (2) multiobjectively robust design: for which, with respect to a target and in a multiobjective sense, minimal distance between worst and best case points (or variability) and minimal distance of a worst case point from a target are obtained. We illustrate and verify the approach with a numerical and an engineering example.
收起
原文获取