11 results on '"Kuhn, Daniel"'
Search Results
2. The decision rule approach to optimization under uncertainty: methodology and applications
- Author
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Georghiou, Angelos, Kuhn, Daniel, Wiesemann, Wolfram, Engineering & Physical Science Research Council (E, and Georghiou, Angelos [0000-0003-4490-4020]
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Mathematical optimization ,Operations Research ,POWER ,0211 other engineering and technologies ,Social Sciences ,Stochastic programming ,02 engineering and technology ,Management Information Systems ,FACILITY LOCATION ,DESIGN ,DUALITY ,0102 Applied Mathematics ,021108 energy ,Mathematics ,021103 operations research ,FINITE ADAPTABILITY ,Stochastic process ,business.industry ,0103 Numerical and Computational Mathematics ,Feasible region ,Robust optimization ,Decision rule ,Social Sciences, Mathematical Methods ,Decision problem ,Partition (database) ,ADJUSTABLE ROBUST OPTIMIZATION ,1503 Business and Management ,Decision rules ,Artificial intelligence ,business ,Optimization under uncertainty ,Mathematical Methods In Social Sciences ,Information Systems ,Curse of dimensionality ,GENERATION - Abstract
Dynamic decision-making under uncertainty has a long and distinguished history in operations research. Due to the curse of dimensionality, solution schemes that naïvely partition or discretize the support of the random problem parameters are limited to small and medium-sized problems, or they require restrictive modeling assumptions (e.g., absence of recourse actions). In the last few decades, several solution techniques have been proposed that aim to alleviate the curse of dimensionality. Amongst these is the decision rule approach, which faithfully models the random process and instead approximates the feasible region of the decision problem. In this paper, we survey the major theoretical findings relating to this approach, and we investigate its potential in two applications areas. 16 4 545 576
- Published
- 2018
3. Data-driven distributionally robust optimization using the Wasserstein metric: performance guarantees and tractable reformulations.
- Author
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Mohajerin Esfahani, Peyman and Kuhn, Daniel
- Subjects
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ROBUST optimization , *MATHEMATICAL optimization , *MATHEMATICAL reformulation , *PROBABILITY theory , *CONVEX programming - Abstract
We consider stochastic programs where the distribution of the uncertain parameters is only observable through a finite training dataset. Using the Wasserstein metric, we construct a ball in the space of (multivariate and non-discrete) probability distributions centered at the uniform distribution on the training samples, and we seek decisions that perform best in view of the worst-case distribution within this Wasserstein ball. The state-of-the-art methods for solving the resulting distributionally robust optimization problems rely on global optimization techniques, which quickly become computationally excruciating. In this paper we demonstrate that, under mild assumptions, the distributionally robust optimization problems over Wasserstein balls can in fact be reformulated as finite convex programs—in many interesting cases even as tractable linear programs. Leveraging recent measure concentration results, we also show that their solutions enjoy powerful finite-sample performance guarantees. Our theoretical results are exemplified in mean-risk portfolio optimization as well as uncertainty quantification. [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
- View/download PDF
4. Conic Programming Reformulations of Two-Stage Distributionally Robust Linear Programs over Wasserstein Balls.
- Author
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Hanasusanto, Grani A. and Kuhn, Daniel
- Subjects
MATHEMATICAL optimization ,ROBUST optimization ,LINEAR programming ,INDUSTRIAL efficiency ,DECISION making - Abstract
Adaptive robust optimization problems are usually solved approximately by restricting the adaptive decisions to simple parametric decision rules. However, the corresponding approximation error can be substantial. In this paper we show that two-stage robust and distributionally robust linear programs can often be reformulated exactly as conic programs that scale polynomially with the problem dimensions. Specifically, when the ambiguity set constitutes a 2-Wasserstein ball centered at a discrete distribution, the distributionally robust linear program is equivalent to a copositive program (if the problem has complete recourse) or can be approximated arbitrarily closely by a sequence of copositive programs (if the problem has sufficiently expensive recourse). These results directly extend to the classical robust setting and motivate strong tractable approximations of two-stage problems based on semidefinite approximations of the copositive cone. We also demonstrate that the two-stage distributionally robust optimization problem is equivalent to a tractable linear program when the ambiguity set constitutes a 1-Wasserstein ball centered at a discrete distribution and there are no support constraints. [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
- View/download PDF
5. Data-driven inverse optimization with imperfect information.
- Author
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Mohajerin Esfahani, Peyman, Shafieezadeh-Abadeh, Soroosh, Hanasusanto, Grani A., and Kuhn, Daniel
- Subjects
INVERSE problems ,MATHEMATICAL optimization ,LIPSCHITZ spaces ,ARTIFICIAL intelligence ,MATHEMATICAL analysis - Abstract
In data-driven inverse optimization an observer aims to learn the preferences of an agent who solves a parametric optimization problem depending on an exogenous signal. Thus, the observer seeks the agent's objective function that best explains a historical sequence of signals and corresponding optimal actions. We focus here on situations where the observer has imperfect information, that is, where the agent's true objective function is not contained in the search space of candidate objectives, where the agent suffers from bounded rationality or implementation errors, or where the observed signal-response pairs are corrupted by measurement noise. We formalize this inverse optimization problem as a distributionally robust program minimizing the worst-case risk that the predicted decision (i.e., the decision implied by a particular candidate objective) differs from the agent's actual response to a random signal. We show that our framework offers rigorous out-of-sample guarantees for different loss functions used to measure prediction errors and that the emerging inverse optimization problems can be exactly reformulated as (or safely approximated by) tractable convex programs when a new suboptimality loss function is used. We show through extensive numerical tests that the proposed distributionally robust approach to inverse optimization attains often better out-of-sample performance than the state-of-the-art approaches. [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
- View/download PDF
6. Robust Growth-Optimal Portfolios.
- Author
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Rujeerapaiboon, Napat, Kuhn, Daniel, and Wiesemann, Wolfram
- Subjects
PORTFOLIO management (Investments) ,MATHEMATICAL optimization ,RATE of return ,INVESTMENTS ,FINANCIAL planners - Abstract
The growth-optimal portfolio is designed to have maximum expected log return over the next rebalancing period. Thus, it can be computed with relative ease by solving a static optimization problem. The growth-optimal portfolio has sparked fascination among finance professionals and researchers because it can be shown to outperform any other portfolio with probability 1 in the long run. In the short run, however, it is notoriously volatile. Moreover, its computation requires precise knowledge of the asset return distribution, which is not directly observable but must be inferred from sparse data. By using methods from distributionally robust optimization, we design fixed-mix strategies that offer similar performance guarantees as the growth-optimal portfolio but for a finite investment horizon and for a whole family of distributions that share the same first- and second-order moments. We demonstrate that the resulting robust growth-optimal portfolios can be computed efficiently by solving a tractable conic program whose size is independent of the length of the investment horizon. Simulated and empirical backtests show that the robust growth-optimal portfolios are competitive with the classical growth-optimal portfolio across most realistic investment horizons and for an overwhelming majority of contaminated return distributions. This paper was accepted by Yinyu Ye, optimization. [ABSTRACT FROM AUTHOR]
- Published
- 2016
- Full Text
- View/download PDF
7. Distributionally Robust Convex Optimization.
- Author
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Wiesemann, Wolfram, Kuhn, Daniel, and Melvyn Sim
- Subjects
ROBUST convex optimization ,DECISION making ,UNCERTAINTY (Information theory) ,MATHEMATICAL optimization ,PROBABILITY theory ,ROBUST optimization - Abstract
Distributionally robust optimization is a paradigm for decision making under uncertainty where the uncertain problem data are governed by a probability distribution that is itself subject to uncertainty. The distribution is then assumed to belong to an ambiguity set comprising all distributions that are compatible with the decision maker's prior information. In this paper, we propose a unifying framework for modeling and solving distributionally robust optimization problems. We introduce standardized ambiguity sets that contain all distributions with prescribed conic representable confidence sets and with mean values residing on an affine manifold. These ambiguity sets are highly expressive and encompass many ambiguity sets from the recent literature as special cases. They also allow us to characterize distributional families in terms of several classical and/or robust statistical indicators that have not yet been studied in the context of robust optimization. We determine conditions under which distributionally robust optimization problems based on our standardized ambiguity sets are computationally tractable. We also provide tractable conservative approximations for problems that violate these conditions. [ABSTRACT FROM AUTHOR]
- Published
- 2014
- Full Text
- View/download PDF
8. Distributionally robust joint chance constraints with second-order moment information.
- Author
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Zymler, Steve, Kuhn, Daniel, and Rustem, Berç
- Subjects
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SEMIDEFINITE programming , *APPROXIMATION theory , *PARAMETERS (Statistics) , *MATHEMATICAL proofs , *QUADRATIC fields , *NUMERICAL analysis , *MATHEMATICAL optimization , *MATHEMATICAL sequences - Abstract
We develop tractable semidefinite programming based approximations for distributionally robust individual and joint chance constraints, assuming that only the first- and second-order moments as well as the support of the uncertain parameters are given. It is known that robust chance constraints can be conservatively approximated by Worst-Case Conditional Value-at-Risk (CVaR) constraints. We first prove that this approximation is exact for robust individual chance constraints with concave or (not necessarily concave) quadratic constraint functions, and we demonstrate that the Worst-Case CVaR can be computed efficiently for these classes of constraint functions. Next, we study the Worst-Case CVaR approximation for joint chance constraints. This approximation affords intuitive dual interpretations and is provably tighter than two popular benchmark approximations. The tightness depends on a set of scaling parameters, which can be tuned via a sequential convex optimization algorithm. We show that the approximation becomes essentially exact when the scaling parameters are chosen optimally and that the Worst-Case CVaR can be evaluated efficiently if the scaling parameters are kept constant. We evaluate our joint chance constraint approximation in the context of a dynamic water reservoir control problem and numerically demonstrate its superiority over the two benchmark approximations. [ABSTRACT FROM AUTHOR]
- Published
- 2013
- Full Text
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9. An Information-Based Approximation Scheme for Stochastic Optimization Problems in Continuous Time.
- Author
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Kuhn, Daniel
- Subjects
MATHEMATICAL optimization ,STOCHASTIC processes ,MATHEMATICAL bounds ,VECTORS (Calculus) ,OPERATIONS research - Abstract
Dynamic stochastic optimization problems with a large (possibly infinite) number of decision stages and high-dimensional state vectors are inherently difficult to solve. In fact, scenario tree-based algorithms are unsuitable for problems with many stages, while dynamic programming-type techniques are unsuitable for problems with many state variables. This paper proposes a stage aggregation scheme for stochastic optimization problems in continuous time, thus having an extremely large (i.e., uncountable) number of decision stages. By perturbing the underlying data and information processes, we construct two approximate problems that provide bounds on the optimal value of the original problem. Moreover, we prove that the gap between the bounds converges to zero as the stage aggregation is refined. If massive aggregation of stages is possible without sacrificing too much accuracy, the aggregate approximate problems can be addressed by means of scenario tree-based methods. The suggested approach applies to problems that exhibit randomness in the objective and the constraints, while the constraint functions are required to be additively separable in the decision variables and random parameters. [ABSTRACT FROM AUTHOR]
- Published
- 2009
- Full Text
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10. An Efficient Method to Estimate the Suboptimality of Affine Controllers.
- Author
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Hadjiyiannis, Michael J., Goulart, Paul J., and Kuhn, Daniel
- Subjects
AFFINAL relatives ,MATHEMATICAL optimization ,PROCESS control systems ,ROBUST control ,FREQUENCY selective surfaces ,MATHEMATICAL variables - Abstract
We consider robust feedback control of time-varying, linear discrete-time systems operating over a finite horizon. For such systems, we consider the problem of designing robust causal controllers that minimize the expected value of a convex quadratic cost function, subject to mixed linear state and input constraints. Determination of an optimal control policy for such problems is generally computationally intractable, but suboptimal policies can be computed by restricting the class of admissible policies to be affine on the observation. By using a suitable re-parameterization and robust optimization techniques, these approximations can be solved efficiently as convex optimization problems. We investigate the loss of optimality due to the use of such affine policies. Using duality arguments and by imposing an affine structure on the dual variables, we provide an efficient method to estimate a lower bound on the value of the optimal cost function for any causal policy, by solving a cone program whose size is a polynomial function of the problem data. This lower bound can then be used to quantify the loss of optimality incurred by the affine policy. [ABSTRACT FROM AUTHOR]
- Published
- 2011
- Full Text
- View/download PDF
11. Optimal decision making under uncertainty.
- Author
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Hochreiter, Ronald and Kuhn, Daniel
- Subjects
OPTIMAL designs (Statistics) ,DECISION making ,UNCERTAINTY (Information theory) ,INDUSTRIAL management ,CONFERENCES & conventions ,MATHEMATICAL optimization - Published
- 2012
- Full Text
- View/download PDF
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