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31
DETERMINANT MAXIMIZATION WITH LINEAR MATRIX INEQUALITY CONSTRAINTS
"... The problem of maximizing the determinant of a matrix subject to linear matrix inequalities arises in many fields, including computational geometry, statistics, system identification, experiment design, and information and communication theory. It can also be considered as a generalization of the s ..."
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Cited by 167 (18 self)
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The problem of maximizing the determinant of a matrix subject to linear matrix inequalities arises in many fields, including computational geometry, statistics, system identification, experiment design, and information and communication theory. It can also be considered as a generalization of the semidefinite programming problem. We give an overview of the applications of the determinant maximization problem, pointing out simple cases where specialized algorithms or analytical solutions are known. We then describe an interiorpoint method, with a simplified analysis of the worstcase complexity and numerical results that indicate that the method is very efficient, both in theory and in practice. Compared to existing specialized algorithms (where they are available), the interiorpoint method will generally be slower; the advantage is that it handles a much wider variety of problems.
Expectation Traps and Discretion
 Journal of Economic Theory
, 1998
"... We develop a dynamic model with optimizing private agents and a benevolent, optimizing monetary authority who cannot commit to future policies. We characterize the set of sustainable equilibria and discuss the implications for institutional reform. We show that there are equilibria in which the mone ..."
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Cited by 52 (6 self)
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We develop a dynamic model with optimizing private agents and a benevolent, optimizing monetary authority who cannot commit to future policies. We characterize the set of sustainable equilibria and discuss the implications for institutional reform. We show that there are equilibria in which the monetary authority pursues in°ationary policies, because that is what private agents expect. We call such equilibria expectation traps. Alternative institutional arrangements for the conduct of monetary policy which impose limited forms of commitment on the policymaker can eliminate expectations traps. Journal of Economic
Online Decision Problems with Large Strategy Sets
, 2005
"... In an online decision problem, an algorithm performs a sequence of trials, each of which involves selecting one element from a fixed set of alternatives (the “strategy set”) whose costs vary over time. After T trials, the combined cost of the algorithm’s choices is compared with that of the single s ..."
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Cited by 24 (2 self)
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In an online decision problem, an algorithm performs a sequence of trials, each of which involves selecting one element from a fixed set of alternatives (the “strategy set”) whose costs vary over time. After T trials, the combined cost of the algorithm’s choices is compared with that of the single strategy whose combined cost is minimum. Their difference is called regret, and one seeks algorithms which are efficient in that their regret is sublinear in T and polynomial in the problem size. We study an important class of online decision problems called generalized multiarmed bandit problems. In the past such problems have found applications in areas as diverse as statistics, computer science, economic theory, and medical decisionmaking. Most existing algorithms were efficient only in the case of a small (i.e. polynomialsized) strategy set. We extend the theory by supplying nontrivial algorithms and lower bounds for cases in which the strategy set is much larger (exponential or infinite) and
Incremental Dynamic Programming for OnLine Adaptive Optimal Control
, 1994
"... Reinforcement learning algorithms based on the principles of Dynamic Programming (DP) have enjoyed a great deal of recent attention both empirically and theoretically. These algorithms have been referred to generically as Incremental Dynamic Programming (IDP) algorithms. IDP algorithms are intended ..."
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Cited by 20 (2 self)
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Reinforcement learning algorithms based on the principles of Dynamic Programming (DP) have enjoyed a great deal of recent attention both empirically and theoretically. These algorithms have been referred to generically as Incremental Dynamic Programming (IDP) algorithms. IDP algorithms are intended for use in situations where the information or computational resources needed by traditional dynamic programming algorithms are not available. IDP algorithms attempt to find a global solution to a DP problem by incrementally improving local constraint satisfaction properties as experience is gained through interaction with the environment. This class of algorithms is not new, going back at least as far as Samuel's adaptive checkersplaying programs,...
The Return to Schooling in Structural Dynamic Models: A Survey of the Literature
, 2006
"... This papers contains a survey of the recent literature devoted to the returns to schooling within a dynamic structural framework. I present a historical perspective on the evolution of the literature, from early static models set in a selectivity framework (Willis and Rosen, 1979) to the recent lite ..."
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Cited by 20 (9 self)
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This papers contains a survey of the recent literature devoted to the returns to schooling within a dynamic structural framework. I present a historical perspective on the evolution of the literature, from early static models set in a selectivity framework (Willis and Rosen, 1979) to the recent literature, stimulated by Keane and Wolpin (1997), and which uses stochastic dynamic programming techniques. After reviewing the literature thoroughly, I compare the structural approach with the IV (experimental) approach. I present their commonalities and I also discuss their fundamental differences. The discussion is focussed on the comprehension of the discrepancy between structural and reducedform estimates of the returns to schooling.
Controlling Risk Exposure and Dividends Payout Schemes: Insurance Company Example
 Mathematical Finance
, 1998
"... The paper represents a model for the financial valuation of a firm which has control on the dividend payment stream and its risk as well as potential profit by choosing different business activities among those available to it. This is an extension of the classical Miller Modigliani theory of firm v ..."
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Cited by 12 (1 self)
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The paper represents a model for the financial valuation of a firm which has control on the dividend payment stream and its risk as well as potential profit by choosing different business activities among those available to it. This is an extension of the classical Miller Modigliani theory of firm valuation theory to the situation of controllable business activities in stochastic environment. We associate the value of the company with the expected present value of the net dividend distributions (under the optimal policy). The example we consider is a large corporation such as an insurance company, whose liquid assets in the absence of control fluctuate as a Brownian motion with a constant positive drift and a constant diffusion coefficient. We interpret the diffusion coefficient as risk exposure, while drift is understood as potential profit. At each moment of time there is an option to reduce risk exposure, simultaneously reducing the potential profit, like using proportional reinsura...
Optimal Risk/Dividend Distribution Control Models. Applications to Insurance
 Company, Mathematical Methods of Operations Research
, 1999
"... The current paper presents a short survey of stochastic models of risk control and dividend optimization techniques for a financial corporation. While being close to consumption /investment models of Mathematical Finance, dividend optimization models possess special features which do not allow th ..."
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Cited by 11 (2 self)
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The current paper presents a short survey of stochastic models of risk control and dividend optimization techniques for a financial corporation. While being close to consumption /investment models of Mathematical Finance, dividend optimization models possess special features which do not allow them to be treated as a particular case of consumption/investment models.
Design of affine controllers via convex optimization
, 2008
"... Abstract—We consider a discretetime timevarying linear dynamical system, perturbed by process noise, with linear noise corrupted measurements, over a finite horizon. We address the problem of designing a general affine causal controller, in which the control input is an affine function of all prev ..."
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Cited by 6 (1 self)
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Abstract—We consider a discretetime timevarying linear dynamical system, perturbed by process noise, with linear noise corrupted measurements, over a finite horizon. We address the problem of designing a general affine causal controller, in which the control input is an affine function of all previous measurements, in order to minimize a convex objective, in either a stochastic or worstcase setting. This controller design problem is not convex in its natural form, but can be transformed to an equivalent convex optimization problem by a nonlinear change of variables, which allows us to efficiently solve the problem. Our method is related to the classicaldesign procedure for timeinvariant, infinitehorizon linear controller design, and the more recent purified output control method. We illustrate the method with applications to supply chain optimization and dynamic portfolio optimization, and show the method can be combined with model predictive control techniques when perfect state information is available. Index Terms—Affine controller, dynamical system, dynamic linear programming (DLP), linear exponential quadratic Gaussian (LEQG), linear quadratic Gaussian (LQG), model predictive control (MPC), proportionalintegralderivative (PID). I.
Stochastic Control of Handoffs in Cellular Networks
, 1995
"... A Dynamic Programming formulation is used to obtain an optimal strategy for the handoff problem in cellular radio systems. The formulation includes the modeling of the underlying randomness in received signal strengths as well as the movements of the mobile. The cost function is designed such that t ..."
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Cited by 6 (1 self)
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A Dynamic Programming formulation is used to obtain an optimal strategy for the handoff problem in cellular radio systems. The formulation includes the modeling of the underlying randomness in received signal strengths as well as the movements of the mobile. The cost function is designed such that there is a cost associated with switching and a reward for improving the quality of the call. The optimum decision is characterized by a threshold on the difference between the measured power that the mobile receives from the base stations. Also we study the problem of choosing the "best" fixed threshold that minimizes the cost function. The performance of the optimal and suboptimal strategies are compared. I. Introduction W IRELESS networks are experiencing rapid growth, a trend likely to continue in the foreseeable future. In both micro and macro cellular networks a key issue for efficient operation is the problem of handoffs. A call on a portable/mobile which leaves one cell (radio cover...