Optimal Strategy Decisions for Dynamic Linear Decision Rules in Feedback Form

Econometrica ◽  
1965 ◽  
Vol 33 (2) ◽  
pp. 307 ◽  
Author(s):  
C. van de Panne
Keyword(s):  
Optimal Strategy ◽  
Decision Rules ◽  
Feedback Form ◽  
Linear Decision Rules

scholarly journals Variable and sub-optimal responses to a choice problem are a persistent default mode

2019 ◽  
Author(s):  
Amelia R. Hunt ◽  
Warren James ◽  
Josephine Reuther ◽  
Melissa Spilioti ◽  
Eleanor Mackay ◽  
...  
Keyword(s):  
Optimal Strategy ◽  
Decision Rules ◽  
Optimal Solution ◽  
The Other ◽  
Rational Decision ◽  
Choice Problem ◽  
Default Mode ◽  
Potential Benefits ◽  
Simple Logic ◽  
Simple Decision Rule

Here we report persistent choice variability in the presence of a simple decision rule. Two analogous choice problems are presented, both of which involve making decisions about how to prioritize goals. In one version, participants choose a place to stand to throw a beanbag into one of two hoops. In the other, they must choose a place to fixate to detect a target that could appear in one of two boxes. In both cases, participants do not know which of the locations will be the target when they make their choice. The optimal solution to both problems follows the same, simple logic: when targets are close together, standing at/fixating the midpoint is the best choice. When the targets are far apart, accuracy from the midpoint falls, and standing/fixating close to one potential target achieves better accuracy. People do not follow, or even approach, this optimal strategy, despite substantial potential benefits for performance. Two interventions were introduced to try and shift participants from sub-optimal, variable responses to following a fixed, rational rule. First, we put participants into circumstances in which the solution was obvious. After participants correctly solved the problem there, we immediately presented the slightly-less-obvious context. Second, we guided participants to make choices that followed an optimal strategy, and then removed the guidance and let them freely choose. Following both of these interventions, participants immediately returned to a variable, sub-optimal pattern of responding. The results show that while constructing and implementing rational decision rules is possible, making variable responses to choice problems is a strong and persistent default mode. Borrowing concepts from classic animal learning studies, we suggest this default may persist because choice variability can provide opportunities for reinforcement learning.

scholarly journals Linear Decision Rules for Seasonal Hydropower Planning: Modelling Considerations

2016 ◽  
Vol 87 ◽  
pp. 28-35 ◽  
Author(s):  
Simen V. Braaten ◽  
Ola Gjønnes ◽  
Knut Hjertvik ◽  
Stein-Erik Fleten
Keyword(s):  
Decision Rules ◽  
Hydropower Planning ◽  
Linear Decision Rules

A Note on Linear Decision Rules

1970 ◽  
Vol 6 (6) ◽  
pp. 1789-1790 ◽  
Author(s):  
Satish C. Nayak ◽  
Sant R. Arora
Keyword(s):  
Decision Rules ◽  
Linear Decision Rules

Robust Optimization for Models with Uncertain Second-Order Cone and Semidefinite Programming Constraints

2021 ◽  
Author(s):  
Jianzhe Zhen ◽  
Frans J. C. T. de Ruiter ◽  
Ernst Roos ◽  
Dick den Hertog
Keyword(s):  
Robust Optimization ◽  
Semidefinite Programming ◽  
Optimization Problems ◽  
Linear Optimization ◽  
Decision Rules ◽  
Second Order ◽  
Minimum Volume ◽  
Second Order Cone ◽  
Linear Decision Rules ◽  
Effectiveness And Efficiency

In this paper, we consider uncertain second-order cone (SOC) and semidefinite programming (SDP) constraints with polyhedral uncertainty, which are in general computationally intractable. We propose to reformulate an uncertain SOC or SDP constraint as a set of adjustable robust linear optimization constraints with an ellipsoidal or semidefinite representable uncertainty set, respectively. The resulting adjustable problem can then (approximately) be solved by using adjustable robust linear optimization techniques. For example, we show that if linear decision rules are used, then the final robust counterpart consists of SOC or SDP constraints, respectively, which have the same computational complexity as the nominal version of the original constraints. We propose an efficient method to obtain good lower bounds. Moreover, we extend our approach to other classes of robust optimization problems, such as nonlinear problems that contain wait-and-see variables, linear problems that contain bilinear uncertainty, and general conic constraints. Numerically, we apply our approach to reformulate the problem on finding the minimum volume circumscribing ellipsoid of a polytope and solve the resulting reformulation with linear and quadratic decision rules as well as Fourier-Motzkin elimination. We demonstrate the effectiveness and efficiency of the proposed approach by comparing it with the state-of-the-art copositive approach. Moreover, we apply the proposed approach to a robust regression problem and a robust sensor network problem and use linear decision rules to solve the resulting adjustable robust linear optimization problems, which solve the problem to (near) optimality. Summary of Contribution: Computing robust solutions for nonlinear optimization problems with uncertain second-order cone and semidefinite programming constraints are of much interest in real-life applications, yet they are in general computationally intractable. This paper proposes a computationally tractable approximation for such problems. Extensive computational experiments on (i) computing the minimum volume circumscribing ellipsoid of a polytope, (ii) robust regressions, and (iii) robust sensor networks are conducted to demonstrate the effectiveness and efficiency of the proposed approach.

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