Another look at the nonclassical information structure problem

Ho, Yu-Chi; Chang, Ting-Wei

doi:10.1109/tac.1980.1102351

Cited by 34 publications

(26 citation statements)

References 2 publications

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“…For example, in [9] the authors analyzed the problem from a discrete version; however, the authors were unable to make progress in deriving the optimal solution. Later, it was proven that the discretized Witsenhausen counterexample expressed in discrete form is NP-complete [18].…”

Section: Introductionmentioning

confidence: 99%

Learning approaches to the Witsenhausen counterexample from a view of potential games

Marden

Shamma

2009

Proceedings of the 48h IEEE Conference on Decision and Control (CDC) Held Jointly With 2009 28th Chinese Control Conference

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Abstract-Since Witsenhausen put forward his remarkable counterexample in 1968, there have been many attempts to develop efficient methods for solving this non-convex functional optimization problem. However there are few methods designed from game theoretic perspectives. In this paper, after discretizing the Witsenhausen counterexample and re-writing the formulation in analytical expressions, we use fading memory JSFP with inertia, one learning approach in games, to search for better controllers from a view of potential games. We achieve a better solution than the previously known best one. Moreover, we show that the learning approaches are simple and automated and they are easy to extend for solving general functional optimization problems.

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Section: Introductionmentioning

confidence: 99%

Learning approaches to the Witsenhausen counterexample from a view of potential games

Marden

Shamma

2009

Proceedings of the 48h IEEE Conference on Decision and Control (CDC) Held Jointly With 2009 28th Chinese Control Conference

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“…A different fast algorithm for median filtering that is independent of picture details and gray level resolution is proposed here. This algorithm works by taking care of all the possible spatial redundancy during computation and uses the idea of the Quicksort algorithm [8] for comparison. The extension of the algorithm to mean filtering as well as to point and line detection is also discussed here.…”

Section: Discussionmentioning

confidence: 99%

Information structures in deterministic decentralized control problems

Li¹,

Singh

1983

IEEE Trans. Syst., Man, Cybern.

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The optimal segmentation scheme leads to simple object track ing methods by deriving the segmentation of a frame in a sequence from the final segmentation of the preceding frame. This introduces additional knowledge into the procedure, and only a few iterations are needed to reach final segmentation at each frame. Two tracking methods were tested and are described in this section.In the first tracking scheme, the final segmentation of a frame is used as the initial segmentation for the following frame. This approach is appropriate when the movement of the objects from frame to frame is small relative to their size and is simple to implement.The second tracking method compares the initial segmentation of a new frame to the final segmentation of the preceding frame. After computing the center of gravity for each label, a correspon dence is established between labels in the two frames to minimize size and location differences. After the correspondence has been established, an estimate is available for the displacement of each object. In updating the labels of each frame, a weight is given to the labeling of the preceeding frame, shifted by the computed displacement estimate. Fig. 5 shows a sequence of three frames. The initial and final segmentation of the first frame, after 12 iterations of ordinary optimization, are displayed in Fig. 6. Segmentation of the second and third frames with two iterations only, for different methods, is displayed in Fig. 7. The two tracking algorithms show much improved results compared with ordinary optimization. VI. CONCLUDING REMARKSAn optimization method has been presented that can perform classification based on optimization of a cost function. Experi ments were performed for image segmentation with cost func tions that include roughness, discrepancy from original image, and fitting the gray level gradient. The general method is not limited to this class of functions only; any function appropriate to the problem can be used. This method can also be used for simple tracking algorithms in sequences of frames. It has also been applied to solve substitution ciphers [11], resulting in fast and accurate solutions.Abstract-The information structures associated with deterministic de centralized control are examined. Conditions are derived under which such structures are partially nested. The tuning regulator approach and the sequential optimization approach are used as examples to examine these conditions in the context of concrete decentralized controller design philos ophies.

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“…Our starting point is the paper [1], which considered a discrete version of the Witsenhausen counterexample where all the random variables and controls were restricted to be integers. This problem formulation can be obtained by quantizing the Witsenhausen problem and rescaling [10], [11]. Furthermore, the distribution of the initial state of the system and the noise were viewed as inputs; in Witsenhausen's original formulation, both of these were taken to be Gaussian.…”

Section: Introductionmentioning

confidence: 99%

“…We will use Φ * (p X0 , p Z ) to refer to the optimal cost as a function of the problem parameters. 1 This problem was essentially introduced in [10]. It is not hard to see that an optimal solution exists: we can restrict our attention to a finite set of maps T, δ, as there is no need to consider maps which move some values in X too far.…”

Section: Introductionmentioning

confidence: 99%

On the Inapproximability of the Discrete Witsenhausen Problem

Olshevsky

2019

IEEE Control Syst. Lett.

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We consider a discrete version of the Witsenhausen problem where all random variables are bounded and take on integer values. Our main goal is to understand the complexity of computing good strategies given the distributions for the initial state and second-stage noise as inputs to the problem. Following Papadimitriou and Tsitsiklis [1], who showed that computing the optimal solution is NP-complete, we construct a sequence of problem instances with the initial state uniform over a set of size n and the noise uniform over a set of size at most n 2 , such that finding a strategy whose cost is a multiplicative n 2−ǫ approximation to the optimal cost is NP-hard for any ǫ > 0.

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Another look at the nonclassical information structure problem

Cited by 34 publications

References 2 publications

Learning approaches to the Witsenhausen counterexample from a view of potential games

Learning approaches to the Witsenhausen counterexample from a view of potential games

Information structures in deterministic decentralized control problems

On the Inapproximability of the Discrete Witsenhausen Problem

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