A tight sufficient condition for Radner–Stiglitz nonconcavity in the value of information

Lara, Michel De; Gilotte, Laurent

doi:10.1016/j.jet.2007.01.014

Cited by 8 publications

(8 citation statements)

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“…Radner and Stiglitz [25] discusses the problem in considerably greater depth, giving general conditions under which the value of information is not concave. This research has been extended more recently by Chade and Schlee [26] and Delara and Gilotte [27] to more general settings.…”

Section: The S-curve Problemmentioning

confidence: 95%

The Knowledge Gradient for Optimal Learning

Powell

2011

Wiley Encyclopedia of Operations Research and Management Science

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Optimal learning addresses the problem of how to collect information so that it benefits future decisions. For off‐line problems, we have to make a series of measurements or observations before choosing a final design or set of parameters; for on‐line problems, we learn from rewards we are receiving, and we want to strike a balance between rewards earned now and better decisions in the future. This article reviews these problems, describes optimal and heuristic policies, and shows how to compare competing policies. Then, the presentation focuses on the concept of the knowledge gradient, which guides information collection by maximizing the marginal value of information. We show how this idea can be applied to both on‐line and off‐line problems, as well as a broad range of other applications which have not previously yielded to formal techniques.

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Section: The S-curve Problemmentioning

confidence: 95%

The Knowledge Gradient for Optimal Learning

Powell

2011

Wiley Encyclopedia of Operations Research and Management Science

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“…They provide joint conditions on a parameterized family of information structures together with a decision problem such that, when the agent is close to receiving no information at all, the marginal value of information is null. Their result was subsequently generalized in [15] and [16], where are provided joint conditions on parameterized information and a decision problem leading to zero marginal value of information.…”

Section: The Marginal Value Of Informationmentioning

confidence: 99%

“…The question of marginal value of information is studied in [32,15,16]. They consider parameterized information structures, and derive general conditions on the pair consisting of the information structures and the decision problem under which the marginal value of information close to no information is zero.…”

Section: Related Literaturementioning

confidence: 99%

Payoffs-Beliefs Duality and the Value of Information

Lara¹,

Gossner²

2020

SIAM J. Optim.

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In decision problems under incomplete information, payoff vectors (indexed by states of nature) and beliefs are naturally paired by bilinear duality. We exploit this duality to analyze the value of information, using concepts and tools from convex analysis. We then derive global estimates of the value of information of any information structure from local properties of the value function and of the set of optimal actions taken at the prior belief only. We apply our results to the marginal value of information at the null, that is, when the agent is close to receiving no information at all.

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“…Nonconcavity in the value of information, a notion akin to non-submodularity in a continuous setting, was examined in several papers (Radner & Stiglitz, 1984;Lara & Gilotte, 2007;Chadeand & Schlee, 2001). Submodularity is an important property, because in cases where the VOI is submodular, simple, greedy algorithms result in provably near-optimal policies (Krause & Guestrin, 2009, 2011Papachristoudis & Fisher III, 2012).…”

Section: Introductionmentioning

confidence: 99%

“…Submodularity is an important property, because in cases where the VOI is submodular, simple, greedy algorithms result in provably near-optimal policies (Krause & Guestrin, 2009, 2011Papachristoudis & Fisher III, 2012). However, the VOI is not submodular in general (Radner & Stiglitz, 1984;Lara & Gilotte, 2007;Chadeand & Schlee, 2001;Krause & Guestrin, 2009), and in particular submodularity does not hold in the selection problem , even in a very limited case involving only two items. Other types of approximate solutions for the batch version of the selection problem exist (Reches, Gal, & Kraus, 2013), with theoretical bounds on the approximation error not based on submodularity.…”

Section: Introductionmentioning

confidence: 99%

Some Properties of Batch Value of Information in the Selection Problem

Shperberg¹,

Shimony²

2017

jair

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Given a set of items of unknown utility, we need to select one with a utility as high as possible (the selection problem). Measurements (possibly noisy) of item values prior to selection are allowed, at a known cost. The goal is to optimize the overall sequential decision process of measurements and selection. Value of information (VOI) is a well-known scheme for selecting measurements, but the intractability of the problem typically leads to using myopic VOI estimates. Other schemes have also been proposed, some with approximation guarantees, based on submodularity criteria. However, it was observed that the VOI is not submodular in general. In this paper we examine theoretical properties of VOI for the selection problem, and identify cases of submodularity and supermodularity. We suggest how to use these properties to compute approximately optimal measurement batch policies, with an example based on a wine selection problem.

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A tight sufficient condition for Radner–Stiglitz nonconcavity in the value of information

Cited by 8 publications

References 1 publication

The Knowledge Gradient for Optimal Learning

The Knowledge Gradient for Optimal Learning

Payoffs-Beliefs Duality and the Value of Information

Some Properties of Batch Value of Information in the Selection Problem

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