Quickest Detection POMDPs With Social Learning: Interaction of Local and Global Decision Makers

Krishnamurthy, Vikram

doi:10.1109/tit.2012.2201372

Cited by 56 publications

(82 citation statements)

References 46 publications

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“…In another related line of work, [6] studies the effect of social learning in a quickest detection problem, in which agents keep updating their beliefs based on previous decisions and detect the time at which an underlying state changes. It has a similar framework to [7], which studied update of private information in a finite memory.…”

Section: Introductionmentioning

confidence: 99%

Social teaching: Being informative vs. being right in sequential decision making

Rhim

Goyal

2013

2013 IEEE International Symposium on Information Theory

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Abstract-We show that it can be suboptimal for Bayesian decision-making agents employing social learning to use correct prior probabilities as their initial beliefs. We consider sequential Bayesian binary hypothesis testing where each individual agent makes a binary decision based on an initial belief, a private signal, and the decisions of all earlier-acting agents-with the actions of precedent agents causing updates of the initial belief. Each agent acts to minimize Bayes risk, with all agents sharing the same Bayes costs for Type I (false alarm) and Type II (missed detection) errors. The effect of the set of initial beliefs on the decisionmaking performance of the last agent is studied. The last agent makes the best decision when the initial beliefs are inaccurate. When the private signals are described by Gaussian likelihoods, the optimal initial beliefs are not haphazard but rather follow a systematic pattern: the earlier-acting agents should act as if the prior probability is larger than it is in reality when the true prior probability is small, and vice versa. We interpret this as being open minded toward the unlikely hypothesis. The earlyacting agents face a trade-off between making a correct decision and being maximally informative to the later-acting agents.

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Section: Introductionmentioning

confidence: 99%

Social teaching: Being informative vs. being right in sequential decision making

Rhim

Goyal

2013

2013 IEEE International Symposium on Information Theory

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“…The proof of the above theorem is in [21]. As a consequence of Theorem 1, there are only Y + 1 possible decision likelihood matrices R π , one per polytope P l , l = 1, .…”

Section: Market Observer's Optimal Strategymentioning

confidence: 99%

“…This work is a novel application of multi-agent signal processing and control methods to the problem of change detection in dynamical models affected by social learning. The proof of the structure of the market maker's optimal strategy involves submodularity on the lattice of posterior Bayesian distributions, see [22,21].…”

Section: Relation To Prior Workmentioning

confidence: 99%

Detecting asset value dislocations in multi-agent models of market microstructure

Krishnamurthy

Aryan

2013

2013 IEEE International Conference on Acoustics, Speech and Signal Processing

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Consider a financial market participant observing the trade flow of an asset traded through a limit order book. Trades are driven by an agent-based model where individual agents observe the trading decisions of previous agents, as well as their private signal on the value of the asset and then execute a trading decision. Given trading decisions of agents, how can a market observer detect a shock to the underlying value of the traded asset? The distribution of shock times is assumed to be phase-type distributed to allow for a general set of change time probabilities beyond geometric change times. We show that this problem is equivalent to change detection with social learning. We provide structural results that allow the optimal detection policy to be characterized by a single threshold policy.

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“…In the case of unbounded likelihood ratios for the private signals, Smith and Sorensen [21] study this problem using martingales and show that the error probability converges to 0. Krishnamurthy [22], [23] studies this problem from the perspective of quickest time change detection. Acemoglu et al [24] show that the nodes can asymptotically learn the underlying truth in more general network structures.…”

Section: A Related Workmentioning

confidence: 99%

Hypothesis Testing in Feedforward Networks With Broadcast Failures

Zhang

Chong

Pezeshki

et al. 2013

IEEE J. Sel. Top. Signal Process.

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Abstract-Consider a large number of nodes, which sequentially make decisions between two given hypotheses. Each node takes a measurement of the underlying truth, observes the decisions from some immediate predecessors, and makes a decision between the given hypotheses. We consider two classes of broadcast failures: 1) each node broadcasts a decision to the other nodes, subject to random erasure in the form of a binary erasure channel; 2) each node broadcasts a randomly flipped decision to the other nodes in the form of a binary symmetric channel. We are interested in conditions under which there does (or does not) exist a decision strategy consisting of a sequence of likelihood ratio tests such that the node decisions converge in probability to the underlying truth, as the number of nodes goes to infinity. In both cases, we show that if each node only learns from a bounded number of immediate predecessors, then there does not exist a decision strategy such that the decisions converge in probability to the underlying truth. However, in case 1, we show that if each node learns from an unboundedly growing number of predecessors, then there exists a decision strategy such that the decisions converge in probability to the underlying truth, even when the erasure probabilities converge to 1. We show that a locally optimal strategy, consisting of a sequence of Bayesian likelihood ratio tests, is such a strategy, and we derive the convergence rate of the error probability for this strategy. In case 2, we show that if each node learns from all of its previous predecessors, then there exists a decision strategy such that the decisions converge in probability to the underlying truth when the flipping probabilities of the binary symmetric channels are bounded away from 1/2. Again, we show that a locally optimal strategy achieves this, and we derive the convergence rate of the error probability for it. In the case where the flipping probabilities converge to 1/2, we derive a necessary condition on the convergence rate of the flipping probabilities such that the decisions based on the locally optimal strategy still converge to the underlying truth. We also explicitly characterize the relationship between the convergence rate of the error probability and the convergence rate of the flipping probabilities.

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Quickest Detection POMDPs With Social Learning: Interaction of Local and Global Decision Makers

Cited by 56 publications

References 46 publications

Social teaching: Being informative vs. being right in sequential decision making

Social teaching: Being informative vs. being right in sequential decision making

Detecting asset value dislocations in multi-agent models of market microstructure

Hypothesis Testing in Feedforward Networks With Broadcast Failures

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