
Active Hypothesis Testing: Beyond ChernoffStein
An active hypothesis testing problem is formulated. In this problem, the...
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Adaptivity in Adaptive Submodularity
Adaptive sequential decision making is one of the central challenges in ...
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Optimal Adaptive Strategies for Sequential Quantum Hypothesis Testing
We consider sequential hypothesis testing between two quantum states usi...
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Policy Design for Active Sequential Hypothesis Testing using Deep Learning
Information theory has been very successful in obtaining performance lim...
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Probing to Minimize
We develop approximation algorithms for setselection problems with dete...
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A ModelBased Active Testing Approach to Sequential Diagnosis
Modelbased diagnostic reasoning often leads to a large number of diagno...
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Sequential Controlled Sensing for Composite Multihypothesis Testing
The problem of multihypothesis testing with controlled sensing of obser...
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Approximation Algorithms for Active Sequential Hypothesis Testing
In the problem of active sequential hypotheses testing (ASHT), a learner seeks to identify the true hypothesis h^* from among a set of hypotheses H. The learner is given a set of actions and knows the outcome distribution of any action under any true hypothesis. While repeatedly playing the entire set of actions suffices to identify h^*, a cost is incurred with each action. Thus, given a target error δ>0, the goal is to find the minimal cost policy for sequentially selecting actions that identify h^* with probability at least 1  δ. This paper provides the first approximation algorithms for ASHT, under two types of adaptivity. First, a policy is partially adaptive if it fixes a sequence of actions in advance and adaptively decides when to terminate and what hypothesis to return. Under partial adaptivity, we provide an O(s^1(1+log_1/δH)log (s^1H log H))approximation algorithm, where s is a natural separation parameter between the hypotheses. Second, a policy is fully adaptive if action selection is allowed to depend on previous outcomes. Under full adaptivity, we provide an O(s^1log (H/δ)log H)approximation algorithm. We numerically investigate the performance of our algorithms using both synthetic and realworld data, showing that our algorithms outperform a previously proposed heuristic policy.
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