An unconventional approach for optimal stopping under model ambiguity is introduced. Besides ambiguity itself, we take into account how
Random Variables with Measurability Constraints with Application to Opportunistic Scheduling
This paper proves a representation theorem regarding sequences of random elements that take values in a Borel space and
are measurable with respect to the sigma algebra generated by an arbitrary union of sigma algebras. This, together with a related
representation theorem of Kallenberg, is used to characterize the set of multidimensional decision vectors in a discrete time
stochastic control problem with measurability and causality constraints, including opportunistic scheduling problems for timevarying
communication networks. A network capacity theorem for these systems is refined, without requiring an implicit and
arbitrarily complex extension of the state space, by introducing two measurability assumptions and using a theory of constructible
sets. An example that makes use of well known pathologies in descriptive set theory is given to show a nonmeasurable scheduling
scheme can outperform all measurable scheduling schemes.
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- Award ID(s):
- 1824418
- PAR ID:
- 10387217
- Date Published:
- Journal Name:
- Arxiv:2207.02345v1
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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