Dynamic programming with total variational distance uncertainty

Charalambos D. Charalambous*, Ioannis Tzortzis, Themistoklis Charalambous

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionScientificpeer-review

1 Citation (Scopus)

Abstract

The aim of this paper is to address optimality of stochastic control strategies via dynamic programming subject to total variational distance uncertainty on the conditional distribution of the controlled process. Utilizing concepts from signed measures, the maximization of a linear functional on the space of probability measures on abstract spaces is investigated, among those probability measures which are within a total variational distance from a nominal probability measure. The maximizing probability measure is found in closed form. These results are then applied to solve minimax stochastic control with deterministic control strategies, under a Markovian assumption on the conditional distributions of the controlled process. The results include: 1) Optimization subject to total variational distance constraints, 2) new dynamic programming recursions, which involve the oscillator seminorm of the value function.

Original languageEnglish
Title of host publication2012 IEEE 51st Annual Conference on Decision and Control (CDC)
PublisherIEEE
Pages1909-1914
Number of pages6
ISBN (Electronic)978-1-4673-2066-5
ISBN (Print)978-1-4673-2065-8
DOIs
Publication statusPublished - 2012
MoE publication typeA4 Article in a conference publication
EventIEEE Conference on Decision and Control - , United States
Duration: 10 Dec 201213 Dec 2012
Conference number: 51

Conference

ConferenceIEEE Conference on Decision and Control
Abbreviated titleCDC
CountryUnited States
Period10/12/201213/12/2012

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