Dynamic programming with total variational distance uncertainty

Charalambos D. Charalambous; Ioannis Tzortzis; Themistoklis Charalambous

doi:10.1109/CDC.2012.6426334

Dynamic programming with total variational distance uncertainty

Charalambos D. Charalambous^*
, Ioannis Tzortzis
, Themistoklis Charalambous

^*Corresponding author for this work

Not published at Aalto University

University of Cyprus
KTH Royal Institute of Technology

Research output: Chapter in Book/Report/Conference proceeding › Conference article in proceedings › Scientific › peer-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 language	English
Title of host publication	2012 IEEE 51st Annual Conference on Decision and Control (CDC)
Publisher	IEEE
Pages	1909-1914
Number of pages	6
ISBN (Electronic)	978-1-4673-2066-5
ISBN (Print)	978-1-4673-2065-8
DOIs	https://doi.org/10.1109/CDC.2012.6426334
Publication status	Published - 2012
MoE publication type	A4 Conference publication
Event	IEEE Conference on Decision and Control - , United States Duration: 10 Dec 2012 → 13 Dec 2012 Conference number: 51

Conference

Conference	IEEE Conference on Decision and Control
Abbreviated title	CDC
Country/Territory	United States
Period	10/12/2012 → 13/12/2012

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10.1109/CDC.2012.6426334

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@inproceedings{558287a1736941d9b37d908824be2a72,

title = "Dynamic programming with total variational distance uncertainty",

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.",

author = "Charalambous, \{Charalambos D.\} and Ioannis Tzortzis and Themistoklis Charalambous",

year = "2012",

doi = "10.1109/CDC.2012.6426334",

language = "English",

isbn = "978-1-4673-2065-8 ",

pages = "1909--1914",

booktitle = "2012 IEEE 51st Annual Conference on Decision and Control (CDC)",

publisher = "IEEE",

address = "United States",

note = "IEEE Conference on Decision and Control, CDC ; Conference date: 10-12-2012 Through 13-12-2012",

}

TY - GEN

T1 - Dynamic programming with total variational distance uncertainty

AU - Charalambous, Charalambos D.

AU - Tzortzis, Ioannis

AU - Charalambous, Themistoklis

N1 - Conference code: 51

PY - 2012

Y1 - 2012

N2 - 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.

AB - 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.

UR - https://www.scopus.com/pages/publications/84874239408

U2 - 10.1109/CDC.2012.6426334

DO - 10.1109/CDC.2012.6426334

M3 - Conference article in proceedings

AN - SCOPUS:84874239408

SN - 978-1-4673-2065-8

SP - 1909

EP - 1914

BT - 2012 IEEE 51st Annual Conference on Decision and Control (CDC)

PB - IEEE

T2 - IEEE Conference on Decision and Control

Y2 - 10 December 2012 through 13 December 2012

ER -

Dynamic programming with total variational distance uncertainty

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