---
_id: '3346'
abstract:
- lang: eng
text: We study Markov decision processes (MDPs) with multiple limit-average (or
mean-payoff) functions. We consider two different objectives, namely, expectation
and satisfaction objectives. Given an MDP with k reward functions, in the expectation
objective the goal is to maximize the expected limit-average value, and in the
satisfaction objective the goal is to maximize the probability of runs such that
the limit-average value stays above a given vector. We show that under the expectation
objective, in contrast to the single-objective case, both randomization and memory
are necessary for strategies, and that finite-memory randomized strategies are
sufficient. Under the satisfaction objective, in contrast to the single-objective
case, infinite memory is necessary for strategies, and that randomized memoryless
strategies are sufficient for epsilon-approximation, for all epsilon>;0. We
further prove that the decision problems for both expectation and satisfaction
objectives can be solved in polynomial time and the trade-off curve (Pareto curve)
can be epsilon-approximated in time polynomial in the size of the MDP and 1/epsilon,
and exponential in the number of reward functions, for all epsilon>;0. Our
results also reveal flaws in previous work for MDPs with multiple mean-payoff
functions under the expectation objective, correct the flaws and obtain improved
results.
article_number: '5970225'
author:
- first_name: Tomáš
full_name: Brázdil, Tomáš
last_name: Brázdil
- first_name: Václav
full_name: Brožek, Václav
last_name: Brožek
- first_name: Krishnendu
full_name: Chatterjee, Krishnendu
id: 2E5DCA20-F248-11E8-B48F-1D18A9856A87
last_name: Chatterjee
orcid: 0000-0002-4561-241X
- first_name: Vojtěch
full_name: Forejt, Vojtěch
last_name: Forejt
- first_name: Antonín
full_name: Kučera, Antonín
last_name: Kučera
citation:
ama: 'Brázdil T, Brožek V, Chatterjee K, Forejt V, Kučera A. Two views on multiple
mean payoff objectives in Markov Decision Processes. In: IEEE; 2011. doi:10.1109/LICS.2011.10'
apa: 'Brázdil, T., Brožek, V., Chatterjee, K., Forejt, V., & Kučera, A. (2011).
Two views on multiple mean payoff objectives in Markov Decision Processes. Presented
at the LICS: Logic in Computer Science, Toronto, Canada: IEEE. https://doi.org/10.1109/LICS.2011.10'
chicago: Brázdil, Tomáš, Václav Brožek, Krishnendu Chatterjee, Vojtěch Forejt, and
Antonín Kučera. “Two Views on Multiple Mean Payoff Objectives in Markov Decision
Processes.” IEEE, 2011. https://doi.org/10.1109/LICS.2011.10.
ieee: 'T. Brázdil, V. Brožek, K. Chatterjee, V. Forejt, and A. Kučera, “Two views
on multiple mean payoff objectives in Markov Decision Processes,” presented at
the LICS: Logic in Computer Science, Toronto, Canada, 2011.'
ista: 'Brázdil T, Brožek V, Chatterjee K, Forejt V, Kučera A. 2011. Two views on
multiple mean payoff objectives in Markov Decision Processes. LICS: Logic in Computer
Science, 5970225.'
mla: Brázdil, Tomáš, et al. Two Views on Multiple Mean Payoff Objectives in Markov
Decision Processes. 5970225, IEEE, 2011, doi:10.1109/LICS.2011.10.
short: T. Brázdil, V. Brožek, K. Chatterjee, V. Forejt, A. Kučera, in:, IEEE, 2011.
conference:
end_date: 2011-06-24
location: Toronto, Canada
name: 'LICS: Logic in Computer Science'
start_date: 2011-06-21
date_created: 2018-12-11T12:02:48Z
date_published: 2011-06-21T00:00:00Z
date_updated: 2021-01-12T07:42:49Z
day: '21'
department:
- _id: KrCh
doi: 10.1109/LICS.2011.10
ec_funded: 1
language:
- iso: eng
main_file_link:
- open_access: '1'
url: http://arxiv.org/abs/1104.3489
month: '06'
oa: 1
oa_version: Submitted Version
project:
- _id: 2584A770-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: P 23499-N23
name: Modern Graph Algorithmic Techniques in Formal Verification
- _id: 25832EC2-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: S 11407_N23
name: Rigorous Systems Engineering
- _id: 2581B60A-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '279307'
name: 'Quantitative Graph Games: Theory and Applications'
- _id: 2587B514-B435-11E9-9278-68D0E5697425
name: Microsoft Research Faculty Fellowship
publication_status: published
publisher: IEEE
publist_id: '3275'
quality_controlled: '1'
scopus_import: 1
status: public
title: Two views on multiple mean payoff objectives in Markov Decision Processes
type: conference
user_id: 4435EBFC-F248-11E8-B48F-1D18A9856A87
year: '2011'
...