---
res:
bibo_abstract:
- "We study the problem of achieving a given value in Markov decision processes
(MDPs) with several independent discounted reward objectives. We consider a generalised
version of discounted reward objectives, in which the amount of discounting depends
on the states visited and on the objective. This definition extends the usual
definition of discounted reward, and allows to capture the systems in which the
value of different commodities diminish at different and variable rates.\r\n\r\nWe
establish results for two prominent subclasses of the problem, namely state-discount
models where the discount factors are only dependent on the state of the MDP (and
independent of the objective), and reward-discount models where they are only
dependent on the objective (but not on the state of the MDP). For the state-discount
models we use a straightforward reduction to expected total reward and show that
the problem whether a value is achievable can be solved in polynomial time. For
the reward-discount model we show that memory and randomisation of the strategies
are required, but nevertheless that the problem is decidable and it is sufficient
to consider strategies which after a certain number of steps behave in a memoryless
way.\r\n\r\nFor the general case, we show that when restricted to graphs (i.e.
MDPs with no randomisation), pure strategies and discount factors of the form
1/n where n is an integer, the problem is in PSPACE and finite memory suffices
for achieving a given value. We also show that when the discount factors are not
of the form 1/n, the memory required by a strategy can be infinite.\r\n@eng"
bibo_authorlist:
- foaf_Person:
foaf_givenName: Krishnendu
foaf_name: Chatterjee, Krishnendu
foaf_surname: Chatterjee
foaf_workInfoHomepage: http://www.librecat.org/personId=2E5DCA20-F248-11E8-B48F-1D18A9856A87
orcid: 0000-0002-4561-241X
- foaf_Person:
foaf_givenName: Vojtěch
foaf_name: Forejt, Vojtěch
foaf_surname: Forejt
- foaf_Person:
foaf_givenName: Dominik
foaf_name: Wojtczak, Dominik
foaf_surname: Wojtczak
bibo_doi: 10.1007/978-3-642-45221-5_17
bibo_volume: 8312
dct_date: 2013^xs_gYear
dct_language: eng
dct_publisher: Springer@
dct_title: Multi-objective discounted reward verification in graphs and MDPs@
...