Author(s):

Chatterjee, Krishnendu; Křetínská, Zuzana; Křetínský, Jan

Article Title: 
Unifying two views on multiple meanpayoff objectives in Markov decision processes

Affiliation 
IST Austria 
Abstract: 
We consider Markov decision processes (MDPs) with multiple limitaverage (or meanpayoff) objectives. There exist two different views: (i) the expectation semantics, where the goal is to optimize the expected meanpayoff objective, and (ii) the satisfaction semantics, where the goal is to maximize the probability of runs such that the meanpayoff value stays above a given vector. We consider optimization with respect to both objectives at once, thus unifying the existing semantics. Precisely, the goal is to optimize the expectation while ensuring the satisfaction constraint. Our problem captures the notion of optimization with respect to strategies that are riskaverse (i.e., ensure certain probabilistic guarantee). Our main results are as follows: First, we present algorithms for the decision problems which are always polynomial in the size of the MDP. We also show that an approximation of the Paretocurve can be computed in time polynomial in the size of the MDP, and the approximation factor, but exponential in the number of dimensions. Second, we present a complete characterization of the strategy complexity (in terms of memory bounds and randomization) required to solve our problem.

Keywords: 
Computer science; Logic in computer science

Journal Title:

Logical Methods in Computer Science

Volume: 
13

Issue 
2

ISSN:

18605974

Publisher:

International Federation of Computational Logic

Date Published:

20170703

Start Page: 
Article number: lmcs: 3757

Copyright Statement: 
CC BYND

URL: 

DOI: 
10.23638/LMCS13(2:15)2017

Open access: 
yes (OA journal) 