{"abstract":[{"text":"We consider Markov decision processes (MDPs) with multiple discounted reward objectives. Such MDPs occur in design problems where one wishes to simultaneously optimize several criteria, for example, latency and power. The possible trade-offs between the different objectives are characterized by the Pareto curve. We show that every Pareto-optimal point can be achieved by a memoryless strategy; however, unlike in the single-objective case, the memoryless strategy may require randomization. Moreover, we show that the Pareto curve can be approximated in polynomial time in the size of the MDP. Additionally, we study the problem if a given value vector is realizable by any strategy, and show that it can be decided in polynomial time; but the question whether it is realizable by a deterministic memoryless strategy is NP-complete. These results provide efficient algorithms for design exploration in MDP models with multiple objectives.\nThis research was supported in part by the AFOSR MURI grant F49620-00-1-0327, and the NSF grants CCR-0225610, CCR-0234690, and CCR-0427202. ","lang":"eng"}],"_id":"4551","citation":{"short":"K. Chatterjee, R. Majumdar, T.A. Henzinger, in:, Springer, 2006, pp. 325–336.","ama":"Chatterjee K, Majumdar R, Henzinger TA. Markov decision processes with multiple objectives. In: Vol 3884. Springer; 2006:325-336. doi:<a href=\"https://doi.org/10.1007/11672142_26\">10.1007/11672142_26</a>","chicago":"Chatterjee, Krishnendu, Ritankar Majumdar, and Thomas A Henzinger. “Markov Decision Processes with Multiple Objectives,” 3884:325–36. Springer, 2006. <a href=\"https://doi.org/10.1007/11672142_26\">https://doi.org/10.1007/11672142_26</a>.","apa":"Chatterjee, K., Majumdar, R., &#38; Henzinger, T. A. (2006). Markov decision processes with multiple objectives (Vol. 3884, pp. 325–336). Presented at the STACS: Theoretical Aspects of Computer Science, Springer. <a href=\"https://doi.org/10.1007/11672142_26\">https://doi.org/10.1007/11672142_26</a>","ista":"Chatterjee K, Majumdar R, Henzinger TA. 2006. Markov decision processes with multiple objectives. STACS: Theoretical Aspects of Computer Science, LNCS, vol. 3884, 325–336.","ieee":"K. Chatterjee, R. Majumdar, and T. A. Henzinger, “Markov decision processes with multiple objectives,” presented at the STACS: Theoretical Aspects of Computer Science, 2006, vol. 3884, pp. 325–336.","mla":"Chatterjee, Krishnendu, et al. <i>Markov Decision Processes with Multiple Objectives</i>. Vol. 3884, Springer, 2006, pp. 325–36, doi:<a href=\"https://doi.org/10.1007/11672142_26\">10.1007/11672142_26</a>."},"date_published":"2006-02-14T00:00:00Z","publication_status":"published","extern":1,"conference":{"name":"STACS: Theoretical Aspects of Computer Science"},"date_updated":"2021-01-12T07:59:38Z","month":"02","page":"325 - 336","doi":"10.1007/11672142_26","day":"14","author":[{"full_name":"Krishnendu Chatterjee","id":"2E5DCA20-F248-11E8-B48F-1D18A9856A87","last_name":"Chatterjee","first_name":"Krishnendu","orcid":"0000-0002-4561-241X"},{"full_name":"Majumdar, Ritankar S","last_name":"Majumdar","first_name":"Ritankar"},{"orcid":"0000−0002−2985−7724","full_name":"Thomas Henzinger","id":"40876CD8-F248-11E8-B48F-1D18A9856A87","last_name":"Henzinger","first_name":"Thomas A"}],"type":"conference","alternative_title":["LNCS"],"acknowledgement":"This research was supported in part by the AFOSR MURI grant F49620-00-1-0327, and the NSF grants CCR-0225610, CCR-0234690, and CCR-0427202.","status":"public","title":"Markov decision processes with multiple objectives","quality_controlled":0,"publisher":"Springer","year":"2006","volume":3884,"publist_id":"161","date_created":"2018-12-11T12:09:26Z","intvolume":"      3884"}