Planning for conjunctive goals
Artificial Intelligence
Dynamic programming: deterministic and stochastic models
Dynamic programming: deterministic and stochastic models
The complexity of Markov decision processes
Mathematics of Operations Research
Arthur-Merlin games: a randomized proof system, and a hierarchy of complexity class
Journal of Computer and System Sciences - 17th Annual ACM Symposium in the Theory of Computing, May 6-8, 1985
A survey of algorithmic methods for partially observed Markov decision processes
Annals of Operations Research
The complexity of stochastic games
Information and Computation
The computational complexity of propositional STRIPS planning
Artificial Intelligence
A subexponential randomized algorithm for the simple stochastic game problem
Information and Computation
An algorithm for probabilistic planning
Artificial Intelligence - Special volume on planning and scheduling
Distinguishing tests for nondeterministic and probabilistic machines
STOC '95 Proceedings of the twenty-seventh annual ACM symposium on Theory of computing
On the complexity of partially observed Markov decision processes
Theoretical Computer Science - Special issue on complexity theory and the theory of algorithms as developed in the CIS
AAAI '99/IAAI '99 Proceedings of the sixteenth national conference on Artificial intelligence and the eleventh Innovative applications of artificial intelligence conference innovative applications of artificial intelligence
Complexity of finite-horizon Markov decision process problems
Journal of the ACM (JACM)
Introduction To Automata Theory, Languages, And Computation
Introduction To Automata Theory, Languages, And Computation
Probabilistic Two-Way Machines
Proceedings on Mathematical Foundations of Computer Science
MFCS '97 Proceedings of the 22nd International Symposium on Mathematical Foundations of Computer Science
Some Recursive Unsolvable Problems Relating to Isolated Cutpoints in Probabilistic Automata
Proceedings of the Fourth Colloquium on Automata, Languages and Programming
Decision Problems for Semi-Thue Systems with a Few Rules
LICS '96 Proceedings of the 11th Annual IEEE Symposium on Logic in Computer Science
Complexity Issues in Markov Decision Processes
COCO '98 Proceedings of the Thirteenth Annual IEEE Conference on Computational Complexity
Algorithms for sequential decision-making
Algorithms for sequential decision-making
Exact and approximate algorithms for partially observable markov decision processes
Exact and approximate algorithms for partially observable markov decision processes
Finite-memory control of partially observable systems
Finite-memory control of partially observable systems
Complexity results for infinite-horizon markov decision processes
Complexity results for infinite-horizon markov decision processes
Algorithms for partially observable markov decision processes
Algorithms for partially observable markov decision processes
Introduction to probabilistic automata (Computer science and applied mathematics)
Introduction to probabilistic automata (Computer science and applied mathematics)
Nonapproximability results for partially observable Markov decision processes
Journal of Artificial Intelligence Research
The computational complexity of probabilistic planning
Journal of Artificial Intelligence Research
Complexity of probabilistic planning under average rewards
IJCAI'01 Proceedings of the 17th international joint conference on Artificial intelligence - Volume 1
Probabilistic propositional planning: representations and complexity
AAAI'97/IAAI'97 Proceedings of the fourteenth national conference on artificial intelligence and ninth conference on Innovative applications of artificial intelligence
Learning finite-state controllers for partially observable environments
UAI'99 Proceedings of the Fifteenth conference on Uncertainty in artificial intelligence
On the complexity of solving Markov decision problems
UAI'95 Proceedings of the Eleventh conference on Uncertainty in artificial intelligence
Survey A survey of computational complexity results in systems and control
Automatica (Journal of IFAC)
Multiagent coordination by Extended Markov Tracking
Proceedings of the fourth international joint conference on Autonomous agents and multiagent systems
Dynamics based control with an application to area-sweeping problems
Proceedings of the 6th international joint conference on Autonomous agents and multiagent systems
Dynamics based control with PSRs
Proceedings of the 7th international joint conference on Autonomous agents and multiagent systems - Volume 1
Reasoning about actions with sensing under qualitative and probabilistic uncertainty
ACM Transactions on Computational Logic (TOCL)
Probabilistic Acceptors for Languages over Infinite Words
SOFSEM '09 Proceedings of the 35th Conference on Current Trends in Theory and Practice of Computer Science
Decision making in large-scale domains: a case study
Proceedings of the 2006 conference on ECAI 2006: 17th European Conference on Artificial Intelligence August 29 -- September 1, 2006, Riva del Garda, Italy
Compact, convex upper bound iteration for approximate POMDP planning
AAAI'06 proceedings of the 21st national conference on Artificial intelligence - Volume 2
The Effect of Tossing Coins in Omega-Automata
CONCUR 2009 Proceedings of the 20th International Conference on Concurrency Theory
Indefinite-horizon POMDPs with action-based termination
AAAI'07 Proceedings of the 22nd national conference on Artificial intelligence - Volume 2
A framework for sequential planning in multi-agent settings
Journal of Artificial Intelligence Research
Quantitative model checking revisited: neither decidable nor approximable
FORMATS'07 Proceedings of the 5th international conference on Formal modeling and analysis of timed systems
On decision problems for probabilistic Büchi automata
FOSSACS'08/ETAPS'08 Proceedings of the Theory and practice of software, 11th international conference on Foundations of software science and computational structures
On the Topology of Discrete Strategies
International Journal of Robotics Research
Probabilistic automata on finite words: decidable and undecidable problems
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming: Part II
Qualitative analysis of partially-observable Markov decision processes
MFCS'10 Proceedings of the 35th international conference on Mathematical foundations of computer science
On model checking techniques for randomized distributed systems
IFM'10 Proceedings of the 8th international conference on Integrated formal methods
Upper confidence trees with short term partial information
EvoApplications'11 Proceedings of the 2011 international conference on Applications of evolutionary computation - Volume Part I
HTN-style planning in relational POMDPs using first-order FSCs
KI'11 Proceedings of the 34th Annual German conference on Advances in artificial intelligence
Journal of the ACM (JACM)
Exploiting symmetries for single- and multi-agent Partially Observable Stochastic Domains
Artificial Intelligence
Feature reinforcement learning in practice
EWRL'11 Proceedings of the 9th European conference on Recent Advances in Reinforcement Learning
Verification of partial-information probabilistic systems using counterexample-guided refinements
ATVA'12 Proceedings of the 10th international conference on Automated Technology for Verification and Analysis
Diagnosability in concurrent probabilistic systems
Proceedings of the 2013 international conference on Autonomous agents and multi-agent systems
A survey of partial-observation stochastic parity games
Formal Methods in System Design
Scalable and efficient bayes-adaptive reinforcement learning based on monte-carlo tree search
Journal of Artificial Intelligence Research
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Automated planning, the problem of how an agent achieves a goal given a repertoire of actions, is one of the foundational and most widely studied problems in the AI literature. The original formulation of the problem makes strong assumptions regarding the agent's knowledge and control over the world, namely that its information is complete and correct, and that the results of its actions are deterministic and known. Recent research in planning under uncertainty has endeavored te relax these assumptions, providing formal and computation models wherein the agent has incomplete or noisy information about the world and has noisy sensors and effectors. This research has mainly taken one of two approaches: extend the classical planning paradigm to a semantics that admits uncertainty, or adopt another framework for approaching the problem, most commonly the Markov Decision Process (MDP) model. This paper presents a complexity analysis of planning under uncertainty. It begins with the "probabilistic classical planning" problem, showing that problem to be formally undecidable. This fundamental result is then applied to a broad class of stochastic optimization problems, in brief any problem statement where the agent (a) operates over an infinite or indefinite time horizon, and (b) has available only probabilistic information about the system's state. Undecidability is established for policy-existence problems for partially observable infinite-horizon Markov decision processes under discounted and undiscounted total reward models, average-reward models, and state-avoidance models. The results also apply to corresponding approximation problems with undiscounted objective functions. The paper answers a significant open question raised by Papadimitriou and Tsitsiklis [Math. Oper. Res. 12 (3) (1987) 441-450] about the complexity of infinite horizon POMDPs.