Merging BSP trees yields polyhedral set operations
SIGGRAPH '90 Proceedings of the 17th annual conference on Computer graphics and interactive techniques
An Algorithm for Finding Best Matches in Logarithmic Expected Time
ACM Transactions on Mathematical Software (TOMS)
Variable Resolution Discretization in Optimal Control
Machine Learning
The Complexity of Decentralized Control of Markov Decision Processes
Mathematics of Operations Research
Dynamic programming for structured continuous Markov decision problems
UAI '04 Proceedings of the 20th conference on Uncertainty in artificial intelligence
Solving factored MDPs with continuous and discrete variables
UAI '04 Proceedings of the 20th conference on Uncertainty in artificial intelligence
Effective approaches for partial satisfaction (over-subscription) planning
AAAI'04 Proceedings of the 19th national conference on Artifical intelligence
Dynamic programming for partially observable stochastic games
AAAI'04 Proceedings of the 19th national conference on Artifical intelligence
Point-based dynamic programming for DEC-POMDPs
AAAI'06 proceedings of the 21st national conference on Artificial intelligence - Volume 2
Lazy approximation for solving continuous finite-horizon MDPs
AAAI'05 Proceedings of the 20th national conference on Artificial intelligence - Volume 3
Anytime coordination using separable bilinear programs
AAAI'07 Proceedings of the 22nd national conference on Artificial intelligence - Volume 1
Decentralized control of cooperative systems: categorization and complexity analysis
Journal of Artificial Intelligence Research
Solving transition independent decentralized Markov decision processes
Journal of Artificial Intelligence Research
Solving factored MDPs with hybrid state and action variables
Journal of Artificial Intelligence Research
A heuristic search approach to planning with continuous resources in stochastic domains
Journal of Artificial Intelligence Research
Sequential optimality and coordination in multiagent systems
IJCAI'99 Proceedings of the 16th international joint conference on Artifical intelligence - Volume 1
A fast analytical algorithm for solving Markov decision processes with real-valued resources
IJCAI'07 Proceedings of the 20th international joint conference on Artifical intelligence
Planning with continuous resources in stochastic domains
IJCAI'05 Proceedings of the 19th international joint conference on Artificial intelligence
Planning under continuous time and resource uncertainty: a challenge for AI
UAI'02 Proceedings of the Eighteenth conference on Uncertainty in artificial intelligence
Incremental pruning: a simple, fast, exact method for partially observable Markov decision processes
UAI'97 Proceedings of the Thirteenth conference on Uncertainty in artificial intelligence
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An approximation method is proposed that solves a class of Decentralized hybrid Markov Decision Processes (DEC-HMDPs). These DEC-HMDPs have both discrete and continuous state variables and represent individual agents with continuous measurable state-spaces, such as resources. Adding to the natural complexity of decentralized problems, continuous state variables lead to a blowup in potential decision points. Representing value functions as Rectangular Piecewise Constant (RPWC) functions, we formalize and detail an extension to the Coverage Set algorithm (CSA) (Becker et al., J Artif Intell Res, 22, 2004) that solves transition independent DEC-HMDPs with controlled error. The resource constraints of each agent lead to problems that are over-subscribed in the number of agents, that is where some agents have no role to play. Based on our extension to the CSA, two heuristics are proposed that allow A*-like search to find the minimal optimal team of agents that is solution to a given problem. We apply and test our algorithms on a range of multi-robot exploration problems with continuous resource constraints.