Dynamic programming: deterministic and stochastic models
Dynamic programming: deterministic and stochastic models
The quickhull algorithm for convex hulls
ACM Transactions on Mathematical Software (TOMS)
Variable Resolution Discretization in Optimal Control
Machine Learning
Making Rational Decisions Using Adaptive Utility Elicitation
Proceedings of the Seventeenth National Conference on Artificial Intelligence and Twelfth Conference on Innovative Applications of Artificial Intelligence
New approaches to optimization and utility elicitation in autonomic computing
AAAI'05 Proceedings of the 20th national conference on Artificial intelligence - Volume 1
Efficient solution algorithms for factored MDPs
Journal of Artificial Intelligence Research
Planning and acting in partially observable stochastic domains
Artificial Intelligence
Constraint-based optimization and utility elicitation using the minimax decision criterion
Artificial Intelligence
Regret-based reward elicitation for Markov decision processes
UAI '09 Proceedings of the Twenty-Fifth Conference on Uncertainty in Artificial Intelligence
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Markov Decision Processes (MDPs) provide a mathematical framework for modelling decision-making of agents acting in stochastic environments, in which transitions probabilities model the environment dynamics and a reward function evaluates the agent's behaviour. Lately, however, special attention has been brought to the difficulty of modelling precisely the reward function, which has motivated research on MDP with imprecisely specified reward. Some of these works exploit the use of nondominated policies, which are optimal policies for some instantiation of the imprecise reward function. An algorithm that calculates nondominated policies is π Witness, and nondominated policies are used to take decision under the minimax regret evaluation. An interesting matter would be defining a small subset of nondominated policies so that the minimax regret can be calculated faster, but accurately. We modified π Witness to do so. We also present the π Hull algorithm to calculate nondominated policies adopting a geometric approach. Under the assumption that reward functions are linearly defined on a set of features, we show empirically that pHull can be faster than our modified version of π Witness.