Sequential decision problems that involve multiple objectives are prevalent. Consider for example a driver of a semi-autonomous car who may want to optimize competing objectives such as travel time and the effort associated with manual driving. We introduce a rich model called Lexicographic MDP (LMDP) and a corresponding planning algorithm called LVI that generalize previous work by allowing for conditional lexicographic preferences with slack. We analyze the convergence characteristics of LVI and establish its game theoretic properties. The performance of LVI in practice is tested within a realistic benchmark problem in the domain of semi-autonomous driving. Finally, we demonstrate how GPU-based optimization can improve the scalability of LVI and other value iteration algorithms for MDPs.

We present a general formal model called MODIA that can tackle a central challenge for autonomous vehicles (AVs), namely the ability to interact with an unspecified, large number of world entities. In MODIA, a collection of possible decisionproblems (DPs), known a priori, are instantiated online and executed as decision-components (DCs), unknown a priori. To combine the individual action recommendations of the DCs into a single action, we propose the lexicographic executor action function (LEAF) mechanism. We analyze the complexity of MODIA and establish LEAF's relation to regret minimization. Finally, we implement MODIA and LEAF using collections of partially observable Markov decision process (POMDP) DPs, and use them for complex AV intersection decision-making. We evaluate the approach in six scenarios within a realistic vehicle simulator and present its use on an AV prototype.

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