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We consider some classical optimization problems in path planning and networktransport, and we introduce new auction-based algorithms for their optimal andsuboptimal solution. The algorithms are based on mathematical ideas that arerelated to competitive bidding by persons for objects and the attendant marketequilibrium, which underlie auction processes. However, the starting point ofour algorithms is different, namely weighted and unweighted path constructionin directed graphs, rather than assignment of persons to objects. The newalgorithms have several potential advantages over existing methods: they areempirically faster in some important contexts, such as max-flow, they arewell-suited for on-line replanning, and they can be adapted to distributedasynchronous operation. Moreover, they allow arbitrary initial prices, withoutcomplementary slackness restrictions, and thus are better-suited to takeadvantage of reinforcement learning methods that use off-line training withdata, as well as on-line training during real-time operation. The newalgorithms may also find use in reinforcement learning contexts involvingapproximation, such as multistep lookahead and tree search schemes, and/orrollout algorithms.

New Auction Algorithms for Path Planning, Network Transport, and Reinforcement Learning