45,266 research outputs found
An analysis of stochastic shortest path problems
Caption title. "October 1988."Includes bibliographical references.Supported by the National Science Foundation under grant NSF-ECS-8519058 Supported by the Army Research Office under grant DAAL03-86-K-0171 The second author supported by a Presidential Young Investigator Award with matching funds from IBM, Inc. and Dupont, Inc.by Dimitri P. Bertsekas and John N. Tsitsiklis
Monotone Causality in Opportunistically Stochastic Shortest Path Problems
When traveling through a graph with an accessible deterministic path to a
target, is it ever preferable to resort to stochastic node-to-node transitions
instead? And if so, what are the conditions guaranteeing that such a stochastic
optimal routing policy can be computed efficiently? We aim to answer these
questions here by defining a class of Opportunistically Stochastic Shortest
Path (OSSP) problems and deriving sufficient conditions for applicability of
non-iterative label-setting methods. The usefulness of this framework is
demonstrated in two very different contexts: numerical analysis and autonomous
vehicle routing. We use OSSPs to derive causality conditions for
semi-Lagrangian discretizations of anisotropic Hamilton-Jacobi equations. We
also use a Dijkstra-like method to solve OSSPs optimizing the timing and
urgency of lane change maneuvers for an autonomous vehicle navigating road
networks with a heterogeneous traffic load
A tutorial on recursive models for analyzing and predicting path choice behavior
The problem at the heart of this tutorial consists in modeling the path
choice behavior of network users. This problem has been extensively studied in
transportation science, where it is known as the route choice problem. In this
literature, individuals' choice of paths are typically predicted using discrete
choice models. This article is a tutorial on a specific category of discrete
choice models called recursive, and it makes three main contributions: First,
for the purpose of assisting future research on route choice, we provide a
comprehensive background on the problem, linking it to different fields
including inverse optimization and inverse reinforcement learning. Second, we
formally introduce the problem and the recursive modeling idea along with an
overview of existing models, their properties and applications. Third, we
extensively analyze illustrative examples from different angles so that a
novice reader can gain intuition on the problem and the advantages provided by
recursive models in comparison to path-based ones
Expectations or Guarantees? I Want It All! A crossroad between games and MDPs
When reasoning about the strategic capabilities of an agent, it is important
to consider the nature of its adversaries. In the particular context of
controller synthesis for quantitative specifications, the usual problem is to
devise a strategy for a reactive system which yields some desired performance,
taking into account the possible impact of the environment of the system. There
are at least two ways to look at this environment. In the classical analysis of
two-player quantitative games, the environment is purely antagonistic and the
problem is to provide strict performance guarantees. In Markov decision
processes, the environment is seen as purely stochastic: the aim is then to
optimize the expected payoff, with no guarantee on individual outcomes.
In this expository work, we report on recent results introducing the beyond
worst-case synthesis problem, which is to construct strategies that guarantee
some quantitative requirement in the worst-case while providing an higher
expected value against a particular stochastic model of the environment given
as input. This problem is relevant to produce system controllers that provide
nice expected performance in the everyday situation while ensuring a strict
(but relaxed) performance threshold even in the event of very bad (while
unlikely) circumstances. It has been studied for both the mean-payoff and the
shortest path quantitative measures.Comment: In Proceedings SR 2014, arXiv:1404.041
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