Variations on the Stochastic Shortest Path Problem

Randour, Mickaël; Raskin, Jean-François; Sankur, Ocan

doi:10.1007/978-3-662-46081-8_1

Cited by 30 publications

(38 citation statements)

References 22 publications

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“…With the above model, we can abstract the robot state by the cell coordinate in which it belongs, namely, (x c , y c ) ∈ Round-Robin Figure 7: The normalized distribution of the total cost of accepting cyclic paths from 1000 Monte Carlo simulations under the optimal plan suffix (left) and the Round-Robin policy (right), for task (19).…”

Section: A Model Descriptionmentioning

confidence: 99%

“…In this case, we demonstrate how the relaxed plan prefix and suffix can be synthesized under scenarios where no AECs can be found. In particular, we consider the surveillance task in (19) but more obstacles are placed in the workspace as shown in Figure 10. The center cell (5m, 5m) has probability 0.9 of being occupied by an obstacle and the four cells above and on the left have probability 0.01 of being occupied by an obstacle.…”

Section: E Surveillance With Clustered Obstaclesmentioning

confidence: 99%

“…On the other hand, the seminal works [19], [20] consider MDPs with multi-dimensional weights under multi-percentile queries that may be conflicting. However, most of the above work does not address cost optimization over the suffix of the system trajectory within the AECs, neither does it address the case where no AECs can be found in the product automaton, which are the main contributions here.…”

Section: Introductionmentioning

confidence: 99%

“…Most aforementioned work [4], [17], [19]- [22], [27] relies on the assumption that the product automaton contains at least one AEC. However, in many situations this assumption does not hold so that the probability of satisfying the task under any policy is zero.…”

Section: Introductionmentioning

confidence: 99%

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Probabilistic Motion Planning Under Temporal Tasks and Soft Constraints

Guo

Zavlanos

2018

IEEE Trans. Automat. Contr.

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This paper studies motion planning of a mobile robot under uncertainty. The control objective is to synthesize a finite-memory control policy, such that a high-level task specified as a Linear Temporal Logic (LTL) formula is satisfied with a desired high probability. Uncertainty is considered in the workspace properties, robot actions, and task outcomes, giving rise to a Markov Decision Process (MDP) that models the proposed system. Different from most existing methods, we consider cost optimization both in the prefix and suffix of the system trajectory. We also analyze the potential trade-off between reducing the mean total cost and maximizing the probability that the task is satisfied. The proposed solution is based on formulating two coupled Linear Programs, for the prefix and suffix, respectively, and combining them into a multi-objective optimization problem, which provides provable guarantees on the probabilistic satisfiability and the total cost optimality. We show that our method outperforms relevant approaches that employ Round-Robin policies in the trajectory suffix. Furthermore, we propose a new control synthesis algorithm to minimize the frequency of reaching a bad state when the probability of satisfying the tasks is zero, in which case most existing methods return no solution. We validate the above schemes via both numerical simulations and experimental studies.

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Section: A Model Descriptionmentioning

confidence: 99%

Section: E Surveillance With Clustered Obstaclesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Probabilistic Motion Planning Under Temporal Tasks and Soft Constraints

Guo

Zavlanos

2018

IEEE Trans. Automat. Contr.

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“…It allows to express various (quantitative or qualitative) properties over the model, and to synthesize strategies accordingly. This new field of research is very rich and ambitious, with various types of objective combinations (see for instance [2,18] for recent overviews). For recent developments on MDPs, one can cite:…”

Section: Introductionmentioning

confidence: 99%

Multi-weighted Markov Decision Processes with Reachability Objectives

Bouyer¹,

Gonzalez²,

Markey³

et al. 2018

Electron. Proc. Theor. Comput. Sci.

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In this paper, we are interested in the synthesis of schedulers in double-weighted Markov decision processes, which satisfy both a percentile constraint over a weighted reachability condition, and a quantitative constraint on the expected value of a random variable defined using a weighted reachability condition. This problem is inspired by the modelization of an electric-vehicle charging problem. We study the cartography of the problem, when one parameter varies, and show how a partial cartography can be obtained via two sequences of opimization problems. We discuss completeness and feasability of the method.

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Simple Strategies in Multi-Objective MDPs

Delgrange

Katoen

Quatmann

et al. 2020

Tools and Algorithms for the Construction and Analysis of Systems

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We consider the verification of multiple expected reward objectives at once on Markov decision processes (MDPs). This enables a trade-off analysis among multiple objectives by obtaining a Pareto front. We focus on strategies that are easy to employ and implement. That is, strategies that are pure (no randomization) and have bounded memory. We show that checking whether a point is achievable by a pure stationary strategy is NP-complete, even for two objectives, and we provide an MILP encoding to solve the corresponding problem. The bounded memory case is treated by a product construction. Experimental results using Storm and Gurobi show the feasibility of our algorithms.

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Variations on the Stochastic Shortest Path Problem

Abstract: International audienc

Cited by 30 publications

References 22 publications

Probabilistic Motion Planning Under Temporal Tasks and Soft Constraints

Probabilistic Motion Planning Under Temporal Tasks and Soft Constraints

Multi-weighted Markov Decision Processes with Reachability Objectives

Simple Strategies in Multi-Objective MDPs

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