ARES:Adaptive receding-horizon synthesis of optimal plans


We introduce ARES, an efficient approximation algorithm for generating optimal plans (action sequences) that take an initial state of a Markov Decision Process (MDP) to a state whose cost is below a specified (convergence) threshold. ARES uses Particle Swarm Optimization, with adaptive sizing for both the receding horizon and the particle swarm. Inspired by Importance Splitting, the length of the horizon and the number of particles are chosen such that at least one particle reaches a next-level state, that is, a state where the cost decreases by a required delta from the previous-level state. The level relation on states and the plans constructed by ARES implicitly define a Lyapunov function and an optimal policy, respectively, both of which could be explicitly generated by applying ARES to all states of the MDP, up to some topological equivalence relation. We also assess the effectiveness of ARES by statistically evaluating its rate of success in generating optimal plans. The ARES algorithm resulted from our desire to clarify if flying in V-formation is a flocking policy that optimizes energy conservation, clear view, and velocity alignment. That is, we were interested to see if one could find optimal plans that bring a flock from an arbitrary initial state to a state exhibiting a single connected V-formation. For flocks with 7 birds, ARES is able to generate a plan that leads to a V-formation in 95% of the 8,000 random initial configurations within 63 s, on average. ARES can also be easily customized into a model-predictive controller (MPC) with an adaptive receding horizon and statistical guarantees of convergence. To the best of our knowledge, our adaptive-sizing approach is the first to provide convergence guarantees in receding-horizon techniques.

Publication DOI:
Divisions: College of Engineering & Physical Sciences
Funding Information: The first author and the last author would like to thank Jan Kret?nsk? for very valuable feedback. This work was partially supported by the Doctoral Program Logical Methods in Computer Science and the Austrian National Research Network RiSE/SHiNE (S11405-
Additional Information: © Springer-Verlag GmbH Germany 2017. The final publication is available at Springer via
Event Title: 23rd International Conference on Tools and Algorithms for the Construction and Analysis of Systems, TACAS 2017 held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2017
Event Type: Other
Event Dates: 2017-04-22 - 2017-04-29
Uncontrolled Keywords: Theoretical Computer Science,Computer Science(all)
ISBN: 9783662545799
Last Modified: 25 Mar 2024 08:09
Date Deposited: 07 Dec 2018 11:43
Full Text Link: https://arxiv.o ... /abs/1612.07059
Related URLs: http://www.scop ... tnerID=8YFLogxK (Scopus URL)
https://link.sp ... -662-54580-5_17 (Publisher URL)
PURE Output Type: Conference contribution
Published Date: 2017-03-31
Published Online Date: 2017-03-31
Accepted Date: 2017-01-01
Authors: Lukina, Anna
Esterle, Lukas (ORCID Profile 0000-0002-0248-1552)
Hirsch, Christian
Bartocci, Ezio
Yang, Junxing
Tiwari, Ashish
Smolka, Scott A.
Grosu, Radu



Version: Accepted Version

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