1,720 research outputs found
A decomposition technique for pursuit evasion games with many pursuers
Here we present a decomposition technique for a class of differential games.
The technique consists in a decomposition of the target set which produces, for
geometrical reasons, a decomposition in the dimensionality of the problem.
Using some elements of Hamilton-Jacobi equations theory, we find a relation
between the regularity of the solution and the possibility to decompose the
problem. We use this technique to solve a pursuit evasion game with multiple
agents
Decomposition of Differential Games
This paper provides a decomposition technique for the purpose of simplifying
the solution of certain zero-sum differential games. The games considered
terminate when the state reaches a target, which can be expressed as the union
of a collection of target subsets; the decomposition consists of replacing the
original target by each of the target subsets. The value of the original game
is then obtained as the lower envelope of the values of the collection of games
resulting from the decomposition, which can be much easier to solve than the
original game. Criteria are given for the validity of the decomposition. The
paper includes examples, illustrating the application of the technique to
pursuit/evasion games, where the decomposition arises from considering the
interaction of individual pursuer/evader pairs.Comment: 10 pages, 2 figure
Deep Reinforcement Learning for Swarm Systems
Recently, deep reinforcement learning (RL) methods have been applied
successfully to multi-agent scenarios. Typically, these methods rely on a
concatenation of agent states to represent the information content required for
decentralized decision making. However, concatenation scales poorly to swarm
systems with a large number of homogeneous agents as it does not exploit the
fundamental properties inherent to these systems: (i) the agents in the swarm
are interchangeable and (ii) the exact number of agents in the swarm is
irrelevant. Therefore, we propose a new state representation for deep
multi-agent RL based on mean embeddings of distributions. We treat the agents
as samples of a distribution and use the empirical mean embedding as input for
a decentralized policy. We define different feature spaces of the mean
embedding using histograms, radial basis functions and a neural network learned
end-to-end. We evaluate the representation on two well known problems from the
swarm literature (rendezvous and pursuit evasion), in a globally and locally
observable setup. For the local setup we furthermore introduce simple
communication protocols. Of all approaches, the mean embedding representation
using neural network features enables the richest information exchange between
neighboring agents facilitating the development of more complex collective
strategies.Comment: 31 pages, 12 figures, version 3 (published in JMLR Volume 20
Two-Dimensional Pursuit-Evasion in a Compact Domain with Piecewise Analytic Boundary
In a pursuit-evasion game, a team of pursuers attempt to capture an evader.
The players alternate turns, move with equal speed, and have full information
about the state of the game. We consider the most restictive capture condition:
a pursuer must become colocated with the evader to win the game. We prove two
general results about pursuit-evasion games in topological spaces. First, we
show that one pursuer has a winning strategy in any CAT(0) space under this
restrictive capture criterion. This complements a result of Alexander, Bishop
and Ghrist, who provide a winning strategy for a game with positive capture
radius. Second, we consider the game played in a compact domain in Euclidean
two-space with piecewise analytic boundary and arbitrary Euler characteristic.
We show that three pursuers always have a winning strategy by extending recent
work of Bhadauria, Klein, Isler and Suri from polygonal environments to our
more general setting.Comment: 21 pages, 6 figure
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