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Networks of learning automata and limiting games Authors: K. Verbeeck, P. Vrancx and A. Nowé Publication Year: 2007 Pages: 171-183
Abstract: Abstract. Learning Automata (LA) were recently shown to be valuable
tools for designing Multi-Agent Reinforcement Learning algorithms. One
of the principal contributions of LA theory is that a set of decentralized,
independent learning automata is able to control a finite Markov Chain
with unknown transition probabilities and rewards. This result was re-
cently extended to Markov Games and analyzed with the use of limiting
games. In this paper we continue this analysis but we assume here that
our agents are fully ignorant about the other agents in the environment,
i.e. they can only observe themselves they don't know how many other
agents are present in the environment, the actions these other agents
took nor the rewards they received for this, nor the location they
occupy in the state space. We prove that in Markov Games, where agents
have this limited type of observability, a network of independent LA is
still able to converge to an equilibrium point of the underlying limiting
game, provided a common ergodic assumption and provided the agents
do not interfere each other's transition probabilities.
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