Although well understood in the single-agent framework, the use of traditional reinforcement learning (RL) algorithms in multi-agent systems (MAS) is not always justified. The feedback an agent experiences in a MAS, is usually influenced by the other agents present in the system. Multi agent environments are therefore non-stationary and convergence and optimality guarantees of RL algorithms are lost. To better understand the dynamics of traditional RL algorithms we analyze the learning process in terms of evolutionary dynamics. More specifically we show how the Replicator Dynamics (RD) can be used as a model for Q-learning in games. The dynamical equations of Q-learning are derived and illustrated by some well chosen experiments. Both reveal an interesting connection between the exploitationexploration scheme from RL and the selection-mutation mechanisms from evolutionary game theory.

Learning automata (LA) were recently shown to be valuable tools for designing multiagent reinforcement learning algorithms. One of the principal contributions of the LA theory is that a set of decentralized independent LA is able to control a finite Markov chain with unknown transition probabilities and rewards. In this paper, we propose to extend this algorithm to Markov games--a straightforward extension of single-agent Markov decision problems to distributed multiagent decision problems. We show that under the same ergodic assumptions of the original theorem, the extended algorithm will converge to a pure equilibrium point between agent policies.

Although well understood in the single-agent framework, the use of traditional reinforcement learning (RL) algorithms in multi-agent systems (MAS) is not always justified. The feedback an agent experiences in a MAS, is usually influenced by the other agents present in the system. Multi agent environments are therefore non-stationary and convergence and optimality guarantees of RL algorithms are lost. To better understand the dynamics of traditional RL algorithms we analyze the learning process in terms of evolutionary dynamics. More specifically we show how the Replicator Dynamics (RD) can be used as a model for Q-learning in games. The dynamical equations of Q-learning are derived and illustrated by some well chosen experiments. Both reveal an interesting connection between the exploitationexploration scheme from RL and the selection-mutation mechanisms from evolutionary game theory.

In this paper we introduce a new multi-agent reinforcement learning algorithm, called exploring selfish reinforcement learning (ESRL). ESRL allows agents to reach optimal solutions in repeated non-zero sum games with stochastic rewards, by using coordinated exploration. First, two ESRL algorithms for respectively common interest and conflicting interest games are presented. Both ESRL algorithms are based on the same idea, i.e. an agent explores by temporarily excluding some of the local actions from its private action space, to give the team of agents the opportunity to look for better solutions in a reduced joint action space. In a latter stage these two algorithms are transformed into one generic algorithm which does not assume that the type of the game is known in advance. ESRL is able to find the Pareto optimal solution in common interest games without communication. In conflicting interest games ESRL only needs limited communication to learn a fair periodical policy, resulting in a good overall policy. Important to know is that ESRL agents are independent in the sense that they only use their own action choices and rewards to base their decisions on, that ESRL agents are flexible in learning different solution concepts and they can handle both stochastic, possible delayed rewards and asynchronous action selection. A real-life experiment, i.e. adaptive load-balancing of parallel applications is added.K. Verbeeck (B) Computational Modeling Lab (COMO), Vrije Universiteit Brussel, Brussels, Belgium

The present study proposes a new selection hyper-heuristic providing several adaptive features to cope with the requirements of managing different heuristic sets. The approach suggested provides an intelligent way of selecting heuristics, determines effective heuristic pairs and adapts the parameters of certain heuristics online. In addition, an adaptive list-based threshold accepting mechanism has been developed. It enables deciding whether to accept or not the solutions generated by the selected heuristics. The resulting approach won the first Cross Domain Heuristic Search Challenge against 19 high-level algorithms. The detailed empirical results concerning the behaviour of the hyper-heuristic and its sub-mechanisms will be presented at the conference.