By Ana L. C. Bazzan, Denise de Oliveira (auth.), Karl Tuyls, Ann Nowe, Zahia Guessoum, Daniel Kudenko (eds.)

This booklet comprises chosen and revised papers of the eu Symposium on Adaptive and studying brokers and Multi-Agent platforms (ALAMAS), variants 2005, 2006 and 2007, held in Paris, Brussels and Maastricht. The target of the ALAMAS symposia, and this linked ebook, is to extend expertise and curiosity in version and studying for unmarried brokers and mul- agent structures, and inspire collaboration among computing device studying specialists, softwareengineeringexperts,mathematicians,biologistsandphysicists,andgive a consultant overviewof present country of a?airs during this quarter. it really is an inclusive discussion board the place researchers can current fresh paintings and talk about their most up-to-date rules for a ?rst time with their friends. Thesymposiaseriesfocusesonallaspectsofadaptiveandlearningagentsand multi-agent structures, with a selected emphasis on find out how to adjust demonstrated studying thoughts and/or create new studying paradigms to deal with the numerous demanding situations provided by way of advanced real-world difficulties. those symposia have been an outstanding luck and supplied a discussion board for the pres- tation of latest rules and effects relating the belief of model and studying for unmarried brokers and multi-agent structures. Over those 3 versions we bought fifty one submissions, of which 17 have been rigorously chosen, together with one invited paper of this year’s invited speaker Simon Parsons. this can be a very c- petitive reputation cost of roughly 31%, which, including evaluation cycles, has ended in a superb LNAI quantity. we are hoping that our readers could be encouraged by means of the papers integrated during this volume.

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Extra info for Adaptive Agents and Multi-Agent Systems III. Adaptation and Multi-Agent Learning: 5th, 6th, and 7th European Symposium, ALAMAS 2005-2007 on Adaptive and Learning Agents and Multi-Agent Systems, Revised Selected Papers

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Continuous-State Reinforcement Learning with Fuzzy Approximation 2 29 Reinforcement Learning In this section, the RL task is briefly introduced and its optimal solution is characterized. The presentation is based on [1, 2]. 2 As a result of the agent’s action uk in state xk at the discrete time step k, the state changes to xk+1 = f (xk , uk ). 3 The agent chooses actions according to its policy h : X → U , using uk = h(xk ). The goal of the agent is to learn a policy that maximizes, starting from the current moment in time (k = 0) and from any state x0 , the discounted return: ∞ ∞ γ k rk+1 = R= k=0 γ k ρ(xk , uk ) (1) k=0 where γ ∈ [0, 1) and xk+1 = f (xk , uk ) for k ≥ 0.

Q∗ = T (Q∗ ). The following result is also well-known. Theorem 1. , for any pair of functions Q and Q , it is true that T (Q) − T (Q ) ∞ ≤ γ Q − Q ∞ . The Q-value iteration (Q-iteration, for short) algorithm starts from an arbitrary Q-function Q0 and in each iteration κ updates the Q-function using the formula Qκ+1 = T (Qκ ). From Theorem 1, it follows that T has a unique fixed point, and since from (4) this point is Q∗ , the iterative scheme converges to Q∗ as κ → ∞. Q-iteration uses an a priori model of the task, in the form of the transition and reward functions f , ρ.

A range of other trading algorithms have been proposed — including those that took part in the Santa Fe double auction tournament [18,19], the reinforcement learning Roth-Erev approach (RE) [17] and the expected-profit maximizing Gjerstad-Dickhaut approach (GD) [5] — and the performance of these algorithms have been evaluated under various market conditions. However, many of the studies of trader behavior leave something to be desired. In particular, those described above, with the honorable exception of the Santa Fe tournament [18], concentrated on the efficiency of markets as a whole and on markets in which the population of traders was homogeneous (in other words they all used the same strategy for deciding what to bid).

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Adaptive Agents and Multi-Agent Systems III. Adaptation and by Ana L. C. Bazzan, Denise de Oliveira (auth.), Karl Tuyls,
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