Inthesummerof2008, reinforcementlearningresearchersfromaroundtheworld gathered in the north of France for a week of talks and discussions on reinfor- ment learning, on how it could be made more e?cient, applied to a broader range of applications, and utilized at more abstract and symbolic levels. As a participant in this 8th European Workshop on Reinforcement Learning, I was struck by both the quality and quantity of the presentations. There were four full days of short talks, over 50 in all, far more than there have been at any p- vious meeting on reinforcement learning in Europe, or indeed, anywhere else in the world. There was an air of excitement as substantial progress was reported in many areas including Computer Go, robotics, and ?tted methods. Overall, the work reported seemed to me to be an excellent, broad, and representative sample of cutting-edge reinforcement learning research. Some of the best of it is collected and published in this volume. The workshopandthe paperscollectedhere provideevidence thatthe ?eldof reinforcement learning remains vigorous and varied. It is appropriate to re?ect on some of the reasons for this. One is that the ?eld remains focused on a pr- lem - sequential decision making - without prejudice as to solution methods. Another is the existence of a common terminology and body of theory

The author considers the problem of sequential probability forecasting in the most general setting, where the observed data may exhibit an arbitrary form of stochastic dependence. All the results presented are theoretical, but they concern the foundations of some problems in such applied areas as machine learning, information theory and data compression.

Stationarity is a very general, qualitative assumption, that can be assessed on the basis of application specifics. It is thus a rather attractive assumption to base statistical analysis on, especially for problems for which less general qualitative assumptions, such as independence or finite memory, clearly fail. However, it has long been considered too general to be able to make statistical inference. One of the reasons for this is that rates of convergence, even of frequencies to the mean, are not available under this assumption alone. Recently, it has been shown that, while some natural and simple problems, such as homogeneity, are indeed provably impossible to solve if one only assumes that the data is stationary (or stationary ergodic), many others can be solved with rather simple and intuitive algorithms. The latter include clustering and change point estimation among others. In this volume these results are summarize. The emphasis is on asymptotic consistency, since this the strongest property one can obtain assuming stationarity alone. While for most of the problem for which a solution is found this solution is algorithmically realizable, the main objective in this area of research, the objective which is only partially attained, is to understand what is possible and what is not possible to do for stationary time series. The considered problems include homogeneity testing (the so-called two sample problem), clustering with respect to distribution, clustering with respect to independence, change point estimation, identity testing, and the general problem of composite hypotheses testing. For the latter problem, a topological criterion for the existence of a consistent test is presented. In addition, a number of open problems is presented.