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Fashion. the hand-coded policies can make use of a memory consisting of a limited number of memory bits. the algorithm is tested in a maze-like domain where planning is sometimes useful and the problem is to learn when it is useful. this is done by treating the policy as stochastic where the probabilities for the policy rules are used for exploration and learned via gradient descent techniques. probabilistic relational models prm ; the approach by guestrin 2003 ; see also guestrin et al. 2003a ; ; improves on the representation of value functions by using the probabilistic relational model framework prm ; getoor et al., 2001 ; . a prm models a probability distribution over a first-order representation. a crucial assumption of the approach is that the relations between objects are static. while this may not look unrealistic for domains such as the subtask of the computer game freecraft on which the approach is tested, the majority of tasks such as used in planning systems or in any of the other rrl systems including blocks world involves relations that change over time. in this limited setting, the global value function is assumed to be decomposed additively into local value functions for each object, so-called class-based value functions. it is assumed that all objects have a certain class and the local value functions can vary from class to class. the local, class-based value functions are assumed to only depend on some of the properties of those objects and objects that might be directly related to them. the method uses an efficient linear programming procedure to find appropriate weights for the linear combination of the local object properties. if all assumptions including the ones described about the additive nature of the value functions hold, the method can be guaranteed to approximate the true value function within some bound. the work provides bounds for the generalization to worlds with different numbers of domain objects and presents good empirical results in large domains. it shares with the other modelling approaches the difficulties of the modelling involved, in this case the definition of basis functions that can be combined into a global value function. reflections on modelling approaches the modelling methods study learning algorithms on a priori defined structures. learning amounts to estimating parameters for these structures. one of the advantages is that by using static structures, one can analyze the relation between the abstraction levels and the underlying rmdp. because the relational aggregations define new, minimized state and action ; spaces, there are obvious relations with model minimization givan et al., 2003 ; and averagers gordon, 1995 ; . rq, lomdp and carcass have independently introduced similar abstraction levels for rmdps. rq and carcass use slightly more powerful state abstractions in that they handle negation and arbitrary state predicates e.g. by using background knowledge ; . in general, all three use abstraction to transform the underlying rmdp into a much smaller abstract mdp, which can then be solved by modifications of traditional rl algorithms. in fact, the abstraction levels are exact aggregations i.e. partitions ; of state-action spaces. kersting et al. 2004 ; show that if one considers only state abstractions and uses only ground actions ; existing convergence proofs for td ; -learning will apply to a state value function on the abstracted state space. however, the more general case of abstract actions such as used in lomdp policies and carcass ; has not been considered yet. rq-learning in contrast, will converge for abstract actions as well, given the fact that separate state and action partitions are defined which can be considered as a new, discrete mdp. 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