Key to reinforcement learning in multi-agent systems is the ability to exploit the fact that agents only directly influence only a small subset of the other agents. Such loose couplings are often modelled using a graphical model: a coordination graph. Finding an (approximately) optimal joint action for a given coordination graph is therefore a central subroutine in cooperative multi-agent reinforcement learning (MARL). Much research in MARL focuses on how to gradually update the parameters of the coordination graph, whilst leaving the solving of the coordination graph up to a known typically exact and generic subroutine. However, exact methods { e.g., Variable Elimination { do not scale well, and generic methods do not exploit the MARL setting of gradually updating a coordination graph and recomputing the joint action to select. In this paper, we examine what happens if we use a heuristic method, i.e., local search, to select joint actions in MARL, and whether we can use outcome of this local search from a previous time-step to speed up and improve local search. We show empirically that by using local search, we can scale up to many agents and complex coordination graphs, and that by reusing joint actions from the previous time-step to initialise local search, we can both improve the quality of the joint actions found and the speed with which these joint actions are found.
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Understanding graphs representing dynamic events is a challenge for many students at all levels. And technological tools can provide support in overcoming some of these difficulties. In our research we developed a digital tool that enables students to create, modify and improve graphs from dynamic events using interactive animations and intrinsic feedback. In order to get insight about why the tool helped (or not), the students we conducted a qualitative study in which we interviewed nine students who used the tool. The results offer insight in students’ learning and thinking about dynamic graphs and how digital feedback can afford that. These results are useful for researchers, developers and teachers.
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An essential condition to use mathematics to solve problems is the ability to recognize, imagine and represent relations between quantities. In particular, covariational reasoning has been shown to be very challenging for students at all levels. The aim of the project Interactive Virtual Math (IVM) is to develop a visualization tool that supports students’ learning of covariation graphs. In this paper we present the initial development of the tool and we discuss its main features based on the results of one preliminary study and one exploratory study. The results suggest that the tool has potential to help students to engage in covariational reasoning by affording construction and explanation of different representations and comparison, relation and generalization of these ones. The results also point to the importance of developing tools that elicit and build upon students' self-productions
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