26,018 research outputs found

    Towards an Intelligent Tutor for Mathematical Proofs

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    Computer-supported learning is an increasingly important form of study since it allows for independent learning and individualized instruction. In this paper, we discuss a novel approach to developing an intelligent tutoring system for teaching textbook-style mathematical proofs. We characterize the particularities of the domain and discuss common ITS design models. Our approach is motivated by phenomena found in a corpus of tutorial dialogs that were collected in a Wizard-of-Oz experiment. We show how an intelligent tutor for textbook-style mathematical proofs can be built on top of an adapted assertion-level proof assistant by reusing representations and proof search strategies originally developed for automated and interactive theorem proving. The resulting prototype was successfully evaluated on a corpus of tutorial dialogs and yields good results.Comment: In Proceedings THedu'11, arXiv:1202.453

    Local and Global Explanations of Agent Behavior: Integrating Strategy Summaries with Saliency Maps

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    With advances in reinforcement learning (RL), agents are now being developed in high-stakes application domains such as healthcare and transportation. Explaining the behavior of these agents is challenging, as the environments in which they act have large state spaces, and their decision-making can be affected by delayed rewards, making it difficult to analyze their behavior. To address this problem, several approaches have been developed. Some approaches attempt to convey the global\textit{global} behavior of the agent, describing the actions it takes in different states. Other approaches devised local\textit{local} explanations which provide information regarding the agent's decision-making in a particular state. In this paper, we combine global and local explanation methods, and evaluate their joint and separate contributions, providing (to the best of our knowledge) the first user study of combined local and global explanations for RL agents. Specifically, we augment strategy summaries that extract important trajectories of states from simulations of the agent with saliency maps which show what information the agent attends to. Our results show that the choice of what states to include in the summary (global information) strongly affects people's understanding of agents: participants shown summaries that included important states significantly outperformed participants who were presented with agent behavior in a randomly set of chosen world-states. We find mixed results with respect to augmenting demonstrations with saliency maps (local information), as the addition of saliency maps did not significantly improve performance in most cases. However, we do find some evidence that saliency maps can help users better understand what information the agent relies on in its decision making, suggesting avenues for future work that can further improve explanations of RL agents
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