199 research outputs found

    A Unified View of Large-scale Zero-sum Equilibrium Computation

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    The task of computing approximate Nash equilibria in large zero-sum extensive-form games has received a tremendous amount of attention due mainly to the Annual Computer Poker Competition. Immediately after its inception, two competing and seemingly different approaches emerged---one an application of no-regret online learning, the other a sophisticated gradient method applied to a convex-concave saddle-point formulation. Since then, both approaches have grown in relative isolation with advancements on one side not effecting the other. In this paper, we rectify this by dissecting and, in a sense, unify the two views.Comment: AAAI Workshop on Computer Poker and Imperfect Informatio

    Toward the automated assessment of entity-relationship diagrams

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    The need to interpret imprecise diagrams (those with malformed, missing or extraneous features) occurs in the automated assessment of diagrams. We outline our proposal for an architecture to enable the interpretation of imprecise diagrams. We discuss our preliminary work on an assessment tool, developed within this architecture, for automatically grading answers to a computer architecture examination question. Early indications are that performance is similar to that of human markers. We will be using Entity-Relationship Diagrams (ERDs) as the primary application area for our investigation of automated assessment. This paper will detail our reasons for choosing this area and outline the work ahead

    Automatic assessment of sequence diagrams

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    In previous work we showed how student-produced entity-relationship diagrams (ERDs) could be automatically marked with good accuracy when compared with human markers. In this paper we report how effective the same techniques are when applied to syntactically similar UML sequence diagrams and discuss some issues that arise which did not occur with ERDs. We have found that, on a corpus of 100 student-drawn sequence diagrams, the automatic marking technique is more reliable that human markers. In addition, an analysis of this corpus revealed significant syntax errors in student-drawn sequence diagrams. We used the information obtained from the analysis to build a tool that not only detects syntax errors but also provides feedback in diagrammatic form. The tool has been extended to incorporate the automatic marker to provide a revision tool for learning how to model with sequence diagrams

    Theoretical and Practical Advances on Smoothing for Extensive-Form Games

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    Sparse iterative methods, in particular first-order methods, are known to be among the most effective in solving large-scale two-player zero-sum extensive-form games. The convergence rates of these methods depend heavily on the properties of the distance-generating function that they are based on. We investigate the acceleration of first-order methods for solving extensive-form games through better design of the dilated entropy function---a class of distance-generating functions related to the domains associated with the extensive-form games. By introducing a new weighting scheme for the dilated entropy function, we develop the first distance-generating function for the strategy spaces of sequential games that has no dependence on the branching factor of the player. This result improves the convergence rate of several first-order methods by a factor of Ω(bdd)\Omega(b^dd), where bb is the branching factor of the player, and dd is the depth of the game tree. Thus far, counterfactual regret minimization methods have been faster in practice, and more popular, than first-order methods despite their theoretically inferior convergence rates. Using our new weighting scheme and practical tuning we show that, for the first time, the excessive gap technique can be made faster than the fastest counterfactual regret minimization algorithm, CFR+, in practice

    Experiments in the automatic marking of ER-Diagrams

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    In this paper we present an approach to the computer understanding of diagrams and show how it can be successfully applied to the automatic marking (grading) of student attempts at drawing entity-relationship (ER) diagrams. The automatic marker has been incorporated into a revision tool to enable students to practice diagramming and obtain feedback on their attempts

    Using patterns in the automatic marking of ER-Diagrams

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    This paper illustrates how the notion of pattern can be used in the automatic analysis and synthesis of diagrams, applied particularly to the automatic marking of ER-diagrams. The paper describes how diagram patterns fit into a general framework for diagram interpretation and provides examples of how patterns can be exploited in other fields. Diagram patterns are defined and specified within the area of ER-diagrams. The paper also shows how patterns are being exploited in a revision tool for understanding ER-diagrams

    A fast and optimal hand isomorphism algorithm

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    Abstract In a section of their 2007 paper, Gilpin, Sandholm, and Sørensen outline a technique for indexing poker hands that accounts for suit isomorphisms. Their implementation is specific to Texas Hold'em as it requires a large case analysis, and is not optimal as many cases are omitted. In this paper, we build on their ideas and provide a fast and optimal technique that generalizes beyond Texas Hold'em as well as provide an inverse mapping from an index to a canonical hand
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