Compact Representation

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Shouxun Lin - One of the best experts on this subject based on the ideXlab platform.

Christopher Kiekintveld - One of the best experts on this subject based on the ideXlab platform.

  • Compact Representation of Value Function in Partially Observable Stochastic Games
    arXiv: Computer Science and Game Theory, 2019
    Co-Authors: Karel Horák, Branislav Bošanský, Christopher Kiekintveld, Charles A. Kamhoua
    Abstract:

    Value methods for solving stochastic games with partial observability model the uncertainty about states of the game as a probability distribution over possible states. The dimension of this belief space is the number of states. For many practical problems, for example in security, there are exponentially many possible states which causes an insufficient scalability of algorithms for real-world problems. To this end, we propose an abstraction technique that addresses this issue of the curse of dimensionality by projecting high-dimensional beliefs to characteristic vectors of significantly lower dimension (e.g., marginal probabilities). Our two main contributions are (1) novel Compact Representation of the uncertainty in partially observable stochastic games and (2) novel algorithm based on this Compact Representation that is based on existing state-of-the-art algorithms for solving stochastic games with partial observability. Experimental evaluation confirms that the new algorithm over the Compact Representation dramatically increases the scalability compared to the state of the art.

  • IJCAI - Compact Representation of Value Function in Partially Observable Stochastic Games
    Proceedings of the Twenty-Eighth International Joint Conference on Artificial Intelligence, 2019
    Co-Authors: Karel Horák, Branislav Bošanský, Christopher Kiekintveld, Charles A. Kamhoua
    Abstract:

    Value methods for solving stochastic games with partial observability model the uncertainty of the players as a probability distribution over possible states, where the dimension of the belief space is the number of states. For many practical problems, there are exponentially many states which causes scalability problems. We propose an abstraction technique that addresses this curse of dimensionality by projecting the high-dimensional beliefs onto characteristic vectors of significantly lower dimension (e.g., marginal probabilities). Our main contributions are (1) a novel Compact Representation of the uncertainty in partially observable stochastic games and (2) a novel algorithm using this Representation that is based on existing state-of-the-art algorithms for solving stochastic games with partial observability. Experimental evaluation confirms that the new algorithm using the Compact Representation dramatically increases scalability compared to the state of the art.

  • combining Compact Representation and incremental generation in large games with sequential strategies
    National Conference on Artificial Intelligence, 2015
    Co-Authors: Branislav Bošanský, Albert Xin Jiang, Milind Tambe, Christopher Kiekintveld
    Abstract:

    Many search and security games played on a graph can be modeled as normal-form zero-sum games with strategies consisting of sequences of actions. The size of the strategy space provides a computational challenge when solving these games. This complexity is tackled either by using the Compact Representation of sequential strategies and linear programming, or by incremental strategy generation of iterative double-oracle methods. In this paper, we present novel hybrid of these two approaches: Compact-strategy double-oracle (CS-DO) algorithm that combines the advantages of the Compact Representation with incremental strategy generation. We experimentally compare CS-DO with the standard approaches and analyze the impact of the size of the support on the performance of the algorithms. Results show that CS-DO dramatically improves the convergence rate in games with non-trivial support.

  • AAAI - Combining Compact Representation and incremental generation in large games with sequential strategies
    2015
    Co-Authors: Branislav Bošanský, Albert Xin Jiang, Milind Tambe, Christopher Kiekintveld
    Abstract:

    Many search and security games played on a graph can be modeled as normal-form zero-sum games with strategies consisting of sequences of actions. The size of the strategy space provides a computational challenge when solving these games. This complexity is tackled either by using the Compact Representation of sequential strategies and linear programming, or by incremental strategy generation of iterative double-oracle methods. In this paper, we present novel hybrid of these two approaches: Compact-strategy double-oracle (CS-DO) algorithm that combines the advantages of the Compact Representation with incremental strategy generation. We experimentally compare CS-DO with the standard approaches and analyze the impact of the size of the support on the performance of the algorithms. Results show that CS-DO dramatically improves the convergence rate in games with non-trivial support.

Branislav Bošanský - One of the best experts on this subject based on the ideXlab platform.

  • Compact Representation of Value Function in Partially Observable Stochastic Games
    arXiv: Computer Science and Game Theory, 2019
    Co-Authors: Karel Horák, Branislav Bošanský, Christopher Kiekintveld, Charles A. Kamhoua
    Abstract:

    Value methods for solving stochastic games with partial observability model the uncertainty about states of the game as a probability distribution over possible states. The dimension of this belief space is the number of states. For many practical problems, for example in security, there are exponentially many possible states which causes an insufficient scalability of algorithms for real-world problems. To this end, we propose an abstraction technique that addresses this issue of the curse of dimensionality by projecting high-dimensional beliefs to characteristic vectors of significantly lower dimension (e.g., marginal probabilities). Our two main contributions are (1) novel Compact Representation of the uncertainty in partially observable stochastic games and (2) novel algorithm based on this Compact Representation that is based on existing state-of-the-art algorithms for solving stochastic games with partial observability. Experimental evaluation confirms that the new algorithm over the Compact Representation dramatically increases the scalability compared to the state of the art.

  • IJCAI - Compact Representation of Value Function in Partially Observable Stochastic Games
    Proceedings of the Twenty-Eighth International Joint Conference on Artificial Intelligence, 2019
    Co-Authors: Karel Horák, Branislav Bošanský, Christopher Kiekintveld, Charles A. Kamhoua
    Abstract:

    Value methods for solving stochastic games with partial observability model the uncertainty of the players as a probability distribution over possible states, where the dimension of the belief space is the number of states. For many practical problems, there are exponentially many states which causes scalability problems. We propose an abstraction technique that addresses this curse of dimensionality by projecting the high-dimensional beliefs onto characteristic vectors of significantly lower dimension (e.g., marginal probabilities). Our main contributions are (1) a novel Compact Representation of the uncertainty in partially observable stochastic games and (2) a novel algorithm using this Representation that is based on existing state-of-the-art algorithms for solving stochastic games with partial observability. Experimental evaluation confirms that the new algorithm using the Compact Representation dramatically increases scalability compared to the state of the art.

  • combining Compact Representation and incremental generation in large games with sequential strategies
    National Conference on Artificial Intelligence, 2015
    Co-Authors: Branislav Bošanský, Albert Xin Jiang, Milind Tambe, Christopher Kiekintveld
    Abstract:

    Many search and security games played on a graph can be modeled as normal-form zero-sum games with strategies consisting of sequences of actions. The size of the strategy space provides a computational challenge when solving these games. This complexity is tackled either by using the Compact Representation of sequential strategies and linear programming, or by incremental strategy generation of iterative double-oracle methods. In this paper, we present novel hybrid of these two approaches: Compact-strategy double-oracle (CS-DO) algorithm that combines the advantages of the Compact Representation with incremental strategy generation. We experimentally compare CS-DO with the standard approaches and analyze the impact of the size of the support on the performance of the algorithms. Results show that CS-DO dramatically improves the convergence rate in games with non-trivial support.

  • AAAI - Combining Compact Representation and incremental generation in large games with sequential strategies
    2015
    Co-Authors: Branislav Bošanský, Albert Xin Jiang, Milind Tambe, Christopher Kiekintveld
    Abstract:

    Many search and security games played on a graph can be modeled as normal-form zero-sum games with strategies consisting of sequences of actions. The size of the strategy space provides a computational challenge when solving these games. This complexity is tackled either by using the Compact Representation of sequential strategies and linear programming, or by incremental strategy generation of iterative double-oracle methods. In this paper, we present novel hybrid of these two approaches: Compact-strategy double-oracle (CS-DO) algorithm that combines the advantages of the Compact Representation with incremental strategy generation. We experimentally compare CS-DO with the standard approaches and analyze the impact of the size of the support on the performance of the algorithms. Results show that CS-DO dramatically improves the convergence rate in games with non-trivial support.

Qun Liu - One of the best experts on this subject based on the ideXlab platform.

Taihei Oki - One of the best experts on this subject based on the ideXlab platform.

  • A Compact Representation for minimizers of k-submodular functions
    Journal of Combinatorial Optimization, 2017
    Co-Authors: Hiroshi Hirai, Taihei Oki
    Abstract:

    A k-submodular function is a generalization of submodular and bisubmodular functions. This paper establishes a Compact Representation for minimizers of a k-submodular function by a poset with inconsistent pairs (PIP). This is a generalization of Ando–Fujishige’s signed poset Representation for minimizers of a bisubmodular function. We completely characterize the class of PIPs (elementary PIPs) arising from k-submodular functions. We give algorithms to construct the elementary PIP of minimizers of a k-submodular function f for three cases: (i) a minimizing oracle of f is available, (ii) f is network-representable, and (iii) f arises from a Potts energy function. Furthermore, we provide an efficient enumeration algorithm for all maximal minimizers of a Potts k-submodular function. Our results are applicable to obtain all maximal persistent labelings in actual computer vision problems. We present experimental results for real vision instances.

  • ISCO - A Compact Representation for Minimizers of k -Submodular Functions (Extended Abstract)
    Lecture Notes in Computer Science, 2016
    Co-Authors: Hiroshi Hirai, Taihei Oki
    Abstract:

    k-submodular functions were introduced by Huber and Kolmogorov as a generalization of bisubmodular functions. This paper establishes a Compact Representation of minimizers of k-submodular functions by posets with inconsistent pairs (PIPs), and completely characterizes the class of PIPs (elementary PIPs) corresponding to minimizers of k-submodular functions. Our Representation coincides with Birkhoff’s Representation theorem if \(k=1\) and with signed-poset Representation by Ando and Fujishige if \(k=2\). We also give algorithms to construct the elementary PIP representing the minimizers of a k-submodular function f for three cases: (i) a minimizing oracle of f is available, (ii) f is network-representable, and (iii) f is the objective function of the relaxation of multiway cut problem. Furthermore, we provide an efficient algorithm to enumerate all maximal minimizers from the PIP Representation. Our results are applied to obtain all maximal persistent assignments in labeling problems arising from computer vision.