因子值迭代收敛

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摘要翻译：
本文提出了一种求解因数马尔可夫决策过程的新算法--因数值迭代法(FVI)。对传统的近似值迭代算法进行了两方面的修正。首先，对最小二乘投影算子进行修正，使其不增加最大范数，从而保持收敛性。另一个改进是，我们从（指数大）状态空间中均匀地抽取多项式多个样本。这样，算法的复杂度就变成了fMDP描述长度的多项式。我们证明了该算法是收敛的。我们还导出了近似解与最优解之差的一个上界，以及由抽样引入的误差的一个上界。分析了各种投影算子的计算复杂度和与近似值迭代相结合时的收敛性。
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英文标题：
《Factored Value Iteration Converges》
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作者：
Istvan Szita and Andras Lorincz
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最新提交年份：
2008
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分类信息：

一级分类：Computer Science        计算机科学
二级分类：Artificial Intelligence        人工智能
分类描述：Covers all areas of AI except Vision, Robotics, Machine Learning, Multiagent Systems, and Computation and Language (Natural Language Processing), which have separate subject areas. In particular, includes Expert Systems, Theorem Proving (although this may overlap with Logic in Computer Science), Knowledge Representation, Planning, and Uncertainty in AI. Roughly includes material in ACM Subject Classes I.2.0, I.2.1, I.2.3, I.2.4, I.2.8, and I.2.11.
涵盖了人工智能的所有领域，除了视觉、机器人、机器学习、多智能体系统以及计算和语言（自然语言处理），这些领域有独立的学科领域。特别地，包括专家系统，定理证明（尽管这可能与计算机科学中的逻辑重叠），知识表示，规划，和人工智能中的不确定性。大致包括ACM学科类I.2.0、I.2.1、I.2.3、I.2.4、I.2.8和I.2.11中的材料。
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一级分类：Computer Science        计算机科学
二级分类：Machine Learning        机器学习
分类描述：Papers on all aspects of machine learning research (supervised, unsupervised, reinforcement learning, bandit problems, and so on) including also robustness, explanation, fairness, and methodology. cs.LG is also an appropriate primary category for applications of machine learning methods.
关于机器学习研究的所有方面的论文（有监督的，无监督的，强化学习，强盗问题，等等），包括健壮性，解释性，公平性和方法论。对于机器学习方法的应用，CS.LG也是一个合适的主要类别。
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英文摘要：
  In this paper we propose a novel algorithm, factored value iteration (FVI), for the approximate solution of factored Markov decision processes (fMDPs). The traditional approximate value iteration algorithm is modified in two ways. For one, the least-squares projection operator is modified so that it does not increase max-norm, and thus preserves convergence. The other modification is that we uniformly sample polynomially many samples from the (exponentially large) state space. This way, the complexity of our algorithm becomes polynomial in the size of the fMDP description length. We prove that the algorithm is convergent. We also derive an upper bound on the difference between our approximate solution and the optimal one, and also on the error introduced by sampling. We analyze various projection operators with respect to their computation complexity and their convergence when combined with approximate value iteration.
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PDF链接：
https://arxiv.org/pdf/0801.2069

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关键词：Intelligence Presentation Modification Applications Approximate 抽样 迭代 our modified 近似值