摘要翻译：
我们探索市场评分规则、基于成本函数的预测市场和无遗憾学习之间存在的惊人的数学联系。我们证明，任何基于成本函数的预测市场都可以被解释为一个算法，用来解决通常研究的从专家建议中学习的问题，将市场上的交易与学习算法观察到的损失等同起来。如果市场组织者的损失是有界的，这个界可以用来导出相应学习算法的一个O（sqrt(T)）后悔界。然后，我们证明了具有凸成本函数的市场类正好对应于跟随正则化领导学习算法的市场类，市场中成本函数的选择对应于学习问题中正则化子的选择。最后，给出了具有凸成本函数的市场评分规则与预测市场之间的等价性。这意味着市场评分规则也可以自然地解释为遵循正则化的领导者算法，并可能是独立的利益。这些联系提供了新的洞察力，让我们了解到，通常研究的市场，如对数市场评分规则，是如何将意见汇总成对未来事件可能性的准确估计的。
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英文标题：
《A New Understanding of Prediction Markets Via No-Regret Learning》
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作者：
Yiling Chen and Jennifer Wortman Vaughan
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最新提交年份：
2010
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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：
  We explore the striking mathematical connections that exist between market scoring rules, cost function based prediction markets, and no-regret learning. We show that any cost function based prediction market can be interpreted as an algorithm for the commonly studied problem of learning from expert advice by equating trades made in the market with losses observed by the learning algorithm. If the loss of the market organizer is bounded, this bound can be used to derive an O(sqrt(T)) regret bound for the corresponding learning algorithm. We then show that the class of markets with convex cost functions exactly corresponds to the class of Follow the Regularized Leader learning algorithms, with the choice of a cost function in the market corresponding to the choice of a regularizer in the learning problem. Finally, we show an equivalence between market scoring rules and prediction markets with convex cost functions. This implies that market scoring rules can also be interpreted naturally as Follow the Regularized Leader algorithms, and may be of independent interest. These connections provide new insight into how it is that commonly studied markets, such as the Logarithmic Market Scoring Rule, can aggregate opinions into accurate estimates of the likelihood of future events.
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PDF链接：
https://arxiv.org/pdf/1003.0034