The article is devoted to investigating an application of aggregating algorithms to the problem of the long-term forecasting. We examine the classic aggregating algorithms based on the exponential reweighing. For the general Vovk’s aggregating algorithm we provide its probabilistic interpretation and its generalization for the long-term forecasting. For the special basic case of Vovk’s algorithm we provide two its modifications for the long-term forecasting. The first one is theoretically close to an optimal algorithm and is based on replication of independent copies. It provides the time-independent regret bound with respect to the best expert in the pool. The second one is not optimal but is more practical (explicitly models dependencies in observations) and has $O(sqrtT)$ regret bound, where $T$ is the length of the game.
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机译：本文致力于研究聚合算法在长期预测中的应用。我们研究了基于指数重称的经典聚合算法。对于一般的Vovk汇总算法，我们提供了其概率解释和长期预测的概括。对于Vovk算法的特殊基本情况，我们为长期预测提供了两种改进。第一个理论上接近于最佳算法，并且基于独立副本的复制。对于池中的最佳专家，它提供了与时间无关的遗憾。第二个不是最优的，而是更实用的（显式地建模观察中的依存关系），并具有$ O（ sqrtT）$的后悔界限，其中$ T $是游戏的长度。
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