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在硬划分的情况下，<math>\Phi_{i, j} = 1\ if\ s_i \in s_j'\ and\ 0\ otherwise</math><ref name=":12" />，即一个表示<math>i</math>属于<math>j</math>列的零一分组矩阵。如果是软划分的话，<math>\Phi</math>则不一定会是零一矩阵。

在硬划分的情况下，<math>\Phi_{i, j} = 1\ if\ s_i \in s_j'\ and\ 0\ otherwise</math><ref name=":12" />，即一个表示<math>i</math>属于<math>j</math>列的零一分组矩阵。如果是软划分的话，<math>\Phi</math>则不一定会是零一矩阵。

在这个词条里，我们主要讨论硬划分<ref name=":0">Zhang, Anru, and Mengdi Wang. "Spectral state compression of markov processes." ''IEEE transactions on information theory'' 66.5 (2019): 3202-3231.</ref>。对Soft state aggregation感兴趣的朋友可以自行参阅这两篇文论S. P. Singh, T. Jaakkola, and M. I. Jordan, “Reinforcement learning with soft state aggregation"<ref>Singh, Satinder, Tommi Jaakkola, and Michael Jordan. "Reinforcement learning with soft state aggregation." ''Advances in neural information processing systems'' 7 (1994).</ref>和<ref name=":11">Duan, Yaqi, Tracy Ke, and Mengdi Wang. "State aggregation learning from markov transition data." ''Advances in Neural Information Processing Systems'' 32 (2019).</ref>

在这个词条里，我们主要讨论硬划分<ref name=":0">Zhang, Anru, and Mengdi Wang. "Spectral state compression of markov processes." ''IEEE transactions on information theory'' 66.5 (2019): 3202-3231.</ref>。对软划分感兴趣的朋友可以自行参阅这两篇文论S. P. Singh, T. Jaakkola, and M. I. Jordan, “Reinforcement learning with soft state aggregation"<ref>Singh, Satinder, Tommi Jaakkola, and Michael Jordan. "Reinforcement learning with soft state aggregation." ''Advances in neural information processing systems'' 7 (1994).</ref>和<ref name=":11">Duan, Yaqi, Tracy Ke, and Mengdi Wang. "State aggregation learning from markov transition data." ''Advances in Neural Information Processing Systems'' 32 (2019).</ref>

 

 

===聚合：对转移概率进行粗粒化===

===聚合：对转移概率进行粗粒化===