更改

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=":1" />，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=":1" />，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Hard partitioning，主要参考的是<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><ref name=":3" />，对Soft state aggregation感兴趣的朋友可以自行参阅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Duan, Yaqi, Tracy Ke, and Mengdi Wang. "State aggregation learning from markov transition data." ''Advances in Neural Information Processing Systems'' 32 (2019).<ref>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，主要参考的是<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Duan, Yaqi, Tracy Ke, and Mengdi Wang. "State aggregation learning from markov transition data." ''Advances in Neural Information Processing Systems'' 32 (2019).<ref>Duan, Yaqi, Tracy Ke, and Mengdi Wang. "State aggregation learning from markov transition data." ''Advances in Neural Information Processing Systems'' 32 (2019).</ref>