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I've never seen this notation before. What does the ellipsis right after the first summation mean:
\begin{equation}<br /> \label{aixi_eq}<br /> a_t^* = \arg\max\limits_{a_t}\sum\limits_{o_t r_t} \dots \max\limits_{a_{t+m}}\sum\limits_{o_{t+m} r_{t+m}}[r_t + \dots + r_{t+m}]<br /> \sum\limits_{q:U(q,a_1...a_{t+m})=o_1 r_1 ... o_{t+m}r_{t+m}}2^{-\ell(q)}.<br /> \end{equation}
\begin{equation}<br /> \label{aixi_eq}<br /> a_t^* = \arg\max\limits_{a_t}\sum\limits_{o_t r_t} \dots \max\limits_{a_{t+m}}\sum\limits_{o_{t+m} r_{t+m}}[r_t + \dots + r_{t+m}]<br /> \sum\limits_{q:U(q,a_1...a_{t+m})=o_1 r_1 ... o_{t+m}r_{t+m}}2^{-\ell(q)}.<br /> \end{equation}