Definition. Global policy entropy [ftip-0062]
Definition. Global policy entropy [ftip-0062]
Fix a finite action space, a finite horizon \(T\), and a declared distribution \(\mu _t\) over public histories at each position. The global policy entropy is the weighted average
\[ H_{\rm global}(\pi ) =\frac 1T\sum _{t=0}^{T-1} \mathbb E_{\mathsf H_t\sim \mu _t} \left [-\sum _a\pi (a\mid \mathsf H_t) \log \pi (a\mid \mathsf H_t)\right ]. \]The history distribution and action alphabet are part of the statistic.
We use the convention \(0\log 0=0\) in this and the following position-entropy formula.