An Interactive Environment E {\displaystyle {\mathcal {E}}} consists of a space of latent states S {\displaystyle {\mathcal {S}}} , a space of partial projections of the latent space O {\displaystyle {\mathcal {O}}} , a partial projection function V : S → O {\displaystyle V:{\mathcal {S}}\rightarrow {\mathcal {O}}} , a set of actions A {\displaystyle {\mathcal {A}}} , and a transition probability function p ( s | a , s ′ ) {\displaystyle p\left(s\,|\,a,s^{\prime }\right)} such that s , s ′ ∈ S , a ∈ A {\displaystyle s,s^{\prime }\in {\mathcal {S}},a\in {\mathcal {A}}} .
consists of a space of latent states 
, a space of partial projections of the latent space 
, a partial projection function 
, a set of actions 
, and a transition probability function 
such that 
.
