What does this equation mean?

Formally, the supervisor’s policy chooses a subgoal for each worker, and each worker then runs its own instance of the general loop against a history that never touches its siblings’: $g^{(i)} \sim \pi_{\text{super}}(g \mid \text{task}), \qquad a_t^{(i)} \sim \pi_{\text{worker}}^{(i)}\bigl(a \mid o_{\le t}^{(i)},\ h_t^{(i)},\ g^{(i)}\bigr)$. Because $h^{(i)}$ and $h^{(j)}$ are disjoint by construction, worker i ’s error cannot enter worker j ’s context directly — it can only reach the supervisor, and only in whatever compressed form the worker chooses to report. That disjointness is the formal reason this pattern offers stronger containment than the single loop for genuinely independent subtasks, and it is also exactly why the pattern is documented to struggle when subtasks are not independent: the architecture has no channel for worker i to see worker j ’s intermediate state even when the task actually requires it. Cost rises with the documented multiplier, latency improves only to the extent that subtasks are truly parallelizable, and debuggability gets harder in a specific way — failures are now spread across several separate transcripts that something has to reconcile after the fact, rather than sitting in one place.