What does this equation mean?

Dreamer-style world models learn a compact latent-dynamics model — a recurrent state-space model that predicts both a stochastic and a deterministic component of future latent state — and then train a policy by backpropagating through imagined rollouts inside that latent space, rather than through real or simulated environment steps directly [ 8 ] . DayDreamer took that specific mechanism, previously demonstrated mostly in video-game and simulated benchmarks, and applied it to physical robots learning online, without a simulator and without human demonstrations, reporting that four different physical robots (a quadruped and several manipulator arms) learned locomotion and manipulation skills directly from real-world interaction using the same world-model architecture across all of them [ 8 ] . The significant claim here is narrower than “world models let robots learn in the real world” in general — it is that this specific latent-imagination training loop, previously validated in simulation, transferred to real hardware without a simulator in the authors’ own experiments, on the specific tasks and robots they report. The equation names the actual asymmetry a world model buys: the policy is optimized against $\hat{s}_{t+1}$ , a predicted latent state, thousands of times per second of imagined rollout, while the real robot only needs to execute the resulting action once per real control cycle. The exposure is that $f_\theta$ is learned from a finite amount of real interaction and is wrong in ways that compound over an imagined rollout’s horizon — which is precisely the boundary the next section is about.