[1] (##) I asked you to watch a video segment (https://youtu.be/L0pVHbEg4Yw) where Karl Friston talks about two main approaches to goal-directed acting by agents: (1) choosing actions that maximize (the expectation of) a value function $V(s)$ of the state ($s$) of the environment; or (2) choosing actions that minimize a functional ($F[q(s)]$) of beliefs ($q(s)$) over environmental states ($s$). Discuss the advantage of the latter appraoch.
[2] (#) The good regulator theorem states that a "successful and efficient" controller of the world must contain a model of the world. But it's hard to imagine how just learning a model of the world leads to goal-directed behavior, like learning how to read or drive a car. Which other ingredient do we need to get learning agents to behave as goal-directed agents?
[3] (##) The figure below reflects the state of a factor graph realization of an active inference agent after having pushed action $a_t$ onto the environment and having received observation $x_t$. In this graph, the variables $x_\bullet$, $u_\bullet$ and $s_\bullet$ correspond to observations, and unobserved control and internal states respectively. Copy the figure onto your sheet and draw a message passing schedule to infer a posterior belief (i.e. after observing $x_t$) over the next control state $u_{t+1}$.