  In POMDPs, information about the hidden state, delivered through
observations, is both valuable to the agent, allowing it to base its actions on
better informed internal states, and a "curse", exploding the size and
diversity of the internal state space. One attempt to deal with this is to
focus on reactive policies, that only base their actions on the most recent
observation. However, even reactive policies can be demanding on resources, and
agents need to pay selective attention to only some of the information
available to them in observations. In this report we present the
minimum-information principle for selective attention in reactive agents. We
further motivate this approach by reducing the general problem of optimal
control in POMDPs, to reactive control with complex observations. Lastly, we
explore a newly discovered phenomenon of this optimization process - period
doubling bifurcations. This necessitates periodic policies, and raises many
more questions regarding stability, periodicity and chaos in optimal control.
