Based on the view of an agent as an information processing system, and the premise that for such a system it is evolutionary advantageous to be parsimonious with respect to informational burden, an information-theoretical framework is set up to study behaviour under information minimisation pressures. This framework is based on the existing method of relevant information, which is adopted and adapted to the study of a range of cognitive aspects. Firstly, the model of a simple reactive actor is extended to include layered decision making and a minimal memory, in which it is shown that these aspects can decrease some form of bandwidth requirements in an agent, but at the cost of an increase at a different stage or moment in time, or for the system as a whole. However, when combined, they do make it possible to operate with smaller bandwidths at each part of the cognitive system, without increasing the bandwidth of the whole or lowering performance. These results motivate the development of the concept of look-ahead information, which extends the relevant information method to include time, and future informational effects of immediate actions in a more principled way. It is shown that this concept can give rise to intrinsic drives to avoid uncertainty, simplify the environment, and develop a predictive memory. Next, the framework is extended to incorporate a set of goals, rather than deal with just a single task. This introduces the task description as a new source of relevant information, and with that the concept of relevant goal information. Studying this quantity results in several observations: minimising goal information bandwidth results in ritualised behaviour; relevant goal and state information may to some point be exchanged for one another without affecting the agent’s performance; the dynamics of goal information give rise to a natural notion of sub-goals; bottlenecks on goal memory, and a measure of efficiency on the use of these bottlenecks, provide natural abstractions of the environment, and a global reference frame that supersedes local features of the environment. Finally, it is shown how an agent or species could actually arrive at having a large repertoire of goals and accompanying optimal sensors and behaviour, while under a strong information-minimisation pressure. This is done by introducing an informational model of sensory evolution, which indicates that a fundamental information-theoretical law may underpin an important evolutionary catalyst; namely, even a fully minimal sensor can carry additional information, dubbed here concomitant information, that is required to unlock the actual relevant information, which enables a minimal agent to still explore, enter and acquire different niches, accelerating a possible evolution to higher acuity and behavioural abilities.

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