A space of goals: the cognitive geometry of informationally bounded agents

Abstract

Traditionally, Euclidean geometry is treated by scientists as a priori and objective. However, when we take the position of an agent, the problem of selecting a best route should also factor in the abilities of the agent, its embodiment and particularly its cognitive effort. In this paper, we consider geometry in terms of travel between states within a world by incorporating information processing costs with the appropriate spatial distances. This induces a geometry that increasingly differs from the original geometry of the given world as information costs become increasingly important. We visualize this ‘cognitive geometry’ by projecting it onto two- and three-dimensional spaces showing distinct distortions reflecting the emergence of epistemic and information-saving strategies as well as pivot states. The analogies between traditional cost-based geometries and those induced by additional informational costs invite a generalization of the notion of geodesics as cheapest routes towards the notion of infodesics . In this perspective, the concept of infodesics is inspired by the property of geodesics that, travelling from a given start location to a given goal location along a geodesic, not only the goal, but all points along the way are visited at optimal cost from the start.

Humans account for cognitive costs when finding shortcuts: An information-theoretic analysis of navigation

“…InfoRL and related approaches based on mutual information, free energy or similar measures have been widely investigated in theoretical studies and to address simple decision or control settings [19,[23][24][25][26]45,60,[65][66][67][68][69][70][71][72][73][74], but not to study more complex behaviors such as wayfinding as done here. One of the reasons is that formalizing (default) policies for planning can be challenging.…”