Information theoretic approach to decision making in continuous domains

Information theory has been often used to analyse the interactions of agents with their environment. For example, frameworks of bounded rationality focus on tradeoffs between utility maximisation and information processing cost. Alternatively, frameworks of planning frequently focus on casting exploration as potential information gain. Here, we will apply multi-variable information decomposition in order to isolate interactions between the agent, its past and future sensations, and its future self. We will then discuss intuition behind the resulting terms and connections to several popular frameworks. Afterwards, we will focus on active sensing - a decision making framework that formalizes exploration as reduction of uncertainty about the current state of the environment. Despite strong theoretical justifications, active sensing has had limited applicability due to difficulty in estimating information gain. Here we will address this issue by proposing a linear approximation to information gain and by implementing efficient gradient-based action selection within an artificial neural network setting. We will compare information gain estimation with state of the art, and validate our model on an active sensing task based on MNIST dataset.