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The exploration-exploitation trade-off is central to the description ofadaptive behaviour in fields ranging from machine learning, to biology, toeconomics. While many approaches have been taken, one approach to solving thistrade-off has been to equip or propose that agents possess an intrinsic'exploratory drive' which is often implemented in terms of maximizing theagents information gain about the world -- an approach which has been widelystudied in machine learning and cognitive science. In this paper wemathematically investigate the nature and meaning of such approaches anddemonstrate that this combination of utility maximizing and information-seekingbehaviour arises from the minimization of an entirely difference class ofobjectives we call divergence objectives. We propose a dichotomy in theobjective functions underlying adaptive behaviour between \emph{evidence}objectives, which correspond to well-known reward or utility maximizingobjectives in the literature, and \emph{divergence} objectives which insteadseek to minimize the divergence between the agent's expected and desiredfutures, and argue that this new class of divergence objectives could form themathematical foundation for a much richer understanding of the exploratorycomponents of adaptive and intelligent action, beyond simply greedy utilitymaximization.

Understanding the Origin of Information-Seeking Exploration in Probabilistic Objectives for Control