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@Article{AB11-jung,
 author="Tobias Jung and Daniel Polani and Peter Stone",
 title="Empowerment for continuous agent-environment systems",
 journal="Adaptive Behavior",
 volume="19",
 number="1",
 pages="16-39",
 year="2011",
 abstract={
           This paper develops generalizations of empowerment to
           continuous states. Empowerment is a recently introduced
           information-theoretic quantity motivated by hypotheses
           about the efficiency of the sensorimotor loop in biological
           organisms, but also from considerations stemming from
           curiosity-driven learning. Empowemerment measures, for
           agent-environment systems with stochastic transitions, how
           much influence an agent has on its environment, but only
           that influence that can be sensed by the agent sensors. It
           is an information-theoretic generalization of joint
           controllability (influence on environment) and
           observability (measurement by sensors) of the environment
           by the agent, both controllability and observability being
           usually defined in control theory as the dimensionality of
           the control/observation spaces.  Earlier work has shown
           that empowerment has various interesting and relevant
           properties, e.g., it allows us to identify salient states
           using only the dynamics, and it can act as intrinsic reward
           without requiring an external reward. However, in this
           previous work empowerment was limited to the case of
           small-scale and discrete domains and furthermore state
           transition probabilities were assumed to be known. The goal
           of this paper is to extend empowerment to the significantly
           more important and relevant case of continuous
           vector-valued state spaces and initially unknown state
           transition probabilities. The continuous state space is
           addressed by Monte-Carlo approximation; the unknown
           transitions are addressed by model learning and prediction
           for which we apply Gaussian processes regression with
           iterated forecasting. In a number of well-known continuous
           control tasks we examine the dynamics induced by
           empowerment and include an application to exploration and
           online model-learning.},
  wwwnote={Available from <a href="http://adb.sagepub.com/content/19/1/16.abstract">Adaptive Behavior</a> page.},
}