Reward is not Necessary: How to Create a Compositional Self-Preserving Agent for Life-Long Learning

We introduce a physiological model-based agent as proof-of-principle that it is possible to define a flexible self-preserving system that does not use a reward signal or reward-maximization as an objective. We achieve this by introducing the Self-Preserving Agent (SPA) with a physiological structure where the system can get trapped in an absorbing state if the agent does not solve and execute goal-directed polices. Our agent is defined using new class of Bellman equations called Operator Bellman Equations (OBEs), for encoding jointly non-stationary non-Markovian tasks formalized as a Temporal Goal Markov Decision Process (TGMDP). OBEs produce optimal goal-conditioned spatiotemporal transition operators that map an initial state-time to the final state-times of a policy used to complete a goal, and can also be used to forecast future states in multiple dynamic physiological state-spaces. SPA is equipped with an intrinsic motivation function called the valence function, which quantifies the changes in empowerment (the channel capacity of a transition operator) after following a policy. Because empowerment is a function of a transition operator, there is a natural synergism between empowerment and OBEs: the OBEs create hierarchical transition operators, and the valence function can evaluate hierarchical empowerment change defined on these operators. The valence function can then be used for goal selection, wherein the agent chooses a policy sequence that realizes goal states which produce maximum empowerment gain. In doing so, the agent will seek freedom and avoid internal death-states that undermine its ability to control both external and internal states in the future, thereby exhibiting the capacity of predictive and anticipatory self-preservation. We also compare SPA to Multi-objective RL, and discuss its capacity for symbolic reasoning and life-long learning.