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Intrinsic motivation generates behaviors that do not necessarily lead toimmediate reward, but help exploration and learning. Here we show that agentshaving the sole goal of maximizing occupancy of future actions and states, thatis, moving and exploring on the long term, are capable of complex behaviorwithout any reference to external rewards. We find that action-state pathentropy is the only measure consistent with additivity and other intuitiveproperties of expected future action-state path occupancy. We provideanalytical expressions that relate the optimal policy with the optimalstate-value function, from where we prove uniqueness of the solution of theassociated Bellman equation and convergence of our algorithm to the optimalstate-value function. Using discrete and continuous state tasks, we show that`dancing', hide-and-seek and a basic form of altruistic behavior naturallyresult from entropy seeking without external rewards. Intrinsically motivatedagents can objectively determine what states constitute rewards, exploitingthem to ultimately maximize action-state path entropy.

Seeking entropy: complex behavior from intrinsic motivation to occupy action-state path space