  This paper proposes a new reinforcement learning with hyperbolic discounting.
Combining a new temporal difference error with the hyperbolic discounting in
recursive manner and reward-punishment framework, a new scheme to learn the
optimal policy is derived. In simulations, it is found that the proposal
outperforms the standard reinforcement learning, although the performance
depends on the design of reward and punishment. In addition, the averages of
discount factors w.r.t. reward and punishment are different from each other,
like a sign effect in animal behaviors.
