  This paper addresses a new interpretation of the traditional optimization
method in reinforcement learning (RL) as optimization problems using reverse
Kullback-Leibler (KL) divergence, and derives a new optimization method using
forward KL divergence, instead of reverse KL divergence in the optimization
problems. Although RL originally aims to maximize return indirectly through
optimization of policy, the recent work by Levine has proposed a different
derivation process with explicit consideration of optimality as stochastic
variable. This paper follows this concept and formulates the traditional
learning laws for both value function and policy as the optimization problems
with reverse KL divergence including optimality. Focusing on the asymmetry of
KL divergence, the new optimization problems with forward KL divergence are
derived. Remarkably, such new optimization problems can be regarded as
optimistic RL. That optimism is intuitively specified by a hyperparameter
converted from an uncertainty parameter. In addition, it can be enhanced when
it is integrated with prioritized experience replay and eligibility traces,
both of which accelerate learning. The effects of this expected optimism was
investigated through learning tendencies on numerical simulations using
Pybullet. As a result, moderate optimism accelerated learning and yielded
higher rewards. In a realistic robotic simulation, the proposed method with the
moderate optimism outperformed one of the state-of-the-art RL method.
