Using a Logarithmic Mapping to Enable Lower Discount Factors in Reinforcement Learning

In an effort to better understand the different ways in which the discount factor affects the optimization process in reinforcement learning, we designed a set of experiments to study each effect in isolation. Our analysis reveals that the common perception that this is caused by (too) small action-gaps requires revision. We propose an alternative hypothesis, which states that the size-difference of the action-gap across the state-space is the primary cause. We then introduce a new method that enables more homogeneous action-gaps by mapping value estimates to a logarithmic space. We prove convergence for this method under standard assumptions and demonstrate empirically that it indeed enables lower discount factors for approximate reinforcement-learning methods. This allows tackling a class of reinforcement-learning problems that are challenging to solve with traditional methods.