  In this paper we consider reinforcement learning tasks with progressive
rewards; that is, tasks where the rewards tend to increase in magnitude over
time. We hypothesise that this property may be problematic for value-based deep
reinforcement learning agents, particularly if the agent must first succeed in
relatively unrewarding regions of the task in order to reach more rewarding
regions. To address this issue, we propose Spectral DQN, which decomposes the
reward into frequencies such that the high frequencies only activate when large
rewards are found. This allows the training loss to be balanced so that it
gives more even weighting across small and large reward regions. In two domains
with extreme reward progressivity, where standard value-based methods struggle
significantly, Spectral DQN is able to make much farther progress. Moreover,
when evaluated on a set of six standard Atari games that do not overtly favour
the approach, Spectral DQN remains more than competitive: While it
underperforms one of the benchmarks in a single game, it comfortably surpasses
the benchmarks in three games. These results demonstrate that the approach is
not overfit to its target problem, and suggest that Spectral DQN may have
advantages beyond addressing reward progressivity.
