  In this paper, we build on advances introduced by the Deep Q-Networks (DQN)
approach to extend the multi-objective tabular Reinforcement Learning (RL)
algorithm W-learning to large state spaces. W-learning algorithm can naturally
solve the competition between multiple single policies in multi-objective
environments. However, the tabular version does not scale well to environments
with large state spaces. To address this issue, we replace underlying Q-tables
with DQN, and propose an addition of W-Networks, as a replacement for tabular
weights (W) representations. We evaluate the resulting Deep W-Networks (DWN)
approach in two widely-accepted multi-objective RL benchmarks: deep sea
treasure and multi-objective mountain car. We show that DWN solves the
competition between multiple policies while outperforming the baseline in the
form of a DQN solution. Additionally, we demonstrate that the proposed
algorithm can find the Pareto front in both tested environments.
