  As the operations of autonomous systems generally affect simultaneously
several users, it is crucial that their designs account for fairness
considerations. In contrast to standard (deep) reinforcement learning (RL), we
investigate the problem of learning a policy that treats its users equitably.
In this paper, we formulate this novel RL problem, in which an objective
function, which encodes a notion of fairness that we formally define, is
optimized. For this problem, we provide a theoretical discussion where we
examine the case of discounted rewards and that of average rewards. During this
analysis, we notably derive a new result in the standard RL setting, which is
of independent interest: it states a novel bound on the approximation error
with respect to the optimal average reward of that of a policy optimal for the
discounted reward. Since learning with discounted rewards is generally easier,
this discussion further justifies finding a fair policy for the average reward
by learning a fair policy for the discounted reward. Thus, we describe how
several classic deep RL algorithms can be adapted to our fair optimization
problem, and we validate our approach with extensive experiments in three
different domains.
