Title: Average Reward Reinforcement Learning with Monotonic Policy Improvement. Abstract: In continuing control tasks, an agent’s average reward per time step is a more natural performance measure compared to the commonly used discounting framework since it can better capture an agent’s long-term behavior. We derive a novel lower bound on the difference of the long-term average reward for two policies.  The lower bound depends on the average divergence between the policies and on the so-called Kemeny constant, which measures to what degree the unichain Markov chains associated with the policies are well-connected. We also show that previous work based on the discounted return (Schulman et al., 2015; Achiam et al., 2017) results in a non-meaningful lower bound in the average reward setting. Based on our lower bound, we develop an iterative procedure which produces a sequence of monotonically improved policies for the average reward criterion. When combined with Deep Reinforcement Learning (DRL) methods, the procedure leads to scalable and efficient algorithms for maximizing the agent’s average reward performance.Empirically we demonstrate the effectiveness of our method on continuing control tasks and show how discounting can lead to unsatisfactory performance.