  In this paper, we propose an off-policy deep reinforcement learning (DRL)
method utilizing the average reward criterion. While most existing DRL methods
employ the discounted reward criterion, this can potentially lead to a
discrepancy between the training objective and performance metrics in
continuing tasks, making the average reward criterion a recommended
alternative. We introduce RVI-SAC, an extension of the state-of-the-art
off-policy DRL method, Soft Actor-Critic (SAC), to the average reward
criterion. Our proposal consists of (1) Critic updates based on RVI Q-learning,
(2) Actor updates introduced by the average reward soft policy improvement
theorem, and (3) automatic adjustment of Reset Cost enabling the average reward
reinforcement learning to be applied to tasks with termination. We apply our
method to the Gymnasium's Mujoco tasks, a subset of locomotion tasks, and
demonstrate that RVI-SAC shows competitive performance compared to existing
methods.
