The architecture of asynchronous one-step Q-learning is very similar to DQN. An agent in DQN was represented by a set of primary and target networks, where one-step loss is calculated as the square of the difference between the state-action value of the current state s predicted by the primary network, and the target state-action value of the current state calculated by the target network. The gradients of the loss is calculated with respect to the parameters of the policy network, and then the loss is minimized using a gradient descent optimizer leading to parameter updates of the primary network.
The difference here in asynchronous one-step Q-learning is that there are multiple such learning agents, for instance, learners running and calculating this loss in parallel. Thus, the gradient calculation also occurs in parallel in different threads...
