Title: Fast Deterministic Stackelberg Actor-Critic. Abstract: Most advanced Actor-Critic (AC) approaches update the actor and critic concurrently through (stochastic) Gradient Descents (GD),  which may be trapped into bad local optimality due to the instability of these simultaneous updating schemes.  
Stackelberg AC learning scheme alleviates these limitations by adding a compensated indirect gradient terms to the GD. However, the indirect gradient terms are time-consuming to calculate, and the convergence rate is also relatively slow.  To alleviates these challenges, we find that in the Deterministic Policy Gradient family, by removing the terms that contain Hessian matrices and adopting the block diagonal approximation technique to approximate the remaining inverse matrices, we can construct an approximated Stackelberg AC learning scheme that is easy to compute and fast to converge. Experiments reveal that ours outperform SOTAs in terms of average returns under acceptable training time.