Actor-Critic or Critic-Actor? A Tale of Two Time Scales

We revisit the standard formulation of tabular actor-critic algorithm as a two time-scale stochastic approximation with value function computed on a faster time-scale and policy computed on a slower time-scale. We observe that reversal of the time scales will in fact emulate value iteration and is a legitimate algorithm. We provide a proof of convergence and compare the two empirically with and without function approximation (with both linear and nonlinear function approximators) and observe that our proposed critic-actor algorithm performs on par with actor-critic in terms of both accuracy and computational effort. The actor-critic algorithm of Barto et al. [1] is one of the foremost reinforcement learning algorithms for data-driven approximate dynamic programming for Markov decision processes. Its rigorous analysis as a two time-scale stochastic approximation was initiated in [14] and [15], first in tabular form, then with linear function approximation, respectively.