Algorithms for variance reduction in a policy-gradient based actor-critic framework

We consider the framework of a set of recently proposed two-timescale actor-critic algorithms for reinforcement-learning (RL) using the long-run average-reward criterion and linear feature-based value-function approximation. The actor and critic updates are based on stochastic policy-gradient ascent and temporal-difference algorithms, respectively. Unlike conventional RL algorithms, policy-gradient-based algorithms guarantee convergence even with value-function approximation but suffer due to high variance of the policy-gradient estimator. To minimize this variance for an existing algorithm, we derive a stochastic-gradient-based novel critic update. We propose a novel baseline structure for variance minimization of an estimator and derive an optimal baseline which makes the covariance matrix a zero matrix - the best achievable. We derive a novel actor update based on the optimal baseline deduced for an existing algorithm. We derive another novel actor update using the optimal baseline for an unbiased policy-gradient estimator which we deduce from the policy-gradient theorem with function approximation. We obtain a novel variance-minimization-based interpretation for an existing algorithm. The computational results demonstrate that the proposed algorithms outperform the state-of-the-art on Garnet problems.