<p>Reinforcement Learning (RL) problems appear in diverse real-world applications and are gaining substantial attention in academia and industry. Policy Direct Search (PDS) is widely recognized as an effective approach to RL problems. However, existing PDS algorithms have some major limitations. First, many step-wise Policy Gradient Search (PGS) algorithms cannot effectively utilize informative historical gradients to accurately estimate policy gradients. Second, although evolutionary PDS algorithms do not rely on accurate policy gradient estimations and can explore learning environments effectively, they are not sample efficient at learning policies in the form of deep neural networks. Third, existing PGS algorithms often diverge easily due to the lack of reliable and flexible techniques for value function learning. Fourth, existing PGS algorithms have not provided suitable mechanisms to learn proper state features automatically. To address these limitations, the overall goal of this thesis is to develop effective policy direct search algorithms for tackling challenging RL problems through technical innovations in four key areas. First, the thesis aims to improve the accuracy of policy gradient estimation by utilizing historical gradients through a Primal-Dual Approximation technique. Second, the thesis targets on surpassing the state-of-the-art performance by properly balancing the exploration-exploitation trade-off via Covariance Matrix Adaption Evolutionary Strategy (CMA-ES) and Proximal Policy Optimization (PPO). Third, the thesis seeks to stabilize value function learning via a self-organized Sandpile Model (SM) meanwhile generalize the compatible condition to support flexible value function learning. Fourth, the thesis endeavors to develop innovative evolutionary feature learning techniques that are capable of automatically extracting useful state features so as to enhance various cutting-edge PGS algorithms. In the thesis, we explore the four key technical areas by studying policies with increasing complexity. First of all, we start the research from a simple linear policy representation, and then proceed to a complex neural network based policy representation. Next, we consider a more complicated situation where policy learning is coupled with a value function learning. Subsequently, we consider policies modeled as a concatenation of two interrelated networks, one for feature learning and one for action selection. To achieve the first goal, this thesis proposes a new policy gradient learning framework where a series of historical gradients are jointly exploited to obtain accurate policy gradient estimations via the Primal-Dual Approximation technique. Under the framework, three new PGS algorithms for step-wise policy training have been derived from three widely used PGS algorithms; meanwhile, the convergence properties of these new algorithms have been theoretically analyzed. The empirical results on several benchmark control problems further show that the newly proposed algorithms can significantly outperform their base algorithms. To achieve the second goal, this thesis develops a new sample efficient evolutionary deep policy optimization algorithm based on CMA-ES and PPO. The algorithm has a layer-wise learning mechanism to improve computational efficiency in comparison to CMA-ES. Additionally, it uses a performance lower bound based surrogate model for fitness evaluation to significantly reduce the sample cost to the state-of-the-art level. More importantly, the best policy found by CMA-ES at every generation is further improved by PPO to properly balance exploration and exploitation. The experimental results confirm that the proposed algorithm outperforms various cutting-edge algorithms on many benchmark continuous control problems. To achieve the third goal, this thesis develops new value function learning methods that are both reliable and flexible so as to further enhance the effectiveness of policy gradient search. Two Actor-Critic (AC) algorithms have been successfully developed from a commonly-used PGS algorithm, i.e., Regular Actor-Critic (RAC). The first algorithm adopts SM to stabilize value function learning, and the second algorithm generalizes the logarithm function used by the compatible condition to provide a flexible family of new compatible functions. The experimental results show that, with the help of reliable and flexible value function learning, the newly developed algorithms are more effective than RAC on several benchmark control problems. To achieve the fourth goal, this thesis develops innovative NeuroEvolution algorithms for automated feature learning to enhance various cutting-edge PGS algorithms. The newly developed algorithms not only can extract useful state features but also learn good policies. The experimental analysis demonstrates that the newly proposed algorithms can achieve better performance on large-scale RL problems in comparison to both well-known PGS algorithms and NeuroEvolution techniques. Our experiments also confirm that the state features learned by NeuroEvolution on one RL task can be easily transferred to boost learning performance on similar but different tasks.</p>
A FE-ADMM algorithm for Lavrentiev-regularized state-constrained elliptic control problem
