Gradient Q$(��, ��)$: A Unified Algorithm with Function Approximation for Reinforcement Learning

Full-sampling (e.g., Q-learning) and pure-expectation (e.g., Expected Sarsa) algorithms are efficient and frequently used techniques in reinforcement learning. Q$(��,��)$ is the first approach unifies them with eligibility trace through the sampling degree $��$. However, it is limited to the tabular case, for large-scale learning, the Q$(��,��)$ is too expensive to require a huge volume of tables to accurately storage value functions. To address above problem, we propose a GQ$(��,��)$ that extends tabular Q$(��,��)$ with linear function approximation. We prove the convergence of GQ$(��,��)$. Empirical results on some standard domains show that GQ$(��,��)$ with a combination of full-sampling with pure-expectation reach a better performance than full-sampling and pure-expectation methods.