CAQL: Continuous Action Q-Learning

A BSTRACT V alue-based reinforcement learning (RL) methods like Q-learning have shown success in a variety of domains. One challenge in applying Q-learning to continuous-action RL problems, however, is the continuous action maximization ( max-Q) required for optimal Bellman backup. In this work, we develop CAQL, a (class of) algorithm(s) for continuous-action Q-learning that can use several plug-and-play optimizers for the max-Q problem. Leveraging recent optimization results for deep neural networks, we show that max-Q can be solved optimally using mixed-integer programming (MIP) . When the Q-function representation has sufficient power, MIP-based optimization gives rise to better policies and is more robust than approximate methods (e.g., gradient ascent, cross-entropy search). We further develop several techniques to accelerate inference in CAQL, which despite their approximate nature, perform well. We compare CAQL with state-of-the-art RL algorithms on benchmark continuous-control problems that have different degrees of action constraints and show that CAQL outperforms policy-based methods in heavily constrained environments, often dramatically. When the action space is finite, value-based algorithms such as Q-learning (Watkins & Dayan, 1992), which implicitly finds a policy by learning the optimal value function, are often very efficient because action optimization can be done by exhaustive enumeration. By contrast, in problems with a continuous action spaces (e.g., robotics (Peters & Schaal, 2006)), policy-based algorithms, such as policy gradient (PG) (Sutton et al., 2000; Silver et al., 2014) or cross-entropy policy search (CEPS) (Mannor et al., 2003; Kalashnikov et al., 2018), which directly learn a return-maximizing policy, have proven more practical. Recently, methods such as ensemble critic (Fujimoto et al., 2018) and entropy regularization (Haarnoja et al., 2018) have been developed to improve the performance of policy-based RL algorithms. Policy-based approaches require a reasonable choice of policy parameterization. In some continuous control problems, Gaussian distributions over actions conditioned on some state representation is used. However, in applications such as RSs, where actions often take the form of high-dimensional item-feature vectors, policies cannot typically be modeled by common action distributions.