<p>Fast forward to this year, folks from DeepMind proposes a deep reinforcement learning actor-critic method for dealing with <strong>both</strong> continuous state and action space. It is based on a technique called deterministic policy gradient. See the paper <a href="http://arxiv.org/abs/1509.02971" rel="noreferrer">Continuous control with deep reinforcement learning</a> and some <a href="https://www.reddit.com/r/MachineLearning/comments/3ytnqc/deep_q_learning_with_continuous_actions_question/" rel="noreferrer">implementations</a>.</p>
How can I apply reinforcement learning to continuous action spaces?
<p>I'm trying to get an agent to learn the mouse movements necessary to best perform some task in a reinforcement learning setting (i.e. the reward signal is the only feedback for learning).</p>

<p>I'm hoping to use the Q-learning technique, but while I've found <a href="http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.17.2539&amp;rep=rep1&amp;type=pdf">a way to extend this method to continuous state spaces</a>, I can't seem to figure out how to accommodate a problem with a continuous action space.</p>

<p>I could just force all mouse movement to be of a certain magnitude and in only a certain number of different directions, but any reasonable way of making the actions discrete would yield a huge action space. Since standard Q-learning requires the agent to evaluate <em>all</em> possible actions, such an approximation doesn't solve the problem in any practical sense.</p>