Deep Reinforcement Learning with Attention for Slate Markov Decision Processes with High-Dimensional States and Actions

Many real-world problems come with action spaces represented as feature vectors. Although high-dimensional control is a largely unsolved problem, there has recently been progress for modest dimensionalities. Here we report on a successful attempt at addressing problems of dimensionality as high as $2000$, of a particular form. Motivated by important applications such as recommendation systems that do not fit the standard reinforcement learning frameworks, we introduce Slate Markov Decision Processes (slate-MDPs). A Slate-MDP is an MDP with a combinatorial action space consisting of slates (tuples) of primitive actions of which one is executed in an underlying MDP. The agent does not control the choice of this executed action and the action might not even be from the slate, e.g., for recommendation systems for which all recommendations can be ignored. We use deep Q-learning based on feature representations of both the state and action to learn the value of whole slates. Unlike existing methods, we optimize for both the combinatorial and sequential aspects of our tasks. The new agent's superiority over agents that either ignore the combinatorial or sequential long-term value aspect is demonstrated on a range of environments with dynamics from a real-world recommendation system. Further, we use deep deterministic policy gradients to learn a policy that for each position of the slate, guides attention towards the part of the action space in which the value is the highest and we only evaluate actions in this area. The attention is used within a sequentially greedy procedure leveraging submodularity. Finally, we show how introducing risk-seeking can dramatically improve the agents performance and ability to discover more far reaching strategies.