Zap Q-learning is a recent class of reinforcement learning algorithms, motivated primarily as a means to accelerate convergence. Stability theory has been absent outside of two restrictive classes: the tabular setting, and optimal stopping. This paper introduces a new framework for analysis of a more general class of recursive algorithms known as stochastic approximation. Based on this general theory, it is shown that Zap Q-learning is consistent under a non-degeneracy assumption, even when the function approximation architecture is nonlinear. Zap Q-learning with neural network function approximation emerges as a special case, and is tested on examples from OpenAI Gym. Based on multiple experiments with a range of neural network sizes, it is found that the new algorithms converge quickly and are robust to choice of function approximation architecture.

Zap Q-learning is a recent class of reinforcement learning algorithms, motivated primarily as a means to accelerate convergence. Stability theory has been absent outside of two restrictive classes: the tabular setting, and optimal stopping. This paper introduces a new framework for analysis of a more general class of recursive algorithms known as stochastic approximation. Based on this general theory, it is shown that Zap Q-learning is consistent under a non-degeneracy assumption, even when the function approximation architecture is nonlinear. Zap Q-learning with neural network function approximation emerges as a special case, and is tested on examples from OpenAI Gym.

The performance of a reinforcement learning (RL) system depends on the computational architecture used to approximate a value function. Deep learning methods provide both optimization techniques and architectures for approximating nonlinear functions from noisy, high-dimensional observations. However, prevailing optimization techniques are not designed for strictly-incremental online updates. Nor are standard architectures designed for observations with an a priori unknown structure: for example, light sensors randomly dispersed in space. This paper proposes an online RL prediction algorithm with an adaptive architecture that efficiently finds useful nonlinear features. The algorithm is evaluated in a spatial domain with high-dimensional, stochastic observations. The algorithm outperforms non-adaptive baseline architectures and approaches the performance of an architecture given side-channel information. These results are a step towards scalable RL algorithms for more general problems, where the observation structure is not available.