Many real-world problems can be reduced to combinatorial optimization on a graph, where the subset or ordering of vertices that maximize some objective function must be found. With such tasks often NP-hard and analytically intractable, reinforcement learning (RL) has shown promise as a framework with which efficient heuristic methods to tackle these problems can be learned. Previous works construct the solution subset incrementally, adding one element at a time, however, the irreversible nature of this approach prevents the agent from revising its earlier decisions, which may be necessary given the complexity of the optimization task. We instead propose that the agent should seek to continuously improve the solution by learning to explore at test time. Our approach of exploratory combinatorial optimization (ECO-DQN) is, in principle, applicable to any combinatorial problem that can be defined on a graph. Experimentally, we show our method to produce state-of-the-art RL performance on the Maximum Cut problem. Moreover, because ECO-DQN can start from any arbitrary configuration, it can be combined with other search methods to further improve performance, which we demonstrate using a simple random search.

Limitations in acquiring training data restrict potential applications of deep reinforcement learning (RL) methods to the training of real-world robots. Here we train an RL agent to align a Mach-Zehnder interferometer, which is an essential part of many optical experiments, based on images of interference fringes acquired by a monocular camera. The agent is trained in a simulated environment, without any hand-coded features or a priori information about the physics, and subsequently transferred to a physical interferometer. Thanks to a set of domain randomizations simulating uncertainties in physical measurements, the agent successfully aligns this interferometer without any fine-tuning, achieving a performance level of a human expert.