Quantum Algorithms for Reinforcement Learning with a Generative Model

TitleQuantum Algorithms for Reinforcement Learning with a Generative Model
Publication TypeJournal Article
Year of Publication2021
AuthorsWang, D, Sundaram, A, Kothari, R, Kapoor, A, Roetteler, M
JournalProceedings of the 38th International Conference on Machine Learning, PMLR
Start Page10916-10926
Date Published12/15/2021
KeywordsFOS: Computer and information sciences, FOS: Physical sciences, Machine Learning (cs.LG), Quantum Physics (quant-ph)

Reinforcement learning studies how an agent should interact with an environment to maximize its cumulative reward. A standard way to study this question abstractly is to ask how many samples an agent needs from the environment to learn an optimal policy for a γ-discounted Markov decision process (MDP). For such an MDP, we design quantum algorithms that approximate an optimal policy (π∗), the optimal value function (v∗), and the optimal Q-function (q∗), assuming the algorithms can access samples from the environment in quantum superposition. This assumption is justified whenever there exists a simulator for the environment; for example, if the environment is a video game or some other program. Our quantum algorithms, inspired by value iteration, achieve quadratic speedups over the best-possible classical sample complexities in the approximation accuracy (ϵ) and two main parameters of the MDP: the effective time horizon (11−γ) and the size of the action space (A). Moreover, we show that our quantum algorithm for computing q∗ is optimal by proving a matching quantum lower bound.