Quantum algorithms for reinforcement learning with a generative model - Wang, Daochen; Sundaram, Aarthi; Kothari, Robin; Kapoor, Ashish; Roetteler, Martin (2021 International Conference on Machine Learning, 2021)
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 ([1][1-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.