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Quantum algorithms for reinforcement learning with a generative model
Daochen Wang · Aarthi Sundaram · Robin Kothari · Ashish Kapoor · Martin Roetteler

Thu Jul 22 09:00 AM -- 11:00 AM (PDT) @ Virtual #None
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 $\gamma$-discounted Markov decision process (MDP). For such an MDP, we design quantum algorithms that approximate an optimal policy ($\pi^*$), 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 ($\epsilon$) and two main parameters of the MDP: the effective time horizon ($\frac{1}{1-\gamma}$) 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.

Author Information

Daochen Wang (University of Maryland)
Aarthi Sundaram (Microsoft)
Robin Kothari (Microsoft)
Ashish Kapoor (Microsoft Research)
Martin Roetteler (Microsoft)

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