  In many computational science and engineering applications, the output of a
system of interest corresponding to a given input can be queried at different
levels of fidelity with different costs. Typically, low-fidelity data is cheap
and abundant, while high-fidelity data is expensive and scarce. In this work we
study the reinforcement learning (RL) problem in the presence of multiple
environments with different levels of fidelity for a given control task. We
focus on improving the RL agent's performance with multifidelity data.
Specifically, a multifidelity estimator that exploits the cross-correlations
between the low- and high-fidelity returns is proposed to reduce the variance
in the estimation of the state-action value function. The proposed estimator,
which is based on the method of control variates, is used to design a
multifidelity Monte Carlo RL (MFMCRL) algorithm that improves the learning of
the agent in the high-fidelity environment. The impacts of variance reduction
on policy evaluation and policy improvement are theoretically analyzed by using
probability bounds. Our theoretical analysis and numerical experiments
demonstrate that for a finite budget of high-fidelity data samples, our
proposed MFMCRL agent attains superior performance compared with that of a
standard RL agent that uses only the high-fidelity environment data for
learning the optimal policy.
