A Multi-Fidelity Control Variate Approach for Policy Gradient Estimation

Many reinforcement learning (RL) algorithms are impractical for training in operational systems or computationally expensive high-fidelity simulations, as they require large amounts of data. Meanwhile, low-fidelity simulators, e.g., reduced-order models, heuristic rewards, or learned world models, can cheaply provide useful data, even if they are too coarse for zero-shot transfer. We propose multi-fidelity policy gradients (MFPGs), a sample-efficient RL framework that mixes scarce target-environment data with a control variate formed from abundant low-fidelity simulation data to construct an unbiased, variance-reduced estimator for on-policy policy gradients. We instantiate the framework with a practical, multi-fidelity variant of the classical REINFORCE algorithm. Under standard assumptions, the MFPG estimator guarantees asymptotic convergence to locally optimal policies in the target environment and achieves faster finite-sample convergence than standard REINFORCE. We evaluate MFPG on robotics benchmark tasks with limited high-fidelity data but abundant off-dynamics, low-fidelity data. When low-fidelity data are neutral or beneficial and dynamics gaps are mild-moderate, MFPG is, among the evaluated off-dynamics RL and low-fidelity-only approaches, the only method that consistently achieves statistically significant improvements over a high-fidelity-only baseline. When low-fidelity data become harmful, MFPG exhibits the strongest robustness, whereas strong off-dynamics RL methods exploit low-fidelity data aggressively and fail much more severely. An additional experiment with anti-correlated high- and low-fidelity rewards shows MFPG can remain effective even under reward misspecification. MFPG thus offers a reliable paradigm for exploiting cheap low-fidelity data (e.g., for efficient sim-to-real transfer) while managing the trade-off between policy performance and data collection cost.