Exploration and Experimentation with a Misspecified Simulator

Randomized experiments are the standard for measuring causal effects that guide decisions, but are costly. Simulators calibrated to historical data offer a cheaper alternative, but their policies can become suboptimal under drift, a change in dynamics after calibration. We study if, when, and how to collect data for recalibrating the simulator. We consider a system with multiple units running in parallel and managed by a single operator. The real-world system is a partially observed process with a latent variable, while the simulator models it as a fully observed Markovian process, and thus is misspecified. Two data collection strategies exploit the current policy: (i) never recalibrating and (ii) recalibrating from on-policy data (passive adaptation). Two others collect off-policy data by trying actions outside the current policy: (iii) continuous exploration across all units and (iv) randomized experimentation on a sample of units over a predefined window. We investigate these strategies theoretically and in a vending-machine simulation. Experiments can improve on passive adaptation when drift is invisible in on-policy data or recalibration lags behind continuing drift. Experimentation is preferable to exploration when trying a worse action is expensive and the dynamics may not have changed.