Flooding is the natural hazard most likely to affect individuals and can be driven by rainfall, river discharge, storm surge, tides, and waves. Compound floods result from their co-occurrence and can generate a larger flood hazard when compared to the synthetic flood hazard generated by the respective flood drivers occurring in isolation from one another. Current state-of-the-art stochastic compound flood risk assessments are based on statistical, hydrodynamic, and impact simulations. However, the stochastic nature of some key variables in the flooding process is often not accounted for as adding stochastic variables exponentially increases the computational costs (i.e., the curse of dimensionality). These simplifications (e.g., a constant flood driver duration or a constant time lag between flood drivers) may lead to a mis-quantification of the flood risk. This study develops a conceptual framework that allows for a better representation of compound flood risk while limiting the increase in the overall computational time. After generating synthetic events from a statistical model fitted to the selected flood drivers, the proposed framework applies a treed Gaussian process (TGP). A TGP uses active learning to explore the uncertainty associated with the response of damages to synthetic events. Thereby, it informs regarding the best choice of hydrodynamic and impact simulations to run to reduce uncertainty in the damages. Once the TGP predicts the damage of all synthetic events within a tolerated uncertainty range, the flood risk is calculated. As a proof of concept, the proposed framework was applied to the case study of Charleston County (South Carolina, USA) and compared with a state-of-the-art stochastic compound flood risk model, which used equidistant sampling with linear scatter interpolation. The proposed framework decreased the overall computational time by a factor of 4 and decreased the root mean square error in damages by a factor of 8. With a reduction in overall computational time and errors, additional stochastic variables such as the drivers' duration and time lag were included in the compound flood risk assessment. Not accounting for these resulted in an underestimation of 11.6 % (USD 25.47 million) in the expected annual damage (EAD). Thus, by accelerating compound flood risk assessments with active learning, the framework presented here allows for more comprehensive assessments as it loosens constraints imposed by the curse of dimensionality.