  Strong gravitational lenses are a singular probe of the universe's
small-scale structure $\unicode{x2013}$ they are sensitive to the gravitational
effects of low-mass $(<10^{10} M_\odot)$ halos even without a luminous
counterpart. Recent strong-lensing analyses of dark matter structure rely on
simulation-based inference (SBI). Modern SBI methods, which leverage neural
networks as density estimators, have shown promise in extracting the
halo-population signal. However, it is unclear whether the constraining power
of these models has been limited by the methodology or the information content
of the data. In this study, we introduce an accelerator-optimized simulation
pipeline that can generate lens images with realistic subhalo populations in a
matter of milliseconds. Leveraging this simulator, we identify the main
methodological limitation of our fiducial SBI analysis: training set size. We
then adopt a sequential neural posterior estimation (SNPE) approach, allowing
us to iteratively refine the distribution of simulated training images to
better align with the observed data. Using only one-fifth as many mock Hubble
Space Telescope (HST) images, SNPE matches the constraints on the low-mass halo
population produced by our best non-sequential model. Our experiments suggest
that an over three order-of-magnitude increase in training set size and GPU
hours would be required to achieve an equivalent result without sequential
methods. While the full potential of the existing strong lens sample remains to
be explored, the notable improvement in constraining power enabled by our
sequential approach highlights that the current constraints are limited
primarily by methodology and not the data itself. Moreover, our results
emphasize the need to treat training set generation and model optimization as
interconnected stages of any cosmological analysis using simulation-based
inference techniques.
