  Modelling reionization often requires significant assumptions about the
properties of ionizing sources. Here, we infer the total output of
hydrogen-ionizing photons (the ionizing emissivity, $\dot{N}_\textrm{ion}$) at
$z=4-14$ from current reionization constraints, being maximally agnostic to the
properties of ionizing sources. We use a Bayesian analysis to fit for a
non-parametric form of $\dot{N}_\textrm{ion}$, allowing us to flexibly explore
the entire prior volume. We infer a declining $\dot{N}_\textrm{ion}$ with
redshift at $z>6$, which can be used as a benchmark for reionization models.
Model-independent reionization constraints from the CMB optical depth and
Ly$\alpha$ and Ly$\beta$ forest dark pixel fraction produce
$\dot{N}_\textrm{ion}$ evolution
($d\log_{10}\dot{N}_\textrm{ion}/dz|_{z=6\rightarrow8} = -0.31\pm0.35$ dex)
consistent with the declining UV luminosity density of galaxies, assuming
constant ionizing photon escape fraction and efficiency. Including measurements
from Ly$\alpha$ damping of galaxies and quasars produces a more rapid decline:
$d\log_{10}\dot{N}_\textrm{ion}/dz|_{z=6\rightarrow8} =-0.44\pm0.22$ dex,
steeper than the declining galaxy luminosity density (if extrapolated beyond
$M_\mathrm{UV} \lesssim -13$), and constrains the mid-point of reionization to
$z = 6.93\pm0.14$.
