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 cosmic microwave background (CMB) optical depth and Ly α and Ly β forest dark pixel fraction produce \dot{N}_\textrm {ion} evolution ( d\log _{10}\dot{\mathbf {N}}_{ion}/ dz|_{z=6\rArr 8} = -0.31± 0.35 dex) consistent with the declining UV luminosity density of galaxies, assuming constant ionizing photon escape fraction and efficiency. Including measurements from Ly α damping of galaxies and quasars produces a more rapid decline: d\log _{10}\dot{\mathbf {N}}_{ion}/ dz|_{z=6\rArr 8} =-0.44± 0.22 dex, steeper than the declining galaxy luminosity density (if extrapolated beyond M_UV≳ -13), and constrains the mid-point of reionization to z = 6.93 ± 0.14.
