  We combine deep optical and radio data, from the Hyper Suprime-Cam and the
Low-Frequency Array (LOFAR) respectively, to study 78 radio AGN in nearby
(z<0.5) dwarf galaxies. Comparison to a control sample, matched in stellar mass
and redshift, indicates that the AGN and controls reside in similar
environments, show similar star-formation rates (which trace gas availability)
and exhibit a comparable incidence of tidal features (which indicate recent
interactions). We explore the AGN properties by combining the predicted gas
conditions in dwarfs from a cosmological hydrodynamical simulation with a
Monte-Carlo suite of simulated radio sources, based on a semi-analytical model
for radio-galaxy evolution. In the subset of LOFAR-detectable simulated
sources, which have a similar distribution of radio luminosities as our
observed AGN, the median jet powers, ages and accretion rates are $\sim
10^{35}$ W, $\sim 5$ Myr and $\sim 10^{-3.4}$ M$_{\odot}$ yr$^{-1}$
respectively. The median mechanical energy output of these sources is $\sim100$
times larger than the median binding energy expected in dwarf gas reservoirs,
making AGN feedback plausible. Since special circumstances (in terms of
environment, gas availability and interactions) are not necessary for the
presence of AGN, and the central gas masses are predicted to be an order of
magnitude larger than that required to fuel the AGN, AGN triggering in dwarfs
is likely to be stochastic and a common phenomenon. Together with the
plausibility of energetic feedback, this suggests that AGN could be important
drivers of dwarf-galaxy evolution, as is the case in massive galaxies.
