\section{Conclusion}
\label{sec:conclusion}
This paper introduced Hot DoG, a learning-rate-free stochastic gradient method
designed for learning coreset weights using Coreset MCMC. Our
method extends DoG, but includes adjustments tailored to the Markovian setting
of Coreset MCMC. In particular, Hot DoG includes a hot-start test detecting
when to start training coreset weights as well as acceleration
techniques. Our method is shown to produce coreset weights that converge to the 
optimum. The quality of coresets constructed by Hot DoG 
and their corresponding posterior approximation are robust to input parameters. 
Empirically, Hot DoG under our recommended setting ($r=0.001$ and $c=0.5$) 
produces better posterior approximations than other learning-rate-free stochastic 
gradient methods, and is competitive to optimally-tuned ADAM.
