  We introduce a deep generative model for functions. Our model provides a
joint distribution p(f, z) over functions f and latent variables z which lets
us efficiently sample from the marginal p(f) and maximize a variational lower
bound on the entropy H(f). We can thus maximize objectives of the form
E_{f~p(f)}[R(f)] + c*H(f), where R(f) denotes, e.g., a data log-likelihood term
or an expected reward. Such objectives encompass Bayesian deep learning in
function space, rather than parameter space, and Bayesian deep RL with
representations of uncertainty that offer benefits over bootstrapping and
parameter noise. In this short paper we describe our model, situate it in the
context of prior work, and present proof-of-concept experiments for regression
and RL.
