  In this work we theoretically show that conservative objective models (COMs)
for offline model-based optimisation (MBO) are a special kind of contrastive
divergence-based energy model, one where the energy function represents both
the unconditional probability of the input and the conditional probability of
the reward variable. While the initial formulation only samples modes from its
learned distribution, we propose a simple fix that replaces its gradient ascent
sampler with a Langevin MCMC sampler. This gives rise to a special
probabilistic model where the probability of sampling an input is proportional
to its predicted reward. Lastly, we show that better samples can be obtained if
the model is decoupled so that the unconditional and conditional probabilities
are modelled separately.
