  The availability of large pre-trained models is changing the landscape of
Machine Learning research and practice, moving from a training-from-scratch to
a fine-tuning paradigm. While in some applications the goal is to "nudge" the
pre-trained distribution towards preferred outputs, in others it is to steer it
towards a different distribution over the sample space. Two main paradigms have
emerged to tackle this challenge: Reward Maximization (RM) and, more recently,
Distribution Matching (DM). RM applies standard Reinforcement Learning (RL)
techniques, such as Policy Gradients, to gradually increase the reward signal.
DM prescribes to first make explicit the target distribution that the model is
fine-tuned to approximate. Here we explore the theoretical connections between
the two paradigms, and show that methods such as KL-control developed for RM
can also be construed as belonging to DM. We further observe that while DM
differs from RM, it can suffer from similar training difficulties, such as high
gradient variance. We leverage connections between the two paradigms to import
the concept of baseline into DM methods. We empirically validate the benefits
of adding a baseline on an array of controllable language generation tasks such
as constraining topic, sentiment, and gender distributions in texts sampled
from a language model. We observe superior performance in terms of constraint
satisfaction, stability and sample efficiency.
