Title: On Reward Maximization and Distribution Matching for Fine-Tuning Language Models. Abstract: 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 intimate connections between the two paradigms and show that methods such as KL-control developed in the RM paradigm 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.