PoEM: Predicting RL Outcomes from Existing Policies

Kimia Hamidieh, Giannis Daras, Antonio Torralba

Foundation models are post-trained with reinforcement learning (RL) to maximize specific rewards, such as human alignment, correctness, or instruction following. This post-training process is computationally intensive, sometimes unstable, and has to be run from scratch every time the reward model changes or when we want to combine multiple rewards. We hence ask: given a new reward function, is it possible to predict the RL outcomes without actually running RL on it? We answer this in the affirmative by introducing PoEM, a framework to predict the outputs of RL on a new reward function using a set of models already post-trained on other rewards. First, we show that if the new reward function can be written as a linear combination of existing ones, then the new policy in log-space can be written as a linear combination of the existing log-policies. Surprisingly, even in cases where the rewards are not linearly connected, we observe that often log-policies from RL training span an approximately low-rank subspace across rewards. To our benefit, the weighting coefficients for this combination can be estimated using only the reward or basis policy outputs on the samples. We turn these…