Scaling Laws for Reward Model Overoptimization
Authors: Leo Gao, John Schulman, Jacob Hilton
AI-generated Key Points
- Optimizing against a reward model trained to predict human preferences can lead to overoptimization and hinder performance of the ground truth
- The study uses a synthetic setup with a fixed "gold-standard" reward model as a substitute for humans
- Two different methods, reinforcement learning and best-of-$n$ sampling, are used to optimize against the proxy reward model
- The relationship between gold reward model scores and proxy reward model scores depends on the optimization method used
- Coefficients in this relationship scale smoothly with the number of reward model parameters
- Factors such as size of the reward model dataset, number of reward model and policy parameters, and coefficient of KL penalty impact this relationship
- Implications for theoretical considerations in AI alignment are discussed based on empirical results
- Optimizing against imperfect proxy models can affect performance in reinforcement learning from human feedback scenarios
- Balancing optimization against such models while maintaining alignment with ground truth objectives is important.
Abstract: In reinforcement learning from human feedback, it is common to optimize against a reward model trained to predict human preferences. Because the reward model is an imperfect proxy, optimizing its value too much can hinder ground truth performance, in accordance with Goodhart's law. This effect has been frequently observed, but not carefully measured due to the expense of collecting human preference data. In this work, we use a synthetic setup in which a fixed "gold-standard" reward model plays the role of humans, providing labels used to train a proxy reward model. We study how the gold reward model score changes as we optimize against the proxy reward model using either reinforcement learning or best-of-$n$ sampling. We find that this relationship follows a different functional form depending on the method of optimization, and that in both cases its coefficients scale smoothly with the number of reward model parameters. We also study the effect on this relationship of the size of the reward model dataset, the number of reward model and policy parameters, and the coefficient of the KL penalty added to the reward in the reinforcement learning setup. We explore the implications of these empirical results for theoretical considerations in AI alignment.
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