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The paper investigates the entropy dynamics of policy gradient algorithms in language model reasoning, revealing a natural tendency for entropy reduction during training, which limits exploration and diversity. They analyze the impact of policy gradient objectives and empirical factors on entropy, and introduce REPO and ADAPO, novel algorithms for explicit entropy control by modifying the advantage function and using adaptive asymmetric clipping, respectively. Experiments demonstrate that models trained with these entropy-preserving methods maintain diversity, achieve higher performance, and retain trainability for sequential learning.
Policy gradient methods may be self-defeating in language model reasoning, as their inherent entropy reduction chokes off exploration and limits downstream performance.
Policy gradient algorithms have driven many recent advancements in language model reasoning. An appealing property is their ability to learn from exploration on their own trajectories, a process crucial for fostering diverse and creative solutions. As we show in this paper, many policy gradient algorithms naturally reduce the entropy -- and thus the diversity of explored trajectories -- as part of training, yielding a policy increasingly limited in its ability to explore. In this paper, we argue that entropy should be actively monitored and controlled throughout training. We formally analyze the contributions of leading policy gradient objectives on entropy dynamics, identify empirical factors (such as numerical precision) that significantly impact entropy behavior, and propose explicit mechanisms for entropy control. These include REPO, a family of algorithms that modify the advantage function to regulate entropy, and ADAPO, an adaptive asymmetric clipping approach. Models trained with our entropy-preserving methods maintain diversity throughout training, yielding final policies that are more performant and retain their trainability for sequential learning in new environments.
