Policy Gradient Post-Training: Optimality and Base Model Barrier
A recent paper on arXiv (2603.06957v2) explores the post-training of linear autoregressive models utilizing both outcome and process rewards. The researchers demonstrate that when the base model reaches a non-trivial likelihood α for test samples, a modified policy gradient (PG) approach can achieve a likelihood of 1 - ε, requiring a minimax optimal number of reward queries, specifically O~((α^{-1} + ε^{-1})/γ^2). However, challenges arise when trying to extend beyond the base model's support. The expected error after post-training with outcome rewards is influenced by a characteristic known as the Likelihood Quantile (LQ). Although variants of PG are minimax optimal, they may necessitate an exponential number of reward queries in N to overcome this limitation. The study also broadens the conventional separability condition to sequences through a γ margin condition, highlighting essential constraints of post-training techniques in AI, particularly in reinforcement learning and model optimization.
Key facts
- Paper arXiv:2603.06957v2 studies post-training linear autoregressive models with outcome and process rewards.
- A γ margin condition extends standard separability to sequences.
- Policy gradient variant achieves likelihood 1 - ε with minimax optimal reward queries O~((α^{-1} + ε^{-1})/γ^2) when base model likelihood is α.
- A barrier exists for going beyond the base model's support.
- Expected error after post-training is governed by the Likelihood Quantile (LQ) property of the base model.
- PG variants may require exponential reward queries in N to overcome the barrier.
- The paper is available on arXiv with announcement type replace-cross.
- The research has implications for AI post-training and reinforcement learning.
Entities
Institutions
- arXiv