From $P(y|x)$ to $P(y)$: Investigating Reinforcement Learning in Pre-train Space

2026-04-15 · Source: Artificial Intelligence · Field: Technology & Digital — Artificial Intelligence & Machine Learning · Depth: Expert, quick

Summary

The paper introduces PreRL (Pre-train Space Reinforcement Learning), a novel approach that applies reward-driven online updates directly to the marginal distribution P(y) in the pre-train space, rather than solely optimizing the conditional distribution P(y|x) as in traditional reinforcement learning with verifiable rewards (RLVR). This method aims to overcome the limitations of base models by encoding reasoning ability and preserving broad exploration capacity, which conventional pre-training on static corpora often hinders due to distribution shifts. PreRL demonstrates strong gradient alignment between log P(y) and log P(y|x), making it a viable surrogate for standard RL. A key finding is that Negative Sample Reinforcement (NSR) within PreRL significantly enhances reasoning by pruning incorrect reasoning spaces and stimulating reflective behaviors, increasing transition and reflection thoughts by 14.89x and 6.54x, respectively. Building on this, Dual Space RL (DSRL) is proposed, a Policy Reincarnation strategy that initializes models with NSR-PreRL before transitioning to standard RL for fine-grained optimization, consistently outperforming strong baselines.

Key takeaway

For AI Engineers and Research Scientists developing advanced LLMs, consider integrating PreRL and Dual Space RL (DSRL) into your training pipelines. Initializing models with NSR-PreRL can significantly expand reasoning horizons and prune incorrect reasoning spaces, leading to more robust and reflective models before fine-tuning with standard RL. This approach offers a path to overcome the inherent limitations of base models and achieve superior reasoning performance.

Key insights

Optimizing the marginal distribution P(y) in pre-train space enhances LLM reasoning and exploration beyond conditional P(y|x) optimization.

Principles

• P(y) optimization can surrogate P(y|x) optimization.
• Negative Sample Reinforcement drives effective reasoning.
• Pre-train space pruning refines reasoning policies.

Method

PreRL applies reward-driven online updates to P(y). DSRL uses NSR-PreRL for initial reasoning expansion, then transitions to standard RL for fine-grained optimization.

In practice

• Apply NSR-PreRL to prune incorrect reasoning paths.
• Use DSRL for LLM reasoning enhancement.
• Explore P(y) optimization for broader exploration.

Topics

• Reinforcement Learning in Pre-train Space
• Large Language Models
• PreRL
• Negative Sample Reinforcement
• Dual Space RL

Best for: AI Engineer, Research Scientist, AI Scientist, Machine Learning Engineer, NLP Engineer

Related on AIssential

• Context-Aware RL for Agentic and Multimodal LLMs — ContextRL uses an indirect RL objective to reward fine-grained grounding by selecting supporting contexts for query-answer pairs.
• Step-by-Step Optimization-like Reasoning in LLMs over Expanding Search Spaces — OPT* tasks enable scalable training and evaluation of LLM optimization reasoning by expanding search spaces without new labels.
• DiPRL: Learning Discrete Programmatic Policies via Architecture Entropy Regularization — DiPRL learns discrete programmatic policies directly, avoiding performance drops from post-hoc continuous-to-discrete conversion.
• JustRL: A Simple RL Recipe Just Works, No Tricks/Patches Needed — A simplified RL approach can outperform complex methods for scaling LLMs in math reasoning.
• Value-Gradient Hypothesis of RL for LLMs — Critic-free RL for LLMs works because the actor's backward pass implicitly propagates a value-gradient signal, approximated via attention.
• Data News — Week 25.43 — Modern AI systems combine pre-training and reinforcement learning (RL) to achieve advanced reasoning and behavioral capabilities.

Open in AIssential →

Editorial summary, takeaway, and curation by AIssential. Original article published by Artificial Intelligence.