Partial Policy Gradients for RL in LLMs

Policy gradient algorithms for language models optimize the same objective $J(θ) = \mathbb{E}*{τ\sim p*θ(τ)}[R(τ)]$, which has exactly two factors: the trajectory probability $p_θ(τ)$ and the reward $R(τ)$. Every method from REINFORCE to PPO to GRPO and their descendants modifies one or both factors to address a specific failure in the preceding formulation. Existing surveys organize these methods by domain or chronology, which obscures the rationale behind each design choice and the precise location of its intervention within the gradient estimator. This survey revisits the landscape of LLM policy optimization from $J(θ)$ on first principles and uses the trajectory side, induced by $p_θ(τ)$, and the reward side, induced by $R(τ)$, as the two axes along which methods are located. It covers the path from REINFORCE and PPO to GRPO, as well as post-GRPO variants, Agentic RL, and GRPO-OPD. The resulting framework is unified, diagnostic, and extensible: it analyzes methods from a shared objective, identifies which side each method modifies and why, and applies the same trajectory and reward axes across these settings. Across these settings, the framework also exposes compound failures that no single-side fix resolves and that therefore require joint design of the trajectory side and the reward side. The boundary cases and coupled failures identified by this map mark where existing solutions run out and provide a principled starting point for designing the next generation of LLM policy optimization algorithms.

We study when large language models (LLMs) can serve as effective black-box policy optimizers for reinforcement learning (RL) tasks, i.e., when can we replace classical RL algorithms with an LLM? We explore this question by introducing Prompted Policy Optimization (PromptPO), an iterative method that prompts an LLM with Python descriptions of the state space, action space, and reward function, then has it generate and refine executable policies based on rollout feedback. Across hard exploration environments, Meta-World robotics tasks, and several real-world control problems, PromptPO often matches or exceeds the performance of standard RL baselines while using substantially fewer environment interactions. To maximize expected return, and without further explicit prompting, the policies PromptPO outputs range from tuned proportional controllers or rule-based plans to policies that run planning algorithms like value iteration. Our results demonstrate that LLM-based policy optimization is sufficient when the LLM can leverage prior knowledge about the environment or optimization strategy. PromptPO underperforms standard RL baselines in MuJoCo domains. This demonstrates possible limitations of LLM-based policy optimization to settings that requiring fine-grained continuous control.

Reinforcement learning (RL) has become central to LLM post-training, yet the methods that dominate current pipelines, PPO and GRPO, represent only a narrow slice of what RL offers. Understanding why these methods prevail, and what alternatives exist, requires a principled examination of the design decisions that underlie any RL algorithm. This survey organizes that examination around three stages of algorithm construction. We begin with MDP creation: how the reward function, state space, action space, termination condition, and discount factor are, or could be, defined for LLM training. We then turn to exploration, covering temperature sampling, entropy regularization, intrinsic motivation, tree search, and curriculum learning. Finally, we address learning along four classical RL dimensions: model-free versus model-based, value-based versus policy-based versus actor-critic, on-policy versus off-policy, and credit assignment, including both Monte Carlo methods, which rely on full return estimates, and bootstrapping methods, which update estimates using other learned predictions. Mapping the LLM literature onto this taxonomy reveals a strikingly non-uniform distribution of research effort. Critic-free policy gradients and Monte Carlo credit assignment are densely populated, while value-based methods, off-policy actor-critic training, and bootstrapping-based credit assignment remain largely unexplored despite well-established counterparts in classical RL. These gaps represent concrete opportunities for transferring proven RL techniques to LLM training. By making these gaps explicit alongside the methods that have proven effective, this survey offers researchers in both RL and LLMs a shared framework for understanding current practice and identifying promising directions for future work.