Soft Sequence Policy Optimization

Proximal Policy Optimization (PPO) is central to aligning Large Language Models (LLMs) in reasoning tasks with verifiable rewards. However, standard token-level PPO struggles in this setting due to the instability of temporal credit assignment over long Chain-of-Thought (CoT) horizons and the prohibitive memory cost of the value model. While critic-free alternatives like GRPO mitigate these issues, they incur significant computational overhead by requiring multiple samples for baseline estimation, severely limiting training throughput. In this paper, we introduce Sequence-Level PPO (SPPO), a scalable algorithm that harmonizes the sample efficiency of PPO with the stability of outcome-based updates. SPPO reformulates the reasoning process as a Sequence-Level Contextual Bandit problem, employing a decoupled scalar value function to derive low-variance advantage signals without multi-sampling. Extensive experiments on mathematical benchmarks demonstrate that SPPO significantly surpasses standard PPO and matches the performance of computation-heavy group-based methods, offering a resource-efficient framework for aligning reasoning 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.

Reinforcement Learning with Verifiable Rewards (RLVR) enhances Large Language Model (LLM) reasoning but is suffer from advantage collapse: when all rollouts of a query receive identical rewards, the group variance vanishes, most damagingly on hard samples, where scaling rollout budgets yields little. We introduce Joint Policy and Prompt Optimization (P O) to mitigate this collapse by alternating continuous policy updates with discrete prompt evolution. P O mines hard samples with a success-rate threshold, evolves reasoning prompts for them with GEPA, and internalizes the elicited trajectories via context distillation, which optimizes each trajectory under the original query and thus removes inference-time prompting, with a Context Ratio Mask (CRM) filtering out extreme likelihood ratios. P O restores critical advantage signals and surpasses the GRPO baseline by up to 8.2 points in average accuracy on six held-out benchmarks across all training datasets and backbones, while also outperforming DAPO and other baselines. The gains are especially pronounced on hard benchmarks, reaching up to 16.3 points above GRPO on average across AIME24 and AIME25. Our findings expose the limits of standard exploration in sparse-reward environments, illuminating the potential of unifying evolutionary algorithms with reinforcement learning. This integration of discrete semantic search and continuous parameter updates provides a self-reinforcing framework that facilitates more effective LLM alignment.