Self-Induced Outcome Potential: Turn-Level Credit Assignment for Agents without Verifiers

Reinforcement learning (RL) with verifiable rewards constructs trajectory-level advantage estimates, yet it often fails to credit the few pivotal decisions that determine outcomes in long-horizon, multi-turn agentic tasks. Recent work introduces privileged self-distillation for credit assignment, providing denser supervision, but it remains unclear how such local signals should represent sequential credit. We propose AgentOPSD, a critic-free, recursive method for turn-level credit assignment in agentic reinforcement learning. AgentOPSD aggregates token-level teacher-student log-probability gaps into turn-level evidence and recursively updates a Bayesian belief state in log-odds space. This yields a principled reweighting scheme that converts sparse outcome supervision into turn-level credit signals and identifies pivotal turns through the marginal belief revision between consecutive states. The method is fully compatible with standard policy optimization and requires neither an additional critic nor extra rollouts. We evaluate AgentOPSD on ALFWorld, WebShop, and Search-QA using Qwen2.5 models at two scales (3B and 7B). AgentOPSD outperforms GRPO and strong self-distillation baselines, achieving 89.1% success on ALFWorld with Qwen2.5-7B. Ablation studies attribute the gains to turn-level aggregation and history-dependent recursive belief updates.

Reinforcement learning from verifiable rewards (RLVR) has improved the reasoning abilities of large language models (LLMs), but most existing approaches rely on sparse outcome-level feedback. This sparsity creates a credit assignment challenge in long-horizon agentic reasoning: a trajectory may fail despite containing many correct intermediate decisions, or succeed despite containing flawed ones. In this work, we study a class of densely-verifiable agentic reasoning problems, where intermediate actions can be objectively checked by symbolic or algorithmic oracles. We propose Verifiable Process Rewards (VPR), a framework that converts such oracles into dense turn-level supervision for reinforcement learning, and instantiate it in three representative settings: search-based verification for dynamic deduction, constraint-based verification for logical reasoning, and posterior-based verification for probabilistic inference. We further provide a theoretical analysis showing that dense verifier-grounded rewards can improve long-horizon credit assignment by providing more localized learning signals, with the benefit depending on the reliability of the verifier. Empirically, VPR outperforms outcome-level reward and rollout-based process reward baselines across controlled environments, and more importantly, transfers to both general and agentic reasoning benchmarks, suggesting that verifiable process supervision can foster general reasoning skills applicable beyond the training environments. Our results indicate that VPR is a promising approach for enhancing LLM agents whenever reliable intermediate verification is available, while also highlighting its dependence on oracle quality and the open challenge of extending VPR to less structured, open-ended environments.

Recent LLM search agents use reinforcement learning with verifiable rewards (RLVR) to learn search-augmented reasoning from outcome rewards. On hard problems, these agents rarely sample end-to-end successful rollouts, leaving outcome-only RLVR with few positive-reward trajectories. We argue that improving learning on such problems requires additional guidance during training, and RLVR already contains verifier-side information that can provide it. This information can identify errors or omissions in the agent's submitted answer and guide revision within the rollout. We propose a training-time mechanism called \textbf{Credit-Attenuated Privileged Feedback} (CAPF), which makes this verifier-side information available through a Privileged Feedback call during training. CAPF lets the policy revise zero-reward attempts into positive-reward repair trajectories and attenuates credit for the feedback call and earlier actions to accommodate deployment without this call. Empirical research demonstrates that CAPF improves Qwen3-4B's average exact-match score from 44.7% under outcome-only RLVR to 48.5% on seven open-domain QA benchmarks.