Optimizing Sparse Outcomes Through Dense Behavioral Signals via Value-Guided Preference Distillation

On-policy distillation (OPD) enhances the capabilities of small language agents by providing dense, token-level supervision from a teacher model on student-generated trajectories. However, standard OPD implicitly assumes that credit is uniformly distributed across long-horizon trajectories, assigning the same strength of teacher supervision to different actions. Through credit-distribution analysis and outcome-reversal counterfactual experiments, we find that trajectory credit is concentrated on a small number of critical actions. Moreover, even when the trajectory is held fixed, reversing only the final outcome substantially changes the credit assigned to multiple interaction turns. These findings show that the uniform-credit assumption fails to identify critical decisions and ultimately degrades the model's reasoning accuracy. To address these challenges, we propose ToolOPD, an outcome-aware on-policy distillation framework designed for long-horizon tool use. ToolOPD first summarizes each completed trajectory and its outcome into a reusable hindsight skill. It then measures how this skill changes the teacher's probability of each student action token and converts the change into outcome-aware credit. The resulting credit preserves supervision that supports successful decisions or discourages failed ones, while suppressing irrelevant and conflicting signals. ToolOPD uses these credits to reweight the action-level distillation loss and jointly optimizes it with reinforcement learning. Extensive experiments across multiple long-horizon tool interaction benchmarks demonstrate that ToolOPD significantly outperforms existing reinforcement learning and self-distillation baselines.

Large Language Model (LLM) agents increasingly solve long-horizon tasks through multi-turn interactions with users and external tools. In these settings, relevant task information often unfolds over time rather than being fully specified at the initial prompt. Service agents make this challenge especially concrete: users may clarify or revise their goals, while tool responses provide information needed for subsequent decisions. Thus, a final reward alone cannot indicate which actions contributed to resolving the task. Recent methods rely on comparative evidence from other trajectories or resampled continuations, or on separately constructed step-level learning signals, to refine credit. However, a completed rollout already records how information and errors flow between agent actions. We introduce Influence-Aware Policy Optimization (IAPO), which represents each rollout as a typed influence-dependency graph over trainable agent actions, with user and tool observations serving as evidence. IAPO converts support-use and failed-use structure into routing weights that redistribute the same trajectory-level advantage. Experiments with Qwen3-4B and Qwen3-8B demonstrate superior performance over multi-turn reinforcement learning (RL) baselines across three service-agent benchmarks: ${τ^2}$-Bench, UserBench, and AgentChangeBench. BFCL-v4 Multi-Turn further shows that these gains do not compromise multi-turn function-calling performance. This work advances the understanding of credit assignment in multi-turn user interactions and provides a principled approach to training service agents from sparse outcome feedback.

Long-horizon agentic tasks pose a fundamental credit assignment challenge for outcome-base reinforcement learning: trajectory-level rewards verify final correctness but provide limited guidance on which intermediate reasoning steps or tool interactions contribute to the outcome. The difficulty is especially pronounced in multi-turn search agents, where successful trajectories may contain misleading actions and failed trajectories may contain valuable evidence-gathering steps. We propose PBSD (Privileged Bayesian Self-Distillation), a Bayes-calibrated self-distillation method for fine-grained credit assignment under sparse final rewards. PBSD measures trajectory quality through the posterior-to-prior probability ratio of the verified answer and applies Bayes' rule to convert this hard-to-estimate answer-side ratio into a tractable likelihood ratio between a standard student model and a privileged answer-conditioned teacher model. Autoregressive decomposition of this Bayesian evidence score yields turn-level signals that identify whether each intermediate turn supports or undermines the verified outcome. Consequently, PBSD provides a principled and elegant reweighting scheme that transforms sparse outcome supervision into Bayes-calibrated turn-level credit signals, while remaining fully compatible with standard policy optimization. Experiments demonstrate that PBSD consistently enhances performance across both in-domain and out-of-domain settings, and effectively transfers knowledge from short-context training to long-context inference, suggesting that its fine-grained credit assignment mechanism facilitates more effective policy learning and yields improved generalization.