On-policy distillation (OPD) trains a student on its own trajectories with token-level teacher feedback and often outperforms off-policy distillation and reinforcement learning with verifiable rewards. However, we find that its standard advantage-weighted policy gradient suffers from three structural weaknesses, including high-variance updates, vanishing gradients in zero-advantage regions, and exploration bottlenecks for models with limited capability. We therefore propose asymmetric on-policy distillation (AOPD), which replaces ineffective policy gradient with localized divergence minimization in non-positive advantage regions while preserving positive reinforcement learning. Experiments on mathematical reasoning benchmarks show that AOPD consistently outperforms standard OPD, with average gains of 4.09 / 8.34 under strong / weak initialization, respectively. AOPD also maintains higher policy entropy during training and better capability retention during sequential tool-use adaptation. Our source code is available at [repository](https://github.com/stargazer319/AOPD).

Text-to-SQL parsing has achieved remarkable progress under the Full Schema Assumption, where the complete database structure is pre-loaded into the model’s context. Yet this assumption overlooks a more fundamental capability question of whether an LLM agent can resolve a query without explicit access to the underlying tables and relations. Moreover, full-schema injection may exceed the effective context window, introduce irrelevant metadata into the reasoning process, and become less reliable as databases evolve. We therefore study the Unknown Schema setting, in which an agent must actively explore the database and commit to only the relevant subset of metadata. To address this, we propose TRUST-SQL (Truthful Reasoning with Unknown Schema via Tools). We formulate the task as a Partially Observable Markov Decision Process in which our autonomous agent follows a structured four-phase protocol to ground reasoning in verified metadata. This protocol provides a structural boundary for our novel Phase-Aware GRPO strategy, which applies token-level masked advantages to isolate exploration rewards from execution outcomes and resolve credit assignment, yielding a 9.9% relative improvement over standard GRPO. Extensive experiments across five benchmarks demonstrate that TRUST-SQL is effective at multiple scales (4B/ 8B/14B). Despite operating entirely without pre-loaded metadata, our agent matches or surpasses prior baselines on most benchmarks that rely on schema prefilling.

Optimizing large language models for industrial sales requires balancing long-term commercial objectives (e.g., conversion rate) with immediate linguistic constraints such as fluency and compliance. Conventional reinforcement learning often merges these heterogeneous goals into a single reward, causing high-magnitude session-level rewards to overwhelm subtler turn-level signals, which leads to unstable training or reward hacking.To address this issue, we propose Dual-Horizon Credit Assignment (DuCA), a framework that disentangles optimization across time scales. Its core, Horizon-Independent Advantage Normalization (HIAN), separately normalizes advantages from turn-level and session-level rewards before fusion, ensuring balanced gradient contributions from both immediate and long-term objectives to the policy update.Extensive experiments with a high-fidelity user simulator show DuCA outperforms the state-of-the-art GRPO baseline, achieving a 6.82% relative improvement in conversion rate, reducing inter-sentence repetition by 82.28%, and lowering identity detection rate by 27.35%, indicating a substantial improvement for an industrial sales scenario that effectively balances the dual demands of strategic performance and naturalistic language generation.