Stale but Stable: Staleness-Adaptive Trust Regions for Stabilizing Asynchronous Reinforcement Learning

Asynchronous reinforcement learning improves throughput by decoupling rollout generation from optimization, but staleness is an inevitable byproduct compounded by policy lag, engine delays, and mixture-of-experts routing. From a trust-region perspective, this mismatch is critical: training-inference divergence governs approximation error in finite-horizon bounds, whereas PPO clipping only gates sampled outward updates, acting as a sampled surrogate rather than a full-policy constraint. As a result, high-staleness updates remain weakly controlled in the asynchronous regime where stale rollouts matter most. We introduce the Staleness-Adaptive Trust Region (SAT), which uses the detached sampled log-ratio as a practical staleness proxy, identifies high-mismatch tails within each batch via staleness-based kernel scaling, and contracts only the sign-selected endpoint of the nominal PPO interval. This preserves baseline behavior on ordinary tokens while enforcing more conservative updates on newly intercepted outward bands. We prove local interval containment and pointwise pessimism relative to PPO, showing how the adaptive rule reshapes update geometry under heterogeneous staleness. We evaluate SAT in a decoupled asynchronous RL setup built on Qwen3-30B-A3B-Base, using SGLang as the inference engine and Megatron for training. In this setting, SAT-GSPO w/ R3 achieves the best observed AIME24 avg@8, reaching 35.83 at lag 1 and 34.79 at lag 8, while SAT-GSPO reaches 34.17 at lag 1. Adaptive clipping and routing replay act as complementary stabilizers targeting mismatch tails and routing inconsistency, respectively. Overall, aligning clip intervals with staleness heterogeneity effectively stabilizes asynchronous RL.

Risk-Constrained Freshness-Aware Semantic Caching for Open-Web Retrieval-Augmented LLMs

Semantic caching reduces the latency and cost of retrieval-augmented generation (RAG) by serving cached answers to semantically similar queries, but most existing methods do not model the time-varying freshness of open-web evidence. We present FreshCache, a three-tier semantic cache that treats cache reuse as a risk-constrained temporal inference problem: before approving a cache hit, FreshCache estimates the probability that the cached result is stale using a fitted exponential decay model enhanced by a learned MLP, and approves reuse only when that probability falls below a per-tier error budget across answers (epsilon = 0.10), URL lists (epsilon = 0.20), and page content (epsilon = 0.35). This allows the system to degrade gracefully as entries age rather than forcing a binary choice between a stale hit and a full pipeline execution. We introduce FreshCache-Bench, a benchmark of 8,072 base queries across five freshness classes with ground truth staleness labels drawn from real web snapshots at 1, 12, 24 hours, and 7 days after a baseline crawl, expanded to 31,201 queries via paraphrase generation. At the 24-hour evaluation window, FreshCache_MLP achieves 97% search API savings at 0.1% hash-based stale error, and an LLM-judge evaluation on 396 confirmed change pairs shows that only 34.3% of detected content changes actually affect answer correctness, placing true answer-affecting stale error at approximately 0.034%. The rule-based FreshCache achieves 98% search savings at 3.3% stale error under a temporal holdout calibration, outperforming SemanticTTL (14.9% stale, 72% saved), vCache (7.2% stale, 47% saved), and SCALM (5.2% stale, 96% saved). Ablations show the temporal risk gate accounts for an 11.6 point reduction in stale error over similarity-only reuse, and the learned MLP reduces stale error a further 3.2 points over the rule-based model.

Staleness-Learning Rate Scaling Laws for Asynchronous RLHF

High-throughput RLHF systems often decouple rollout generation from policy optimization, leading to the use of stale rollouts during learner updates. In this work, we study the effect of such staleness in asynchronous GRPO. We make the behavior policy explicit in the GRPO surrogate objective and distinguish between the surrogate-gradient mapping used by the learner and the true total derivative of a distribution-dependent population objective. Under assumptions of local boundedness, distributional smoothness, and behavior-policy smoothness, we show that stale rollouts introduce a per-step surrogate-gradient bias of order O(S * eta), where S denotes the maximum rollout lag and eta denotes the learning rate. We further derive a conditional collapse-time scaling law: when within-cycle drift remains below a batch-level clipping radius, collapse is governed primarily by cumulative learner drift T * eta; when the stale-rollout constraint is active, stability instead depends explicitly on S * eta. This yields a two-constraint stability condition eta << min{R_batch / (S * G_upd), R_crit / (T * G_upd)}, explaining why the maximum stable learning rate may appear weakly dependent on staleness in the horizon-limited regime.

Inverse Probability Weighting and Age-of-Information Aggregation for Decentralized Federated Learning under Partial Reception

Decentralized Federated Learning (DFL) over lossy wireless networks faces two key challenges: selection bias, where updates from poor-quality links are systematically underrepresented due to partial model reception, and update staleness, where asynchronous nodes contribute outdated information. We show that uniform gossip aggregation with local-fill reconstruction introduces persistent link-quality-induced bias, while completeness-based weighting further amplifies this effect. To address these challenges, we propose DFL-AA (Decentralized Federated Learning with Adaptive AoI-weighted Aggregation), which combines Inverse Probability Weighting with online EWMA-based channel estimation to correct selection bias and Age-of-Information-based weighting to mitigate staleness without requiring global synchronization. We theoretically show that DFL-AA removes link-quality distortion in expectation and experimentally demonstrate consistent improvements over state-of-the-art baselines across varying loss rates, network sizes, and heterogeneous wireless conditions.

FOAM: Frequency and Operator Error-Based Adaptive Damping Method for Reducing Staleness-Oriented Error for Shampoo

Shampoo is attracting considerable attention for its superior performance on large-scale optimization benchmarks; yet it faces a significant practical bottleneck: the prohibitive computational overhead of matrix inversion. To mitigate this, practitioners typically rely on stale preconditioner updates, creating a fundamental trade-off between computational efficiency and optimization fidelity. In this work, we provide a theoretical study of staleness through the complementary lenses of convergence and stability. While staleness improves computational efficiency, it inherently degrades performance and introduces numerical instability. Crucially, we identify that damping, acting as a numerical stabilizer, can effectively suppress these negative effects. Guided by this analysis, we propose FOAM, an adaptive algorithm that stabilizes training by dynamically controlling both the damping factor and the eigendecomposition frequency based on an approximation of the staleness-oriented error. Experimental results demonstrate that FOAM reduces wall-clock time compared to standard Shampoo while maintaining robust convergence.