Towards Stable and Effective Reinforcement Learning for Mixture-of-Experts

Recent advances in reinforcement learning (RL) have substantially improved the training of large-scale language models, leading to significant gains in generation quality and reasoning ability. However, most existing research focuses on dense models, while RL training for Mixture-of-Experts (MoE) architectures remains underexplored. To address the instability commonly observed in MoE training, we propose a novel router-aware approach to optimize importance sampling (IS) weights in off-policy RL. Specifically, we design a rescaling strategy guided by router logits, which effectively reduces gradient variance and mitigates training divergence. Experimental results demonstrate that our method significantly improves both the convergence stability and the final performance of MoE models, highlighting the potential of RL algorithmic innovations tailored to MoE architectures and providing a promising direction for efficient training of large-scale expert models.

Never Too Rigid to Reach: Adaptive Virtual Model Control with LLM- and Lyapunov-Based Reinforcement Learning

Robotic arms are increasingly deployed in uncertain environments, yet conventional control pipelines often become rigid and brittle when exposed to perturbations or incomplete information. Virtual Model Control (VMC) enables compliant behaviors by embedding virtual forces and mapping them into joint torques, but its reliance on fixed parameters and limited coordination among virtual components constrains adaptability and may undermine stability as task objectives evolve. To address these limitations, we propose Adaptive VMC with Large Language Model (LLM)- and Lyapunov-Based Reinforcement Learning (RL), which preserves the physical interpretability of VMC while supporting stability-guaranteed online adaptation. The LLM provides structured priors and high-level reasoning that enhance coordination among virtual components, improve sample efficiency, and facilitate flexible adjustment to varying task requirements. Complementarily, Lyapunov-based RL enforces theoretical stability constraints, ensuring safe and reliable adaptation under uncertainty. Extensive simulations on a 7-DoF Panda arm demonstrate that our approach effectively balances competing objectives in dynamic tasks, achieving superior performance while highlighting the synergistic benefits of LLM guidance and Lyapunov-constrained adaptation.

Incentivizing Agentic Reasoning in LLM Judges via Tool-Integrated Reinforcement Learning

Large Language Models (LLMs) are widely used as judges to evaluate response quality, providing a scalable alternative to human evaluation. However, most LLM judges operate solely on intrinsic text-based reasoning, limiting their ability to verify complex constraints or perform accurate computation. Motivated by the success of tool-integrated reasoning (TIR) in numerous tasks, we propose TIR-Judge, an end-to-end RL framework for training LLM judges that integrates a code executor for precise evaluation. TIR-Judge is built on three principles: (i) diverse training across verifiable and non-verifiable domains, (ii) flexible judgment formats (pointwise, pairwise, listwise), and (iii) iterative RL that bootstraps directly from the initial model without distillation. On seven public benchmarks, TIR-Judge surpasses strong reasoning-based judges by up to 6.4% (pointwise) and 7.7% (pairwise), and achieves listwise performance comparable to Claude-Opus-4 despite having only 8B parameters. Remarkably, TIR-Judge-Zero - trained entirely without distilled judge trajectories, matches the performance of distilled variants, demonstrating that tool-augmented judges can self-evolve through iterative reinforcement learning.

AirFed: Federated Graph-Enhanced Multi-Agent Reinforcement Learning for Multi-UAV Cooperative Mobile Edge Computing

Multiple Unmanned Aerial Vehicles (UAVs) cooperative Mobile Edge Computing (MEC) systems face critical challenges in coordinating trajectory planning, task offloading, and resource allocation while ensuring Quality of Service (QoS) under dynamic and uncertain environments. Existing approaches suffer from limited scalability, slow convergence, and inefficient knowledge sharing among UAVs, particularly when handling large-scale IoT device deployments with stringent deadline constraints. This paper proposes AirFed, a novel federated graph-enhanced multi-agent reinforcement learning framework that addresses these challenges through three key innovations. First, we design dual-layer dynamic Graph Attention Networks (GATs) that explicitly model spatial-temporal dependencies among UAVs and IoT devices, capturing both service relationships and collaborative interactions within the network topology. Second, we develop a dual-Actor single-Critic architecture that jointly optimizes continuous trajectory control and discrete task offloading decisions. Third, we propose a reputation-based decentralized federated learning mechanism with gradient-sensitive adaptive quantization, enabling efficient and robust knowledge sharing across heterogeneous UAVs. Extensive experiments demonstrate that AirFed achieves 42.9% reduction in weighted cost compared to state-of-the-art baselines, attains over 99% deadline satisfaction and 94.2% IoT device coverage rate, and reduces communication overhead by 54.5%. Scalability analysis confirms robust performance across varying UAV numbers, IoT device densities, and system scales, validating AirFed's practical applicability for large-scale UAV-MEC deployments.

Softmax is $1/2$-Lipschitz: A tight bound across all $\ell_p$ norms

The softmax function is a basic operator in machine learning and optimization, used in classification, attention mechanisms, reinforcement learning, game theory, and problems involving log-sum-exp terms. Existing robustness guarantees of learning models and convergence analysis of optimization algorithms typically consider the softmax operator to have a Lipschitz constant of $1$ with respect to the $\ell_2$ norm. In this work, we prove that the softmax function is contractive with the Lipschitz constant $1/2$, uniformly across all $\ell_p$ norms with $p \ge 1$. We also show that the local Lipschitz constant of softmax attains $1/2$ for $p = 1$ and $p = \infty$, and for $p \in (1,\infty)$, the constant remains strictly below $1/2$ and the supremum $1/2$ is achieved only in the limit. To our knowledge, this is the first comprehensive norm-uniform analysis of softmax Lipschitz continuity. We demonstrate how the sharper constant directly improves a range of existing theoretical results on robustness and convergence. We further validate the sharpness of the $1/2$ Lipschitz constant of the softmax operator through empirical studies on attention-based architectures (ViT, GPT-2, Qwen3-8B) and on stochastic policies in reinforcement learning.

RL-AUX: Reinforcement Learning for Auxiliary Task Generation

Auxiliary Learning (AL) is a special case of Multi-task Learning (MTL) in which a network trains on auxiliary tasks to improve performance on its main task. This technique is used to improve generalization and, ultimately, performance on the network's main task. AL has been demonstrated to improve performance across multiple domains, including navigation, image classification, and natural language processing. One weakness of AL is the need for labeled auxiliary tasks, which can require human effort and domain expertise to generate. Meta Learning techniques have been used to solve this issue by learning an additional auxiliary task generation network that can create helpful tasks for the primary network. The most prominent techniques rely on Bi-Level Optimization, which incurs computational cost and increased code complexity. To avoid the need for Bi-Level Optimization, we present an RL-based approach to dynamically create auxiliary tasks. In this framework, an RL agent is tasked with selecting auxiliary labels for every data point in a training set. The agent is rewarded when their selection improves the performance on the primary task. We also experiment with learning optimal strategies for weighing the auxiliary loss per data point. On the 20-Superclass CIFAR100 problem, our RL approach outperforms human-labeled auxiliary tasks and performs as well as a prominent Bi-Level Optimization technique. Our weight learning approaches significantly outperform all of these benchmarks. For example, a Weight-Aware RL-based approach helps the VGG16 architecture achieve 80.9% test accuracy while the human-labeled auxiliary task setup achieved 75.53%. The goal of this work is to (1) prove that RL is a viable approach to dynamically generate auxiliary tasks and (2) demonstrate that per-sample auxiliary task weights can be learned alongside the auxiliary task labels and can achieve strong results.

Advantage Shaping as Surrogate Reward Maximization: Unifying Pass@K Policy Gradients

This note reconciles two seemingly distinct approaches to policy gradient optimization for the Pass@K objective in reinforcement learning with verifiable rewards: (1) direct REINFORCE-style methods, and (2) advantage-shaping techniques that directly modify GRPO. We show that these are two sides of the same coin. By reverse-engineering existing advantage-shaping algorithms, we reveal that they implicitly optimize surrogate rewards. We specifically interpret practical ``hard-example up-weighting'' modifications to GRPO as reward-level regularization. Conversely, starting from surrogate reward objectives, we provide a simple recipe for deriving both existing and new advantage-shaping methods. This perspective provides a lens for RLVR policy gradient optimization beyond our original motivation of Pass@K.

Multi-Agent Conditional Diffusion Model with Mean Field Communication as Wireless Resource Allocation Planner

In wireless communication systems, efficient and adaptive resource allocation plays a crucial role in enhancing overall Quality of Service (QoS). While centralized Multi-Agent Reinforcement Learning (MARL) frameworks rely on a central coordinator for policy training and resource scheduling, they suffer from scalability issues and privacy risks. In contrast, the Distributed Training with Decentralized Execution (DTDE) paradigm enables distributed learning and decision-making, but it struggles with non-stationarity and limited inter-agent cooperation, which can severely degrade system performance. To overcome these challenges, we propose the Multi-Agent Conditional Diffusion Model Planner (MA-CDMP) for decentralized communication resource management. Built upon the Model-Based Reinforcement Learning (MBRL) paradigm, MA-CDMP employs Diffusion Models (DMs) to capture environment dynamics and plan future trajectories, while an inverse dynamics model guides action generation, thereby alleviating the sample inefficiency and slow convergence of conventional DTDE methods. Moreover, to approximate large-scale agent interactions, a Mean-Field (MF) mechanism is introduced as an assistance to the classifier in DMs. This design mitigates inter-agent non-stationarity and enhances cooperation with minimal communication overhead in distributed settings. We further theoretically establish an upper bound on the distributional approximation error introduced by the MF-based diffusion generation, guaranteeing convergence stability and reliable modeling of multi-agent stochastic dynamics. Extensive experiments demonstrate that MA-CDMP consistently outperforms existing MARL baselines in terms of average reward and QoS metrics, showcasing its scalability and practicality for real-world wireless network optimization.

Offline Preference Optimization via Maximum Marginal Likelihood Estimation

Aligning Large Language Models (LLMs) with human preferences is crucial, but standard methods like Reinforcement Learning from Human Feedback (RLHF) are often complex and unstable. In this work, we propose a new, simpler approach that recasts alignment through the lens of Maximum Marginal Likelihood (MML) estimation. Our new MML based Preference Optimization (MMPO) maximizes the marginal log-likelihood of a preferred text output, using the preference pair as samples for approximation, and forgoes the need for both an explicit reward model and entropy maximization. We theoretically demonstrate that MMPO implicitly performs preference optimization, producing a weighted gradient that naturally up-weights chosen responses over rejected ones. Across models ranging from 135M to 8B parameters, we empirically show that MMPO: 1) is more stable with respect to the hyperparameter $\beta$ compared to alternative baselines, and 2) achieves competitive or superior preference alignment while better preserving the base model's general language capabilities. Through a series of ablation experiments, we show that this improved performance is indeed attributable to MMPO's implicit preference optimization within the gradient updates.

PASS-Enhanced MEC: Joint Optimization of Task Offloading and Uplink PASS Beamforming

A pinching-antenna system (PASS)-enhanced mobile edge computing (MEC) architecture is investigated to improve the task offloading efficiency and latency performance in dynamic wireless environments. By leveraging dielectric waveguides and flexibly adjustable pinching antennas, PASS establishes short-distance line-of-sight (LoS) links while effectively mitigating the significant path loss and potential signal blockage, making it a promising solution for high-frequency MEC systems. We formulate a network latency minimization problem to joint optimize uplink PASS beamforming and task offloading. The resulting problem is modeled as a Markov decision process (MDP) and solved via the deep reinforcement learning (DRL) method. To address the instability introduced by the $\max$ operator in the objective function, we propose a load balancing-aware proximal policy optimization (LBPPO) algorithm. LBPPO incorporates both node-level and waveguide-level load balancing information into the policy design, maintaining computational and transmission delay equilibrium, respectively. Simulation results demonstrate that the proposed PASS-enhanced MEC with adaptive uplink PASS beamforming exhibit stronger convergence capability than fixed-PA baselines and conventional MIMO-assisted MEC, especially in scenarios with a large number of UEs or high transmit power.