A Note on Hybrid Online Reinforcement and Imitation Learning for LLMs: Formulations and Algorithms

We present a unified framework for Large Language Model (LLM) fine-tuning that integrates Imitation Learning and Reinforcement Learning. By analyzing the gradient of a composite objective combining trajectory-level KL divergence with task rewards, we derive a natural decomposition into two components: (1) an analytically computable Dense Gradient for token-level imitation, and (2) a Monte Carlo estimated Sparse Gradient for long-horizon reward optimization. The Dense Gradient admits a closed-form logit-level formula, enabling efficient GPU implementation.

Trust Region Masking for Long-Horizon LLM Reinforcement Learning

Policy gradient methods for large language models optimize a surrogate objective computed from samples of a rollout policy $π_{\text{roll}}$. When $π_{\text{roll}} \ne π_θ$, there is approximation error between the surrogate and the true objective. Prior work has shown that this off-policy mismatch is unavoidable in modern LLM-RL due to implementation divergence, mixture-of-experts routing discontinuities, and distributed training staleness. Classical trust region bounds on the resulting error scale as $O(T^2)$ with sequence length $T$, rendering them vacuous for long-horizon tasks. We derive two tighter bounds: a Pinsker-Marginal bound scaling as $O(T^{3/2})$ and a Mixed bound scaling as $O(T)$. Crucially, both bounds depend on $D_{kl}^{tok,max}$ -- the maximum token-level KL divergence across all positions in a sequence. This is inherently a sequence-level quantity: it requires examining the entire trajectory to compute, and therefore cannot be controlled by token-independent methods like PPO clipping. We propose Trust Region Masking (TRM), which excludes entire sequences from gradient computation if any token violates the trust region, providing the first non-vacuous monotonic improvement guarantees for long-horizon LLM-RL.

Taming the Tail: Stable LLM Reinforcement Learning via Dynamic Vocabulary Pruning

Reinforcement learning for large language models (LLMs) faces a fundamental tension: high-throughput inference engines and numerically-precise training systems produce different probability distributions from the same parameters, creating a training-inference mismatch. We prove this mismatch has an asymmetric effect: the bound on log-probability mismatch scales as $(1-p)$ where $p$ is the token probability. For high-probability tokens, this bound vanishes, contributing negligibly to sequence-level mismatch. For low-probability tokens in the tail, the bound remains large, and moreover, when sampled, these tokens exhibit systematically biased mismatches that accumulate over sequences, destabilizing gradient estimation. Rather than applying post-hoc corrections, we propose constraining the RL objective to a dynamically-pruned ``safe'' vocabulary that excludes the extreme tail. By pruning such tokens, we trade large, systematically biased mismatches for a small, bounded optimization bias. Empirically, our method achieves stable training; theoretically, we bound the optimization bias introduced by vocabulary pruning.

Harnessing Uncertainty: Entropy-Modulated Policy Gradients for Long-Horizon LLM Agents

In long-horizon tasks, recent agents based on Large Language Models (LLMs) face a significant challenge that sparse, outcome-based rewards make it difficult to assign credit to intermediate steps. Previous methods mainly focus on creating dense reward signals to guide learning, either through traditional reinforcement learning techniques like inverse reinforcement learning or by using Process Reward Models for step-by-step feedback. In this paper, we identify a fundamental problem in the learning dynamics of LLMs: the magnitude of policy gradients is inherently coupled with the entropy, which leads to inefficient small updates for confident correct actions and potentially destabilizes large updates for uncertain ones. To resolve this, we propose Entropy-Modulated Policy Gradients (EMPG), a framework that re-calibrates the learning signal based on step-wise uncertainty and the final task outcome. EMPG amplifies updates for confident correct actions, penalizes confident errors, and attenuates updates from uncertain steps to stabilize exploration. We further introduce a bonus term for future clarity that encourages agents to find more predictable solution paths. Through comprehensive experiments on three challenging agent tasks, WebShop, ALFWorld, and Deep Search, we demonstrate that EMPG achieves substantial performance gains and significantly outperforms strong policy gradient baselines. Project page is at https://empgseed-seed.github.io/

GLM-4.5: Agentic, Reasoning, and Coding (ARC) Foundation Models

We present GLM-4.5, an open-source Mixture-of-Experts (MoE) large language model with 355B total parameters and 32B activated parameters, featuring a hybrid reasoning method that supports both thinking and direct response modes. Through multi-stage training on 23T tokens and comprehensive post-training with expert model iteration and reinforcement learning, GLM-4.5 achieves strong performance across agentic, reasoning, and coding (ARC) tasks, scoring 70.1% on TAU-Bench, 91.0% on AIME 24, and 64.2% on SWE-bench Verified. With much fewer parameters than several competitors, GLM-4.5 ranks 3rd overall among all evaluated models and 2nd on agentic benchmarks. We release both GLM-4.5 (355B parameters) and a compact version, GLM-4.5-Air (106B parameters), to advance research in reasoning and agentic AI systems. Code, models, and more information are available at https://github.com/zai-org/GLM-4.5.

Logit Dynamics in Softmax Policy Gradient Methods

We analyzes the logit dynamics of softmax policy gradient methods. We derive the exact formula for the L2 norm of the logit update vector: $$ \|\Delta \mathbf{z}\|_2 \propto \sqrt{1-2P_c + C(P)} $$ This equation demonstrates that update magnitudes are determined by the chosen action's probability ($P_c$) and the policy's collision probability ($C(P)$), a measure of concentration inversely related to entropy. Our analysis reveals an inherent self-regulation mechanism where learning vigor is automatically modulated by policy confidence, providing a foundational insight into the stability and convergence of these methods.

OWL: Optimized Workforce Learning for General Multi-Agent Assistance in Real-World Task Automation

Large Language Model (LLM)-based multi-agent systems show promise for automating real-world tasks but struggle to transfer across domains due to their domain-specific nature. Current approaches face two critical shortcomings: they require complete architectural redesign and full retraining of all components when applied to new domains. We introduce Workforce, a hierarchical multi-agent framework that decouples strategic planning from specialized execution through a modular architecture comprising: (i) a domain-agnostic Planner for task decomposition, (ii) a Coordinator for subtask management, and (iii) specialized Workers with domain-specific tool-calling capabilities. This decoupling enables cross-domain transferability during both inference and training phases: During inference, Workforce seamlessly adapts to new domains by adding or modifying worker agents; For training, we introduce Optimized Workforce Learning (OWL), which improves generalization across domains by optimizing a domain-agnostic planner with reinforcement learning from real-world feedback. To validate our approach, we evaluate Workforce on the GAIA benchmark, covering various realistic, multi-domain agentic tasks. Experimental results demonstrate Workforce achieves open-source state-of-the-art performance (69.70%), outperforming commercial systems like OpenAI's Deep Research by 2.34%. More notably, our OWL-trained 32B model achieves 52.73% accuracy (+16.37%) and demonstrates performance comparable to GPT-4o on challenging tasks. To summarize, by enabling scalable generalization and modular domain transfer, our work establishes a foundation for the next generation of general-purpose AI assistants.

Divergence-Augmented Policy Optimization

In deep reinforcement learning, policy optimization methods need to deal with issues such as function approximation and the reuse of off-policy data. Standard policy gradient methods do not handle off-policy data well, leading to premature convergence and instability. This paper introduces a method to stabilize policy optimization when off-policy data are reused. The idea is to include a Bregman divergence between the behavior policy that generates the data and the current policy to ensure small and safe policy updates with off-policy data. The Bregman divergence is calculated between the state distributions of two policies, instead of only on the action probabilities, leading to a divergence augmentation formulation. Empirical experiments on Atari games show that in the data-scarce scenario where the reuse of off-policy data becomes necessary, our method can achieve better performance than other state-of-the-art deep reinforcement learning algorithms.

Adaptive Foundation Models for Online Decisions: HyperAgent with Fast Incremental Uncertainty Estimation

Foundation models often struggle with uncertainty when faced with new situations in online decision-making, necessitating scalable and efficient exploration to resolve this uncertainty. We introduce GPT-HyperAgent, an augmentation of GPT with HyperAgent for uncertainty-aware, scalable exploration in contextual bandits, a fundamental online decision problem involving natural language input. We prove that HyperAgent achieves fast incremental uncertainty estimation with $\tilde{O}(\log T)$ per-step computational complexity over $T$ periods under the linear realizable assumption. Our analysis demonstrates that HyperAgent's regret order matches that of exact Thompson sampling in linear contextual bandits, closing a significant theoretical gap in scalable exploration. Empirical results in real-world contextual bandit tasks, such as automated content moderation with human feedback, validate the practical effectiveness of GPT-HyperAgent for safety-critical decisions. Our code is open-sourced at \url{https://github.com/szrlee/GPT-HyperAgent/}.

Prior-dependent analysis of posterior sampling reinforcement learning with function approximation

This work advances randomized exploration in reinforcement learning (RL) with function approximation modeled by linear mixture MDPs. We establish the first prior-dependent Bayesian regret bound for RL with function approximation; and refine the Bayesian regret analysis for posterior sampling reinforcement learning (PSRL), presenting an upper bound of ${\mathcal{O}}(d\sqrt{H^3 T \log T})$, where $d$ represents the dimensionality of the transition kernel, $H$ the planning horizon, and $T$ the total number of interactions. This signifies a methodological enhancement by optimizing the $\mathcal{O}(\sqrt{\log T})$ factor over the previous benchmark (Osband and Van Roy, 2014) specified to linear mixture MDPs. Our approach, leveraging a value-targeted model learning perspective, introduces a decoupling argument and a variance reduction technique, moving beyond traditional analyses reliant on confidence sets and concentration inequalities to formalize Bayesian regret bounds more effectively.