Organizations: Shanghai Jiao Tong University · The Hong Kong University of Science and Technology (Guangzhou) · The University of Science and Technology of China · Nanjing University · The University of Hong Kong
Abstract
Modern reasoning agents are increasingly evaluated on their ability to generate multiple valid solution paths, plans, or tool-use traces for a given input. Standard reward-maximizing RL tends to collapse onto the most easily reinforced high-reward mode, whereas distribution-matching RL aims to allocate probability mass across the entire reward-shaped solution set. Achieving this objective requires computing a prompt-dependent partition function over the trajectory space. Because existing distribution-matching methods learn this partition function online alongside the policy, calibration errors in the partition function directly distort policy updates and remain impossible to diagnose independently. We introduce DISA, short for Decoupled Importance-Sampled Anchoring, which moves this calibration problem outside the RL loop. DISA draws proposal trajectories offline, estimates the partition function via importance sampling, and freezes the resulting partition-function estimate before policy optimization begins. This decoupling preserves the distribution-matching objective while strictly separating partition-function estimation from policy learning in data, gradients, loss, and diagnostics. Empirically, on two open-weight backbones across six math and three code benchmarks, DISA matches or exceeds the online-coupled distribution-matching baseline FlowRL, outperforms rewardmaximization baselines GRPO and GSPO on math averages, and exceeds LoRASFT distillation by up to 13.8 Mean@8 points on the same offline trajectories. An LLM-as-judge evaluation further shows that DISA retains substantially more strategy-level diversity than reward-maximization baselines, and sensitivity studies on the proposal strength and inverse temperature follow the bias-variance pattern predicted by the analysis.
Diffusion large language models (dLLMs) are promising alternatives to autoregressive large language models (AR-LLMs), as they potentially allow higher inference throughput. Reinforcement learning (RL) is crucial to enabling dLLMs to achieve performance comparable to that of AR-LLMs on important tasks, such as reasoning. However, RL algorithms well-suited to dLLMs' unique characteristics have yet to be developed. This paper proposes Distribution Matching Policy Optimization (DMPO), a principled and theoretically grounded RL fine-tuning method specifically designed to enhance the reasoning capabilities of dLLMs by matching the dLLM policy distribution to the optimal, reward-tilted one through cross-entropy optimization. We identify a key implementation challenge with small training batch sizes and propose several effective solutions based on a novel weight baseline subtraction technique. DMPO exhibits superior performance on multiple reasoning benchmarks without supervised fine-tuning, achieving up to a 39.63 percentage-point improvement in accuracy over prior non-DMPO RL baselines and 67.97 percentage points over the base model, underscoring the effectiveness of the distribution-matching framework. Our code is available at https://github.com/yuchen-zhu-zyc/DMPO.
Recent analyses question whether reinforcement learning (RL) is responsible for strong reasoning in large language models (LLMs). At the same time, distillation and inference-time sampling, including power sampling, have emerged as effective ways to improve LLM performance. However, the relationship among RL, distillation, and sampling remains unclear. In this study, we focus on the power distribution, the target distribution of power sampling, and show that the power distribution bridges sampling, self-reward KL-regularized RL, and self-distillation. From the sampling perspective, we show that inexpensive local approximations cannot reproduce sequence-level power without information about possible suffixes. From the RL perspective, the power distribution is the closed-form optimizer of KL-regularized RL when the model's sequence-level log-probabilities are used as the reward. This identification leads to power self-distillation, an offline distillation surrogate that shares the same target distribution and amortizes the cost of power sampling into supervised training on teacher samples. We further show that power self-distillation can achieve self-reward sharpening, while improvement in a downstream true reward is governed by the covariance between true reward and self-reward under the power distribution. Experiments on reasoning tasks support our analysis: power sampling raises self-reward, true-reward gains depend on alignment with self-reward, and power self-distillation can match or exceed the performance of power sampling at much lower inference cost.
Reasoning models have advanced rapidly, but the dominant reinforcement learning from verifiable rewards (RLVR) recipe remains surprisingly narrow: sample many responses and reward each with a single bit indicating whether the final answer is correct. Yet many settings provide rich feedback, including execution traces, tool outputs, expert corrections, and model self-evaluations. We study how to use such feedback through a distributional variant of the classic imitation learning algorithm DAgger, where the learner has local access to an expert distribution on states visited by the current policy. This yields a simple forward cross-entropy objective that admits a blackbox expert and whose sequence-level gradient {conduct rich credit assignment by propagating} future expert-student disagreement back to earlier decisions. We show that prior RL with self-distillation objectives based on reverse KL or Jensen-Shannon fail to guarantee monotonic policy improvement: even when the expert has higher reward, their updates may increase probability on worse actions. In contrast, we show that forward cross-entropy admits monotonic policy improvement and enjoys guarantees on regret. We further show that our objective optimizes a lower bound on teacher-weighted likelihood of success, leading to improved Pass@N. Empirically, our approach, DistIL, improves over RLVR and RL with self-distillation baselines across a variety of domains: scientific reasoning, coding, and solving hard mathematical problems.
Rishabh Agrawal, Jacob Fein-Ashley, Paria Rashidinejad