Reinforcement learning from human feedback (RLHF) has emerged as a powerful yet sample-inefficient approach for learning reward models from human preferences, making active learning a critical component in synthesizing informative preference queries. However, effective uncertainty quantification required for active learning remains a key challenge for large neural network reward models. In this paper, we introduce PreferenceEKF, a sample-efficient approach that tracks reward model uncertainty by framing active preference learning as a sequential Bayesian filtering problem. Instead of relying on computationally prohibitive posterior inference over the full neural network parameter space, our method performs sequential inference via an extended Kalman filter within a low-dimensional parameter subspace, continuously updating the reward model posterior as new preference queries arrive. Our approach enables scalable sampling of neural network parameters to efficiently compute acquisition functions for active reward learning. Experiments on the D4RL and V-D4RL benchmarks demonstrate that our approach achieves better sample efficiency, runtime, scalability, and calibration compared to other Bayesian deep learning approaches, and the learned reward models lead to competitive offline reinforcement learning policy performance. This highlights the potential of scalable Bayesian methods for preference-based reward modeling in RLHF. Our code is available at https://github.com/yutaizhou/bnn_pref.
Reinforcement learning typically optimizes average reward. For generative policies, the average can hide an important distinction: two policies can achieve the same mean reward while having very different chances of producing a rare but high-reward rollout. This matters as sampling increases during training and inference, since its benefit depends on retaining probability mass on high-reward outcomes. We propose to optimize this coverage directly. Rather than considering only expected reward, we consider all of its upper tails: for each reward threshold, how likely is the policy to exceed it? This turns a continuous reward into a family of binary success events. We introduce Tail-Likelihood Reinforcement Learning (TailRL), which maximizes the log-probability of exceeding a randomly chosen reward threshold. Its gradient gives more weight to rare, high-reward rollouts and can be interpreted as a mixture of Best-of-(k) gradients. TailRL requires only a simple modification to the advantage function, making it compatible with existing reinforcement learning pipelines. Across object localization, maze navigation, GUI grounding, and code optimization, TailRL leverages rare high-reward training samples to avoid suboptimal solutions and yields models that benefit more from additional samples at inference time.
Rubric-based reinforcement learning decomposes open-ended instructions into prompt-specific, flexible rubrics, making it better suited than reinforcement learning with verifiable rewards for post-training LLMs on open-ended tasks. However, static rubrics are inevitably hacked as the policy evolves, and existing dynamic approaches introduce new problems: undirected rubric extraction, unreliable hack detection, and unbounded rubric proliferation. We propose $\textbf{CARE}$ ($\textbf{C}$ontrastive $\textbf{A}$nchor-based $\textbf{R}$ubric $\textbf{E}$volution), which grounds every rubric evolution step in a high-quality anchor response generated by a frontier model conditioned on the prompt and its rubrics. At each training step, CARE contrasts the highest-scoring rollout against the anchor, enabling two complementary mechanisms: an Adaptive branch that reactively repairs reward misspecification; and a Chase branch that proactively converts frontier-level quality gaps into sharper rubrics. Together, the two branches $\textbf{maintain discriminative accuracy in the high-reward region}$---the precise region where reward over-optimization mostly originates. Experiments on WildChecklist-9K with Qwen2.5-7B-Base and Qwen2.5-7B-Instruct show that CARE achieves state-of-the-art performance on Arena-Hard-2.0, InfoBench, and FollowBench, and is the $\textbf{only}$ method whose win rate against GPT-4.1 anchor responses shows sustained improvement throughout 300 training steps; additional results on Llama-3.1-8B-Instruct and Qwen3-8B further indicate that CARE generalizes across model families.
Rubric-based reinforcement learning extends RL beyond tasks with exact answers or rule-based verifiers by scoring responses against instance-specific criteria. However, this makes reward computation expensive: training requires repeated rubric judging, often with proprietary APIs or local generative LLM judges with 7B parameters or more. We study whether smaller language models can serve as efficient and reliable rubric-based judges. To make this question measurable, we construct PointRubric and RaR-Science-Static, two pointwise rubric-based evaluation datasets with instance-specific criteria and itemwise satisfaction labels. We compare three ways of extracting criterion-level judgments from small models: Generative verdicts, Yes/No Logprob margins, and Probe judges. Across both datasets, the Qwen3-1.7B Probe judge achieves the strongest criterion-level agreement among these methods, outperforming Generative and Logprob judges. Used as a GRPO reward model, it trains a policy from 0.232 to 0.643 on RaR-Science rubric score, compared with 0.594 for an 8B Generative judge baseline, while the baseline requires 10.7$\times$ more reward-judge time. Task and domain transfer experiments further suggest that Probe judges preserve criterion-level reward structure across settings.
Generative model alignment has received broad interest, and significant progress has been made in supervised fine-tuning and inference-time computation. Yet, alignment has remained poorly understood from a statistical learning perspective. We formulate inference-time alignment as a weak-to-strong learning problem, where a reference policy (weak model) is assumed to be fairly good and the goal is to produce a strong model that predicts a good response at test time with arbitrarily high probability. Our problem is formulated as learning from scratch --- everything is learned from data rather than assuming access to a good reward estimate, and thus differs from the existing inference-time alignment theory. Our framework shares similarity to the recent work of Joshi et al., (arXiv:2510.15464), where for each prompt, there could be multiple good responses. Our definition of the alignment learnability follows the standard PAC learning principle. We introduce a novel combinatorial dimension of the reward class which we call the alignment dimension, and show that it completely characterizes the alignment learnability --- a reward class is alignment learnable if and only if its alignment dimension is finite. The core of our learning procedure works by learning a pairwise comparator and then running a tournament over candidate responses. We believe that our results might shed light toward establishing a complete theoretical understanding of alignment.
Reinforcement learning (RL) for terminal agents needs executable training environments with reliable rewards and useful difficulty. Fixed recipes such as few-shot, Self-Instruct, and Evol-Instruct apply the same prompting policy to every seed, even when the current policy would benefit from a harder, easier, or simply different task. We present Envs-FORGE, a prompting policy that converts verifier rewards into per-seed environment-synthesis actions. Envs-FORGE estimates seed pass rates, scores six projection--direction actions around a target learning frontier, and solves a per-seed mixed-integer linear program (MILP) to choose the action that conditions generation. The selected action drives synchronized rewriting of the instruction, fixtures, oracle solution, tests, and Docker environment; only gold-verified bundles enter RL training. The indexed MILP form also supports optional soft skill coverage for portfolio planning. On Qwen 3.5 35B, Envs-FORGE improves Pass@1 over Base by 9.2 percentage points on tb-core (40.0% to 49.2%) and 6.4 points on tb-2.0 (23.0% to 29.4%), exceeding the strongest fixed-recipe baseline by 2.4 and 2.1 points. It reaches 77.1% on SWE-bench Verified versus 73.4% for Base, and improves tb-core by 6.8--9.2 points across the evaluated 4B--35B models. All synthesis methods export 100 verified environments and use 2.27M--2.88M synthesis tokens, placing the comparison at the same downstream training-set size and the same operational scale. The source code is available at https://github.com/DataArcTech/DataArc-SynData-Toolkit/.
Multi-agent reinforcement learning (MARL) is a powerful framework for solving complex collaborative tasks, but it relies heavily on well-defined global reward functions. Designing such rewards is challenging, especially in systems with heterogeneous agents, where a single scalar objective may fail to capture diverse behaviors. In this paper, we introduce Multi-AGent Preference-Integrated lEarning (MAGPIE), which addresses these challenges through agent-specific preference modeling. Each agent is evaluated by a dedicated expert through preference signals, eliminating the need for global evaluation. We theoretically prove that optimizing these decentralized preferences converges to a Nash equilibrium policy. To integrate local preferences into a coherent global objective, we construct agent-specific reward models from preference data and combine them via a monotonic aggregation mechanism. We further prove that optimizing this aggregate reward model is equivalent to training the Nash equilibrium policy. Extensive experiments on benchmark multi-agent tasks and a sequential production line task show that MAGPIE achieves performance comparable to reward-engineered baselines, demonstrating its potential to facilitate policy learning in scenarios where precise reward engineering is impractical.
Chenglong Wang, Ziming Zhu, Yifu Huo +9cs.LG cs.CL
Recent advances in reward modeling show a paradigm shift from discriminative reward models to generative reward models. However, despite their strong capabilities in response ranking, generative reward models have not realized their potential in reinforcement learning (RL). Our analysis reveals that this limitation arises from a mismatch between the comparative nature of generative reward modeling and the scalar scoring paradigm adopted by existing RL algorithms. To bridge this gap, we propose a Ranking-based Reward Construction (RRC) approach, which enables generative reward models to provide more effective RL learning signals by deriving rewards from relative preference rankings. RRC introduces two complementary strategies: self-competitive ranking, which exploits comparisons among sampled responses, and anchor-guided ranking, which enables scalable ranking-based reward construction with a small set of reference responses. Experiments across open-ended chat and reasoning benchmarks demonstrate that RRC substantially improves RL training with generative reward models, achieving consistent gains over existing reward construction approaches. Our code can be found at https://github.com/wangclnlp/RRC.
Seongyoon Kim, Boryeong Cho, Jihwan Oh +2cs.LG cs.AI
Large language models are increasingly aligned to human preferences via reward modeling, but user preference data are sensitive and often cannot be centralized. Federated learning keeps such data local while learning a shared initial reward model, which is later personalized for each client through local fine-tuning. Because users often assign opposite labels to the same pair of responses, existing federated methods address preference heterogeneity by clustering similar clients and training one reward model per group, assuming that each group requires its own initialization. We show that this assumption is unnecessary. Under balanced preference groups, a single FedAvg model, despite starting at nearly random accuracy, surpasses reward models trained separately for each ground-truth group after only a few local optimization steps. We attribute this phenomenon to the flatness of the shared initialization: averaging across all clients learns richer shared representations that distinguish responses while canceling conflicting preference directions, leaving the model near a decision boundary that can be rapidly adapted. Group imbalance breaks this effect as the cancellation becomes asymmetric and leaves minority clients too far from the boundary to recover. Motivated by this observation, we propose FedGD (Federated Learning with Group Debiasing), which discovers latent preference groups during federated training and learns a single reward model using group-debiased client sampling. By counteracting the effect of group imbalance, FedGD learns an initialization that remains highly adaptable, enabling effective personalization without prior knowledge of the underlying groups.
Chinmay Rane, Kanishka Tyagi, Michael Manrycs.LG cs.AI
PPO and the GRPO baseline studied here use clipped surrogate objectives whose favorable-direction saturation introduces an abrupt change in the scalar objective's derivative. We ask whether Output Reset (OR), a smooth one-sided saturation rule, offers a useful alternative for large language model post-training. PPO-OR and GRPO-OR replace the clipped policy term with an OR squared-margin loss in rollout-relative token log-ratio space; the advantage sign determines the update direction, and a token contributes zero direct OR residual after crossing the favorable margin. We compare PPO-clip with PPO-OR under generalized advantage estimation (GAE), and GRPO with GRPO-OR under group-relative advantages, using \texttt{Llama-3.2-1B-Instruct} on Anthropic \texttt{hh-rlhf} with one shared reward model and three seeds per method. Under GAE, PPO-OR has a mean final training-time reward-model score $0.305$ higher than PPO-clip, with a larger observed across-seed spread. Under group-relative advantages, GRPO-OR does not have a higher mean score, but shows a smaller observed spread, a near-zero terminal OR residual, and a declining overshoot fraction, while the matched GRPO clipped-objective trace remains variable. Both group-relative methods exhibit substantially larger rollout-to-current log-ratio displacement than the GAE methods, and OR does not consistently reduce it. Thus, OR changes optimization behavior in both matched comparisons, but the observed reward effect differs between them. At $G=2$, the GRPO-OR diagnostics do not translate into a reward-score gain. Whether larger groups change this outcome remains open. The reported scores are training-time reward-model measurements, not held-out human-preference performance.
Reinforcement learning for multi-turn search reasoning typically relies on terminal outcome rewards, which cannot distinguish useful, redundant, and harmful intermediate interactions. We propose LAPO, a self-generated process-supervision method based on backward leave-one-turn attribution. For each search turn, LAPO replaces the turn and its retrieval observation with a fixed [DELETE] placeholder and measures the resulting change in the current policy's mean log-likelihood of the gold answer. This Answer-Likelihood Gain estimates the turn's contribution while preserving all downstream interactions, allowing early evidence to be evaluated in the complete reasoning context. LAPO further applies sign-consistency gating, retaining only normalized process advantages whose directions agree with their raw attribution scores. The method requires no additional reward model, teacher, verifier, or LLM-as-a-Judge. Across seven knowledge-intensive question-answering datasets with local retrieval, LAPO achieves an average exact-match score of 0.326, outperforming the strongest step-reward baseline, IGPO, by 0.053. Ablations show complementary benefits from backward attribution and sign-consistency gating, demonstrating that policy-derived retrospective attribution can provide effective process supervision for multi-turn search agents.
Simone Drago, Marco Mussi, Leonardo Bianconi +1cs.LG
In this work, we study the reinforcement learning (RL) problem from pairwise trajectory comparisons provided by a human expert. We generalize preference-based RL by formalizing a novel setting in which the expert can also label trajectory pairs as incomparable, i.e., when neither trajectory dominates the other. We introduce the learning problem and the desiderata that its solution should satisfy. Then, we propose a novel Bradley-Terry-inspired rationality model that effectively captures incomparabilities and infers a multi-dimensional reward function, and we study its properties. We provide a sample complexity analysis for learning the model parameters when a dataset is available. Finally, we evaluate our model's ability to reconstruct a reward function that aligns with the expert's comparisons in simulated environments and to recover the Pareto frontier of policies, along with a robustness analysis across varying levels of expert rationality.
Yong Yi Bay, Kathleen A. Yearickcs.LG cs.AI cs.CL stat.ML
Three of the most popular methods for training language models to reason look like three different tricks. They are not. All three adjust a single number: standard deviation, reflecting how much a prompt's sampled answers disagree. When such a model is trained, it answers each problem many times, and an automatic checker marks every answer right or wrong. The standard deviation of those marks measures the disagreement: largest when the answers split evenly between right and wrong, and zero when they all agree. Group Relative Policy Optimization (GRPO) divides by this number, GRPO Done Right (Dr. GRPO) drops the division, and Decoupled Clip and Dynamic Sampling Policy Optimization (DAPO) discards the groups where it is zero. Each is presented as its own fix, yet this paper proves they are three settings of one dial. That dial is not cosmetic: for right-or-wrong rewards, the disagreement is exactly the size of the training update, the group-standard-deviation identity. A split group teaches the most, while a unanimous group teaches nothing and falls silent. The same result says which problems deserve the most weight and how many tries each one needs. This paper confirms the intuition on a large real difficulty dataset (Big-Math) and in a controlled training run. What looks like a harmless normalization step is the dial that decides where learning happens and how strongly.
Rajat Ghosh, Datta Nimmaturi, Aryan Singhal +4cs.LG stat.ML
We develop a first-principles reduced-order model of these dynamics. Under a single mean-field assumption that summarizes the policy by its expected reward, we reduce the GRPO update to a stochastically-forced damped oscillator whose mass, damping, and stiffness are fixed in closed form by the optimizer hyperparameters together with a single measured curvature scale -- momentum supplies the inertia, off-policy lag erodes the damping, and the group size enters, to leading order, as a noise temperature. The reduction has three consequences. First, it subsumes the empirical single-exponential saturation law as its overdamped limit, recasting the fitted plateau, timescale, and size exponent as the fixed point, inverse stiffness, and curvature-scaling exponent of the underlying potential, and adding, through the retained inertial term, the slow-start phase the single exponential cannot represent. Second, it yields predictions tied to independently measurable quantities rather than fitted ones: group-size invariance of the deterministic trajectory with a $1/G$ stationary fluctuation, a sharp stability threshold in the refresh interval, and an overdamped-to-oscillatory transition. Third, it furnishes diagnostics that separate failure modes a reward curve alone conflates -- reward hacking, advantage degeneracy, policy concentration, and dynamical instability. Across three models and two group sizes, the closed-form trajectory fits training reward to $R^2 \geq 0.91$ and the mean trajectory is group-size invariant to leading order -- on both the reward curve and out-of-distribution transfer to eight math benchmarks -- while the within-group reward spread retains a residual $G$-dependence that the leading-order temperature picture does not capture.
While reinforcement learning (RL) significantly enhances LLM reasoning, its efficacy is severely undermined by Pre-RL data overlap, where RL datasets overlap with pretraining or SFT corpora, causing models to exploit shortcuts by memorizing correct answers and fabricating post-hoc reasoning. To address this, we introduce HIPPO, a novel RL framework that integrates hint-injected aggregation with a tailored pairwise reward model. By utilizing hint injection to deliberately trigger overlap-induced behaviors, the resulting traces naturally serve as explicit anchors for pairwise comparison. This provides highly discriminable preference signals, enabling a lightweight judge model to reliably distinguish genuine reasoning deduction from shortcut-driven rationalization, while the pairwise formulation ensures stable and robust optimization compared to standard PRMs. Extensive experiments demonstrate that HIPPO yields substantial improvements over standard baselines and generalizes effectively to out-of-distribution general tasks, showing it extracts authentic, transferable reasoning skills rather than superficial shortcut patterns.
Reward models for Reinforcement Learning from Human Feedback (RLHF) pool preferences across thousands of annotators and fit one global affine calibrator, collapsing raters with systematically different rating-scale offsets and slopes into a single average-rater fit that does not match any individual annotator. PEBS is a per-rater empirical-Bayes shrinkage estimator: it fits per-rater affine calibrators on a held-out slice of each annotator's ratings and applies Morris-James-Stein empirical-Bayes shrinkage toward the population mean, in closed form and without retraining the reward model. On PRISM, PEBS reduces within-user held-out RMSE by 8.58% over the pooled population-slope baseline. The procedure replicates on PluriHarms harm ratings (Qwen-2.5 base, in-family) with a +9.66% RMSE reduction over the same population-slope baseline. PEBS is a closed-form post-hoc estimator for annotator-specific affine calibration in RLHF reward modeling; it leaves the reward base model unchanged and estimates only the rater-level map used at inference time for new ratings.
Andreas Chouliaras, Luke Connolly, Dimitris Chatzpouloscs.AI cs.HC
Training safe Reinforcement Learning (RL) systems is inherently challenging, with no guarantee of avoiding unwanted behaviors. The most effective defenses against this are (i) transparency through explainability and (ii) alignment via human feedback. While both show promising results, no publicly available framework currently combines them. To address this, we introduce Themis, an XAI-enabled testing and evaluation framework for Reinforcement Learning from Human Feedback. Themis supports over 200 widely used environments and is easily configurable for experiments in RL, transparency, and alignment. Our results show that Themis can train reward models that match or outperform the environment's true reward signal using human preferences. We also provide a cloud-based platform for collecting human feedback and managing experiments. It is user-friendly, auto-scalable, and supports large participant groups across multiple experiments without extra development overhead. Tests show Themis can support one thousand users in back-to-back experiments on a modest commercial machine.
Rubric-based rewards offer interpretable and fine-grained optimization signals for reinforcement learning in open-ended tasks where verifiable answers are unavailable. However, pre-constructed rubrics remain static throughout training, creating a fundamental mismatch with the evolving policy: fixed criteria gradually lose discriminative power as the model improves, leading to reward saturation and potential hacking. Recent dynamic rubric methods partially address this but rely on external frontier models or ground-truth answers, and update rubrics only at coarse granularity. We propose EvoRubrics, a co-evolutionary RL framework where a Policy LLM and a Rubric Generator jointly improve through adversarial interaction within each training step. As the policy improves under the rubric generator's guidance, the rubric generator adapts its criteria to remain discriminative and informative, enabling evaluation to track the policy in real time and naturally inducing an automatic curriculum. Experiments show that EvoRubrics consistently outperforms static and dynamic rubric baselines across benchmarks. The learned Rubric Generator further generalizes as a transferable reward model. Notably, even a fully self-supervised variant without any external supervision achieves meaningful gains, suggesting that co-evolution between generation and evaluation alone can provide sufficiently rich learning signals. Our code is publicly available at https://anonymous.4open.science/r/EvoRubrics-2155/.
Licheng Pan, Haocheng Yang, Haoxuan Li +7cs.LG cs.AI
Reinforcement learning from human feedback (RLHF) aligns large language models by training reward models on preference data and optimizing policies to maximize predicted rewards. However, this pipeline faces two fundamental challenges: (1) reward models cannot signal when their predictions are unreliable, since they usually act as deterministic point estimators; and (2) modern group-based policy optimization can amplify unreliable reward signals, as exemplified by GRPO's uniform treatment of rewards during advantage computation. As policies explore increasingly diverse responses, these two limitations create a critical vulnerability: unreliable reward estimates may be granted disproportionate influence, triggering severe reward hacking. We propose Uncertainty-Aware Reward Modeling (UARM), which equips reward models with calibrated uncertainty via quantile-based conformal prediction and reweights GRPO advantages through heteroscedastic variance decomposition. Experiments across HelpSteer, UltraFeedback, and PKU-SafeRLHF demonstrate that UARM significantly improves reward model calibration, reduces reward hacking, and enhances downstream alignment quality compared to standard GRPO and uncertainty-agnostic baselines.
Han Zhou, Adam X. Yang, Laurence Aitchison +2cs.LG cs.AI cs.CL
Reinforcement learning with verifiable rewards (RLVR) has become a leading paradigm for improving the reasoning ability of large language models through outcome-based supervision. However, verifiable rewards frequently become uninformative at the group level: when all sampled traces of a given prompt receive identical rewards, group-relative advantage estimation provides no gradient signal, even though the traces may differ substantially in reasoning quality. We propose Reasoning Arena, an adaptive training framework that routes such non-diverse reward groups to a judge system instead of discarding them. Beyond examining the final answer, Reasoning Arena constructs trace tournaments, where reasoning traces are compared head-to-head to expose finer-grained preferences within the group, converting reasoning quality into rich relative reward signals. To make reward estimation efficient, rather than exhaustively comparing every pair, each new trace is evaluated against a small, dynamically updated pool of previously generated traces as anchors to efficiently establish a relative ranking. We then fit a Bradley-Terry model on the incomplete comparison graph, enabling scalable RL integration without quadratic pairwise comparisons. Empirical results demonstrate that Reasoning Arena consistently outperforms the RLVR baseline by 7.6% on average in competition mathematics and coding benchmarks. By converting otherwise wasted zero-advantage samples into useful gradient updates, our method accelerates training by 27% to 41%, saving nearly 50% of generation compute, and substantially improves overall reasoning performance.
Shuning Shang, Hubert Strauss, Stanley Wei +2cs.LG cs.AI stat.ML
Training language models via reinforcement learning often relies on imperfect proxy rewards, since ground truth rewards that precisely define the intended behavior are rarely available. Standard metrics for assessing the quality of proxy rewards, such as ranking accuracy, treat incorrect rewards as strictly harmful. In this work, however, we highlight that not all deviations from the ground truth are equal. By theoretically analyzing which outputs attract probability during policy gradient optimization, we categorize reward errors according to their effect on the increase in ground truth reward. The analysis establishes that reward errors, though conventionally viewed as harmful, can also be benign or even beneficial by preventing the policy from stalling around outputs with mediocre ground truth reward. We then present two practical implications of our theory. First, for reinforcement learning from human feedback (RLHF), we develop reward model evaluation metrics that account for the harmfulness of reward errors. Compared to standard ranking accuracy, these metrics typically correlate better with the performance of a language model after RLHF, yet gaps remain in robustly evaluating reward models. Second, we provide insights for reward design in settings with verifiable rewards. A key theme underlying our results is that the effectiveness of a proxy reward function depends heavily on its interaction with the initial policy and learning algorithm.