Learning from Less: Measuring the Effectiveness of RLVR in Low Data and Compute Regimes
Authors: Justin Bauer, Thomas Walshe, Derek Pham, Harit Vishwakarma, Armin Parchami, Frederic Sala, Paroma Varma
Organizations: Snorkel AI · University of Wisconsin-Madison · University of Oxford
Abstract
Fine-tuning Large Language Models (LLMs) typically relies on large quantities of high-quality annotated data, or questions with well-defined ground truth answers in the case of Reinforcement Learning with Verifiable Rewards (RLVR). While previous work has explored the benefits to model reasoning capabilities by scaling both data and compute used for RLVR, these results lack applicability in many real-world settings where annotated data and accessible compute may be scarce. In this work, we present a comprehensive empirical study of open-source Small Language Model (SLM) performance after RLVR in low data regimes. Across three novel datasets covering number counting problems, graph reasoning, and spatial reasoning, we characterize how model performance scales with dataset size, diversity, and complexity. We demonstrate that (1) procedural datasets allow for fine-grained evaluation and training dataset development with controllable properties (size, diversity, and complexity), (2) under RLVR, models trained on lower complexity tasks can generalize to higher complexity tasks, and (3) training on mixed complexity datasets is associated with the greatest benefits in low data regimes, providing up to 5x sample efficiency versus training on easy tasks. These findings inspire future work on the development of data scaling laws for RLVR and the use of procedural data generators to further understand effective data development for efficient LLM fine-tuning.
Reinforcement learning with verifiable rewards (RLVR) improves large language model reasoning, but its practical scaling is constrained by expensive on-policy rollouts and the cost of obtaining reliable targets at scale. Existing methods address sample selection, incomplete supervision, or noisy labels separately, often entangling supervision logic with distributed training and hindering controlled comparison and reuse. We present DE-Venus, a unified framework for data-efficient RLVR that treats supervision as evolving state across data preparation and policy optimization. It organizes this lifecycle into three modules: Active Data Selection allocates training and annotation budgets; Weak Supervision Construction derives learning signals from unlabeled examples; and Training-Time Supervision Refinement filters or corrects unreliable supervision. DE-Venus supports seven representative methods and a data-selection pipeline by expressing method-specific decisions as offline dataset transitions or online transformations of targets, rewards, batches, and advantages while preserving verl's distributed execution contracts. Across public benchmarks and three business scenarios, separate configurations preserve or improve model quality with only 10% of labels or as little as 13% of relevant data; selected business configurations also reduce observed convergence steps by 63%--75%. DE-Venus thus reduces annotation and training costs without sacrificing scalable RL execution.
While reinforcement learning with verifiable rewards (RLVR) is widely used to improve the reasoning capabilities of large language models (LLMs), the generalizability of the resulting models remains poorly understood. In this work, we establish the first non-vacuous generalization bounds for parameter-efficient RLVR fine-tuning at the billion-parameter scale. Our approach adapts PAC-Bayes compression bounds to this setting, and addresses the inherent stochasticity of token generation by applying the Gumbel-max reparameterization trick. To operationalize these bounds, we propose the Progressive RLVR framework, which integrates RLVR with on-policy distillation, TinyLoRA, and model quantization. Progressive RLVR empirically retains 84-97% performance of standard LoRA fine-tuning while producing models that are 14,796x more compressible. We show that this framework yields non-vacuous generalization bounds in four domains: mathematical problem-solving, programming, general-knowledge reasoning, and Text-to-SQL. Our bounds exceed the accuracy of the base model by 9-51% and lie within 6-11% of the accuracy of the fine-tuned models.
Reinforcement Learning with Verifiable Reward (RLVR) has proven effective in improving Large Language Model's (LLM) reasoning ability. However, the learning dynamics of RLVR remain underexplored. In this paper, we reveal a counterintuitive phenomenon: among hard examples that the model initially struggles with, a substantial subset remains unlearnable even when correct rollouts are present. To understand the phenomenon, we first demonstrate that existing optimization and sampling techniques fail to resolve unlearnability. With cross-example gradient analysis, we show that unlearnable examples have fundamental representation issue, characterized by low gradient similarity with the rest of the examples and ungeneralizable reasoning patterns. We further show that representation flaws are difficult to mitigate in RL, as data augmentation does not improve gradient similarity. Our study provides the first systematic characterization of unlearnable data in RLVR training and reveals fundamental limitations in current RL approaches for reasoning tasks. Code and data are available at \url{https://github.com/yulinchen99/unlearnability-rlvr}.