Group Relative Policy Optimization (GRPO) is widely studied for reinforcement learning with verifiable rewards, where its advantage estimator assigns each rollout a magnitude from within-group reward statistics. In the common case, this magnitude rewards rollouts that reach the correct answer through reasoning. Yet, an overlooked case shares the same surface: a rollout may land on it by guessing, and the formula still assigns a high magnitude, which we identify as the spurious advantage. This arises in three cases: bounded-answer tasks with a small candidate set; open-answer sets hosting bounded sub-cases; and search agents whose budget opens many paths to the same answer. In all three, this misleads the policy toward guess-like behaviors. We propose SIGNBALANCE, whose magnitude is composition-free: it keeps the verifier sign, uses a global scale, and restores zero-mean balance via a stop-gradient per-class rescaling. Across math and search agent benchmarks at different scales, SIGNBALANCE matches GRPO on open-answer math and improves on bounded-answer math and search agents. Code will be released.
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.
Reinforcement learning (RL) post-training has emerged as a powerful framework for enhancing the capabilities of large language models (LLMs), enabling impressive reasoning, math, and coding capabilities. Yet for many researchers and practitioners, the principles behind classical RL remain a "black box". In this work, we deconstruct the RL post-training algorithm, investigating each step to clarify what is actually happening beneath the surface. By isolating the mechanics of RL with Verifiable Rewards in a controlled and simplified environment, we examine how RL outcomes are shaped by the base model's prior distribution, the granularity of the reward signal, the diversity of the prompt distribution, and model scale. We use the entropy of the policy's output distribution as a lens to compare the distributions learned through pretraining, SFT, and RL post-training, revealing how each stage shapes model certainty. Our investigation sheds light on how these choices interact to affect post-training success. For example, we show that the effect of so-called 'spurious rewards' depends on the prompt distribution used for post-training. We also provide insight into why the success of RL post-training depends on whether the base model already places sufficient probability mass on the desired behavior, linking it to the classical concept of exploration in RL. Ultimately, we provide this primer as a resource to those in the NLP community wishing to incorporate RL as a tool in their toolbox.
Reinforcement learning with verifiable rewards has become the dominant recipe for improving large language model reasoning, yet it presumes large human-curated task collections. Zero-data self-play removes this dependency, but existing methods vet learnability only by probing candidates and rejecting post hoc, never learning where along an environment's difficulty axis to place a task, and credit the solver with sparse terminal rewards alone. We recast zero-data self-play as a pursuit-evasion game: in LURE, an LLM evader positions tasks along each environment's difficulty axis to stay one step ahead of a planner-executor pursuer that hunts it down through verifiable interaction. The evader is trained on a capture-frontier reward that peaks when the solver captures it on exactly half of its rollouts, turning barely catchable into a learned positioning strategy rather than a hand-tuned rejection band. The pursuer earns capture-anchored dense process credit, in which monotone verifier progress is group-normalized jointly with the terminal capture under a round-anchored KL that keeps the co-evolution stable. Across three verifiable reasoning environments and three backbone families, LURE outperforms advanced baselines under unified/specialist settings, while the unified model attains stronger aggregate OOD zero-shot accuracy than all trained baselines across nine held-out benchmarks from three task families.
We show that on-policy reinforcement learning with verifiable rewards (RLVR) can improve the current objective while making successful behaviors for later objectives too rare to sample and reinforce. We call this verifier-induced support reshaping and define effective rewardable support as successful trajectories reachable within a fixed rollout budget. Across two model families, we study this effect through repeated verifier-scored sampling and bidirectional training on mathematical reasoning and constrained instruction following, including sequential training with the opposite verifier. Math-RLVR raises average instruction-following success but reduces the number of prompts with any successful response under repeated sampling. On IFEval with Qwen3-8B-Base, pass@1 rises by 6.5 percentage points while best@32 falls by 9.8 percentage points, and the same divergence appears across both models and IF benchmarks. Conversely, IF-RLVR shifts math responses from step-by-step openings toward direct answers, lowers best@k across sampling budgets, and reduces reward variation for later Math-RLVR. Token-distribution analyses and controlled opening interventions show that these changes concentrate in the first few response tokens. RLVR mainly reranks openings already available in the base policy, and the selected opening causally affects math searchability. The tested reference-policy constraints, routing priors, and on-policy distillation preserve cross-task support only partially; MathIF and ReasonIF show that marginal gains translate only partly into responses that are both correct and constraint-following. Therefore, endpoint improvements do not guarantee future trainability or joint capability under on-policy optimization. Code is available at https://github.com/sylvain-wei/verifier-induced-support-reshaping
Reinforcement Learning with Verifiable Rewards (RLVR) has driven recent progress in reasoning-oriented large language models (LLMs) by enabling large-scale optimization. However, its applicability remains largely limited to domains such as mathematics and coding, where correctness can be deterministically verifiable. Open-ended tasks instead often rely on human preferences, reward models, or LLM-based judges, introducing evaluation bias, judge capability bottlenecks, and additional inference costs. Drawing on the principle of self-supervised learning, which constructs pretext tasks to derive supervision from the data itself, we propose Reinforcement Learning with Self-Verifiable Rewards (RLSVR), a task-transformation-based training paradigm for extending RLVR to open-ended tasks. RLSVR transforms open-ended tasks into verifiable proxy environments whose internal rules and interaction outcomes automatically generate reward signals. We instantiate RLSVR with SpyRL, a Self-PlaY Reinforcement Learning method inspired by social deduction game Who Is the Spy?. Agents receive asymmetric information, complete the same target task, and vote to identify a designated spy. Because the spy identity is predetermined, voting outcomes provide fully verifiable rewards, while successful identification remains closely related to output quality. Experiments on text summarization, creative writing, and mathematical reasoning show that SpyRL outperforms existing self-improvement methods on non-verifiable tasks and yields consistent gains on verifiable reasoning tasks. These results demonstrate that task transformation can extend scalable RLVR-based self-improvement beyond inherently verifiable domains. Models and code have been released at https://github.com/wangqinsi1/RLSVR/tree/SpyRL.
Test-time scaling through iterative self-evolution with environment feedback, as demonstrated by AlphaEvolve, shows remarkable performance gains. We hypothesize that the success of such evolution frameworks hinges on meta-skills, such as self-reflection with environment feedback, that enable effective multi-round refinement, yet are largely neglected by traditional post-training. To bridge this gap, we present MetaEvolve, a framework designed to develop these meta-skills via a data synthesis pipeline, evolution-aware reinforcement learning (RL), and inference-time evolutionary search. Concretely, we ground MetaEvolve in coding, where program execution provides natural, continuous reward signals beyond binary correctness. Building on these signals, we synthesize evolution trajectories as training data, each containing a current program, its fitness score (combining correctness and efficiency), and a history of prior attempts, and train the model via RL with verifiable rewards derived from test case execution. By training on large-scale code data, we aim to inspire generalizable domain-agnostic meta-skills that can transfer broadly to open-ended problems where such rich training signals are scarce. Across seven coding benchmarks, MetaEvolve outperforms the strongest baseline by 10.01% absolute on in-distribution tasks and 24.12% on out-of-distribution tasks. On open-ended algorithm optimization problems entirely outside the training domain, it further achieves a 46.9% relative improvement. These results demonstrate that explicitly cultivating self-evolution meta-skills offers a principled path toward more capable and autonomously self-evolving AI.
Agents acting on our behalf in the real world (e.g. placing phone calls) must learn online from costly, often irreversible interactions rather than cheap simulator steps. Two things follow. First, deployability depends on the path, not only the outcome. An agent must respect outcome-neutral constraints such as not repeatedly calling an unresponsive user, respecting business hours, or completing required authentication constraints that outcome-based rewards cannot express, since violating them frequently improves apparent success. Second, because each interaction is expensive, the agent must learn efficiently from very few examples. Reinforcement learning from verifiable rewards (RLVR) is blind to both challenges: it optimizes solely on the outcome and wastes expensive rollouts on all-fail groups where group-relative advantage collapses to zero. Attempts to densify supervision by rewarding progress target the hard-to-verify direction. In contrast, real agentic environments can cheaply detect bad moves. Since group-relative advantage is equivalent to within-group variance, a dense signal helps only when it supplies variance the outcome lacks. A verifiable penalty on the path meets this condition reliably, while a progress potential helps only where partial progress is reachable. The resulting recipe "penalize the path, reward the outcome" achieves high task success with near-zero violations, where outcome-only training violates constraints on nearly every episode. We provide four design rules for effective penalties, including avoidance of the inaction trap that arises when a penalty is used in isolation.
Reinforcement learning with verifiable rewards can in principle train calibrated probabilistic forecasters, since a proper scoring rule such as the Brier score is computed from outcomes alone and is minimized in expectation by the true probability. In practice it degrades calibration, and existing remedies address epistemic uncertainty, where a model's confidence accompanies a verifiably correct or incorrect answer. We study aleatoric forecasting, where the forecast itself is the output and the label is one stochastic outcome, taking NFL in-game win probability as a testbed with the betting market as a reference. Rewarding the realized per-play outcome fails, because the single outcome is a noisy target and the policy gradient corrupts the chain of thought. We introduce a verifiable, label-free reward, a state-conditioned empirical win rate estimated from past outcomes, that removes the label noise, and we keep the gradient off the reasoning, by direct prediction or a gradient mask, so it cannot be corrupted. Trained with this reward alone, without human labels or supervised fine-tuning, a 7B model reaches the calibration of the betting market by direct prediction and is better calibrated than a zero-shot frontier model. That frontier model and a tabular estimator reach the same Brier score as this model, identifying the market's small remaining edge as live in-game information beyond their shared inputs. Masking the gradient, rather than dropping the chain of thought, preserves reasoning from which the forecast follows, which ordinary chain-of-thought training corrupts.
RL with verifiable rewards can substantially improve LLM reasoning, yet standard GRPO-style training often treats easy, hard, and learnable questions alike through uniform sampling and weighting, leading to inefficient compute allocation. We study GRPO by tracking token log-probabilities, group-normalized advantages, and the induced token-level update weights. This reveals three recurring dynamics as training proceeds: (1) confidence inflation, (2) advantage contraction, and (3) hierarchical convergence. These findings suggest that the utility of each update depends strongly on both question difficulty and the model's current competence. Motivated by this, we propose Confidence and Difficulty-adaptive Policy Optimization (CoDaPO), which assigns each question a bounded value from rollout confidence and empirical difficulty. CoDaPO then uses this value to reweight policy updates and resample high-value learnable questions within mini-batches, thereby increasing discovery within the learnable band under a fixed compute budget. Across twelve benchmarks, CoDaPO consistently improves accuracy over existing RL methods. Our code is publicly available at https://github.com/tmlr-group/CoDaPO.
Shota Takashiro, Soichiro Nishimori, Paavo Parmas +6cs.LG cs.AI cs.CL
Reinforcement learning with verifiable rewards is widely used for post-training reasoning models, but sparse outcome rewards make exploration difficult. A complementary approach is to optimize inference-time objectives such as pass@K and max@K directly, yet existing policy-gradient estimators for these objectives use different signals, baselines, and normalizations, making their relationships unclear. We study this issue through baseline design and advantage centering. Starting from the advantage estimator of a leading method in the field, we show that it is policy-gradient unbiased but yields a non-centered advantage. We then introduce a Leave-Two-Out baseline that preserves policy-gradient unbiasedness while making realized batch advantages exactly centered. The resulting method, MaxPO, has an efficient quadratic-time implementation and integrates naturally into group-based RL for LLM post-training. We further derive the canonical finite-batch advantage for max@K, providing a unified view of existing advantage estimators. Empirically, we verify that the L2O baseline reduces gradient variance and outperforms non-centered alternatives.
Reinforcement learning with verifiable rewards improves reasoning and tool use, yet long-horizon language agents still learn unsupported evidence chains, belief drift, and shortcut actions that satisfy terminal checks. Existing process rewards are mostly correlational: they reward retrieval-, reflection-, or verification-like steps without estimating whether the step contributes to final verified success under a specified intervention. We propose CVT-RL, a constrained policy-gradient algorithm with dense verifiable rewards, intervention-validity gating, and a policy-conditioned counterfactual contribution (PCCC) estimator. Deletion, semantic substitution, evidence substitution, and tool-output perturbation define separate controlled interventions; continuations are sampled from a frozen reference policy, and a selection-adjusted doubly robust estimator augments the advantage. Belief control uses only prefix-observable labels, while an augmented Lagrangian constrains unsupported claims, skipped verification, tool tampering, and unsafe calls. On long-context QA, ALFWorld, ScienceWorld, and web/tool tasks, CVT-RL improves average task success from 71.8% for compute-matched non-causal RL and 75.4% for an information-matched counterfactual-process baseline to 78.9%, improves evidence F1 from 78.9 to 82.8 over the information-matched baseline, and reduces measured hacking from 7.2% to 3.9%. Independent human audit estimates 4.6% hacking for CVT-RL versus 8.1% for the information-matched baseline, and adaptive detector-evasion attacks raise hacking only to 7.1%. Stratified bootstrap and mixed-effects tests give p<0.01 after Holm correction for all primary metrics. Carefully scoped counterfactual credit, paired with validity gating, diagnostics, and verifiable constraints, provides a reproducible route toward more reliable long-horizon RL for language agents.
Reinforcement learning with verifiable rewards (RLVR) improves the ability of large language model, yet headline accuracy gains often conceal a hidden cost: previously solved problems quietly become unsolvable as training proceeds. We frame this phenomenon as \emph{correct-set turnover}, representing the coupled dynamics of solution acquisition and regression over the mastered set. Under this view, retention becomes an explicit optimization target alongside acquisition. We analytically and empirically establish the \emph{repair-window principle}: the cost of restoring a regressed prompt grows sharply with review delay, defining a low-cost window that standard RLVR pipelines fail to exploit. To address this, we propose \textbf{\method{}}, a retention-aware review mechanism that tracks mastered prompts and periodically reintroduces them to \textbf{remind} the model of previous solutions. By utilizing pre-rollout batch replacement, \method{} incurs zero additional rollout overhead. Evaluated across 20 benchmarks spanning image-text, video, and text-only tasks with Qwen3-VL and Qwen2.5-Math, \method{} consistently improves performance over GRPO, DAPO, and replay baselines, demonstrating robust generalizability across modalities and algorithms.
Reinforcement learning with verifiable rewards has become the standard recipe for improving LLM reasoning, but the dominant algorithm GRPO assigns a single trajectory-level advantage to every token, diluting the signal at pivotal reasoning steps and injecting noise at uninformative ones. Critic-free alternatives derived from on-policy distillation supply per-token signals through oracle-conditioned likelihood ratios, yet apply each signal in isolation from the trajectory-level evidence accumulated up to that position. We propose Oracle-Prompted Policy Optimization (OPPO), which rests on a single observation: the oracle signal used by prior distillation-style methods for local discrimination is also the natural Bayesian update of the model's belief about eventual success. Accumulating the signal along a trajectory yields, in closed form and at the cost of one extra forward pass, a running estimate of the success probability at every position, together with a token-level advantage that requires no learned value network and no additional rollouts. A first-order analysis factorizes the advantage into the per-token discrimination signal used by distillation methods modulated by a state weight that concentrates credit on genuinely pivotal tokens, with a directional variance-reduction guarantee. The framework admits two estimators differing only in which model scores the evidence: a \textit{self-oracle} that reuses the student and recovers the on-policy distillation reward as a strict special case, and a \textit{teacher-oracle} that delegates scoring to a stronger frozen model. On two base LLMs across seven mathematics, science, and code reasoning benchmarks, OPPO improves over GRPO, DAPO, and SDPO by up to $+6.0$ points on AMC'23 and $+5.2$ points on AIME'24, with gains that widen monotonically with response length.