Reinforcement learning (RL) is used to improve the reasoning abilities of LLMs, while training data span heterogeneous tasks. However, most RL post-training pipelines rely on fixed or manually designed task mixtures, even though task usefulness changes as training progresses. Online curriculum methods often define learnability by update magnitude, ignoring whether the update translates into reward gains, which can misallocate rollout budget toward tasks with large but ineffective updates. We propose PAC, a Progress-Augmented Advantage Curriculum for multi-task RL of LLMs that combines two task-level signals: advantage-derived learnability, which measures the magnitude of the policy update a task can induce, and recent reward gains, which show whether those updates have improved task performance. A Bayesian Thompson Sampling controller uses these signals to allocate rollouts across tasks during GRPO training. We evaluate PAC under two settings: a multi-level reasoning setting and a multi-domain reasoning setting. PAC improves sample efficiency and final performance: it reaches comparable validation scores with fewer rollout steps and achieves higher final averages than random sampling and advantage-based curriculum baselines in both settings. These results show that jointly tracking advantage signals and actual reward gains yields an effective online curriculum for LLM post-training.
We present a reinforcement-learning agent that solves symbolic equations step by step, covering both nonlinear closed equations (radicals, exponentials, trigonometric) and a controlled class of restricted-open families requiring a change of variables (CoV) such as completing the square. We cast algebra as an MDP with a dynamic action space and a tree-structured policy (TreeMLP). The main policy learns from reward alone with no supervised solution traces; the CoV substitution comes from a supervised generator interchangeable with a CAS call. On closed equations the agent matches the prior best on CommonCore (0.93 greedy vs. ConPoLe's 0.925) under a single policy. On four hand-designed restricted-open families (quadratic, cubic, quartic, exponential) it reaches 0.79 beam / 0.67 greedy, exceeding the strongest non-learned search (A-star, 0.64). Learned CoV timing has content only on the exponential family, the one requiring a nested CoV, where a natural rule solves none of the held-out equations while the policy solves 75% from reward alone. At 10x scale a sharp seed-level bimodality emerges; a UCB learning-progress curriculum shows a non-significant positive trend toward mitigating it. We do not claim general open-equation solving: every open-equation result is confined to these four controlled families.
In many reinforcement learning (RL) domains, environments are connected by prerequisite relations, such as difficulty-increasing edits or parameter increments, which induce a directed acyclic curriculum graph (DAG). Although this structure is often exploited only implicitly, explicitly modeling it can improve training. We introduce PATH, a curriculum-learning framework that performs active learning over the curriculum graph. PATH first expands coverage by sampling diverse curriculum paths and then reallocates training toward regions that remain unmastered. Experiments across diverse environments show that PATH explicitly leverages the graph structure to achieve strong robustness and generalization.
We study dynamic context scheduling as a training instrument for contextual re- inforcement learning. Rather than treating intra-episode context variation as a deployment reality, we treat it as a controlled shaping mechanism. Thereby, context evolves within each training episode according to a predetermined schedule, expos- ing the policy to a richer and more temporally structured region of the environment parameter space. We introduce DYNAMICCARLENV, a framework that wraps contextual environments with pluggable schedule families, such as sinusoidal off- sets or cosine annealing. Across CartPole, BipedalWalker and VehicleRacing with CARL contextualization, we show that dynamic schedules match or outperform static context baselines in the out-of-distribution (OOD) regimes. Interestingly, for the more complex BipedalWalker and VehicleRacing environments we also achieve higher in-distribution (ID) evaluation performance. Preliminary findings indicate that automatic search for multi-stage curricula can successfully discover schedules that improve generalization, performing comparably to extensive grid search over single-stage schedulers.
Learning a reward model from human feedback and optimizing a policy against it is one approach to aligning AI systems with individual users. From a fairness perspective, existing work improves such alignment by developing data-efficient and accurate reward models that capture minority preferences despite scarce data. We push this line of inquiry one step further and argue that data-efficient and accurate per-user reward models are not sufficient: users whose reward models are difficult to \textit{optimize} at the policy level can become a new underserved group. We start from the observation that one user's reward model can be easy to optimize from the initial policy while another's is not. We argue that, given a sufficiently diverse user population, a curriculum naturally emerges between easy- and hard-to-optimize reward models. Building on this insight, we propose CurriPO, which grows a tree-structured curriculum to accommodate diverse user-specific objectives, covering the population in a single traversal. Specifically, CurriPO automatically constructs a curriculum over diverse user reward models, allowing it to branch from the existing curriculum and reuse reward models previously incorporated into the curriculum. To the best of our knowledge, this is the first work to explicitly exploit multi-user structure to address optimization in AI alignment. Extensive experiments on personalized continuous control in a simulated environment show that CurriPO achieves $1.2$--$2.1\times$ the population satisfaction of the strongest baseline while substantially reducing training time. Additional analysis attributes much of this improvement to the users left underserved by conventional optimization.
Robust navigation policies for autonomous agents must generalize across continuously varying environmental conditions such as turn rates, obstacles, friction, pits, and slopes. Curriculum generation provides a principled mechanism for improving generalization by progressively adapting training environments, but designing such curricula in a sample-efficient and automated manner remains challenging. This paper proposes a reparameterized curriculum generation framework for structured continuous environment parameters using unidirectional gradient-based optimization. To improve robustness in multimodal observation spaces consisting of image-based and scalar inputs, a distribution-shift regularization objective is incorporated to encourage the learning of finer-grained latent representations. The proposed method is evaluated across two continuous-control OpenAI Gym environments: a 2D obstacle-based Car Racing variant and Bipedal Walker variant, where coupled environment parameters jointly influence policy performance. Across five random seeds, our method consistently outperforms vanilla policy training, random parameter sampling, manual curricula, frontier-based methods, Self-Paced Reinforcement Learning (SPRL), Absolute Learning Progress with Gaussian Mixture Models (ALP-GMM), and reverse curriculum learning baselines. Ablation studies further demonstrate the effectiveness of the reparameterized curriculum mechanism across both environments, while highlighting environment-dependent benefits of the auxiliary regularization objective.
Ziqi Jia, Yalu Ouyang, Bo Pang +5cs.CL cs.AI cs.LG
Reinforcement learning (RL) has emerged as an effective method for enhancing the reasoning capabilities of large language models (LLMs). However, existing methods suffer from insufficient precision in feedback on generated answer trajectories and exhibit the phenomenon of problem difficulty drift. To address these challenges, we propose CVPO - Curriculum-guided Value-Variance Policy Optimization. At the response trajectory level, we find that token-level value-variance correlates with exploration intensity. Our theoretical analysis shows this variance bounds policy update magnitude. We then use the estimated trajectory value-variance to quantify the intrinsic randomness in generation. Based on this, we design a variance-aware advantage adjustment mechanism for different reward types. At the question level, we introduce a dynamic curriculum weighting method that adapts to question difficulty. This helps the model focus on tasks matched to its current ability during each training stage. Experimental results show our method outperforms strong value-based baselines like VAPO. It achieves better performance and stronger exploration, enabling more accurate and robust reasoning in language models across various math tasks.
Longtian Bao, Jianyou Wang, Yang Zhang +2cs.LG cs.AI cs.CL
Teaching a language model a skill it has not mastered is obstructed by three recurring difficulties: training data is scarce, ground-truth reasoning traces are usually unavailable, and models often exhibit an apparent ceiling beyond which additional data yields no further improvement. We study these difficulties in a controlled setting, fine-tuning Qwen2.5-Math-7B on competition mathematics (AIME), a task on which it initially solves only 5.6\% of problems (pass@1). To address data scarcity, we introduce Question-begets-Question (QbQ), a scalable procedure in which a teacher transforms existing problems into diverse variants that probe the same underlying skills; to model the absence of oracle reasoning, we train exclusively via reinforcement learning on problem statements and final answers, never on teacher reasoning traces. Static training on such data, however, plateaus well short of the task: real-plus-synthetic augmentation and non-curriculum QbQ generated synthetic data training cap pass@1 at 12.5\% and 14.5\% respectively, despite large increases in data. Our central finding is that this ceiling is not intrinsic to the model. We propose a self-evolving curriculum that, each round, evaluates the current checkpoint, seeds QbQ from the problems it can mostly get right, and trains on the resulting variants; under an identical data budget, this breaks the ceiling and lifts pass@1 to 16.5\% with no sign of saturation after 20 rounds. Counterintuitively, we find that models improve when trained on variants of problems they can mostly get right, and that models trained this way go on to solve harder problems never seen during training.
Sparse-reward reinforcement learning often fails because rollouts from the unassisted evaluation start rarely reach later task stages. Reset curricula address this by starting some training rollouts from easier intermediate states, called scaffolds. Such a curriculum faces two decisions: scaffold access, obtaining informative starts, and scaffold allocation, deciding how quickly that assistance is removed. Most prior curricula pace removal on one shared schedule, which can fail when task instances, or contexts, learn at different rates. We introduce SCOUT, an online, learner-agnostic reset controller that gives every context its own curriculum. Using only binary rollout success, SCOUT removes assistance after sustained success, restores it after failure, and cautiously tests a harder start when progress stalls, without changing the reward, optimizer, or learner. A counting construction shows that synchronized global pacing can be insufficient when contexts need conflicting amounts of assisted practice. Across six navigation and manipulation settings, scaffold access improves learning and enables success in three where unassisted training fails within the reported budget. In a constructed pacing conflict, each tested global schedule leaves one group unsolved, while SCOUT solves both. Average success can conceal this failure, so we also report the least successful group. Group-level pacing works when learning differences follow known groups but can fail when they occur within one group. SCOUT needs no group labels and remains consistently strong in both cases. A reset curriculum should remove assistance at the scale where learning progress differs.
Group Relative Policy Optimization (GRPO) stalls on a model's hardest problems: when no rollout in a group succeeds, the group-relative advantages vanish and the problem contributes no gradient, wasting the frontier examples we most want to learn from. Prepending a correct prefix of a reference solution raises the success rate, making prefix length a continuous knob on difficulty. Concurrent methods set the knob once; AdaPrefix-GRPO turns it into a feedback controller: throughout training it adjusts how much of the solution each problem gets, holding its success rate near 50%, where GRPO's gradient signal is largest, then withdraws the assistance entirely, so the deployed model solves problems unaided. On hard math, at matched training FLOPs, it more than doubles GRPO's accuracy on held-out problems from the training distribution for a 0.6B model (2.1x), with 1.6x on Qwen3-1.7B and 1.7x on AIME, while roughly halving trace length. The method is implemented in data preparation plus a loss mask on prefix tokens; the trainer is otherwise stock. The smaller the model, the larger the gain.
Nima Kelidari, Mohammadsaeed Haghi, Mahdi Salmanics.LG cs.AI cs.GT
Reinforcement learning agents for imperfect-information card games are only as strong as the opponents they train against, and they are hard to grade, since they beat a random opponent over 99 percent of the time and only tie copies of themselves. So we build a strong, fixed, rule-based expert for Gin Rummy and use it only as a yardstick, never for training. It beats every agent we trained 70 to 99 percent of the time. Across more than a hundred runs, we isolate what makes a lightweight agent stronger. Trust region updates, a well-aimed reward, a curriculum of tougher opponents, warm starting, and keeping the best checkpoint all help, and stacking them lifts a self-play champion from about 30 to 36 percent against the expert. Several ideas did not pay off. Short-term and longer-term reward shaping, learned state embeddings, imitation and DAgger, and a live large language model opponent were each unhelpful, too slow, or too heavy to train at scale. Comparing MLP, convolutional, set-based, attention, and recurrent encoders shows that extra capacity does little to break the ceiling, suggesting the limit is information rather than network size. We add standard baselines (neural fictitious self-play and information set Monte Carlo search) and confirm the approach carries over to Leduc Hold'em, where the optimum is computable. The result is a lightweight, game-agnostic recipe that trains competitive agents without training on the expert, for any game a small model can handle, reported with robust statistics and released as a reusable package.
Haisen Luo, Yiwei Liu, Haoning Wang +13cs.LG cs.AI
Enabling large language models to achieve stable self-improvement without external expert supervision remains a central challenge in complex reasoning tasks. Existing self-distillation and reinforcement learning methods lack explicit mechanisms for tracking problem-level learning progress and adapting optimization strategies accordingly. Consequently, training may over-optimize easy problems, receive weak supervision from hard problems, and fail to sufficiently explore borderline cases. To resolve these issues, we propose DRIFT, an online self-evolution policy optimization framework for large language models. DRIFT regulates the model's self-improvement process through the joint use of Difficulty Routing and Rhythm Gating. The former identifies the model's learning state at the problem level and dynamically allocates self-distillation and reinforcement learning signals, while the latter refines policy updates at the token level, concentrating exploration on critical reasoning positions. By further incorporating a success buffer and a two-stage curriculum learning strategy, DRIFT preserves high-quality historical experience while progressively guiding the model from reliable behavior acquisition toward stable policy evolution. Evaluated across five benchmarks and three model scales, DRIFT surpasses the peak performance of both GRPO and SDPO across all evaluated metrics. On the average score over the five benchmarks, DRIFT achieves 79.5$\%$, outperforming GRPO by 9.5$\%$ and SDPO by 7.5$\%$, establishing a new state-of-the-art result. Notably, on ToolUse, DRIFT reaches an accuracy of 79.2$\%$, improving over GRPO by 13.5$\%$ and SDPO by 10.7$\%$, setting a new state-of-the-art and substantially outperforming all concurrent methods.
World 1-1 of Super Mario Bros is widely celebrated as a masterclass in game design: its progressive structure is credited with teaching players core mechanics through the level itself. We ask whether that structure is empirically measurable using reinforcement learning. We implement World 1-1 from scratch as a fully discrete environment and compare four algorithms -- Q-Learning, SARSA, Monte Carlo, and Deep Q-Network (DQN) -- across three progressively complex versions of the same level. Monte Carlo emerges as the strongest agent (94.9% $\pm$ 1.5% win rate), outperforming DQN (76.4% $\pm$ 3.4%) by learning to maximize intermediate rewards along winning paths rather than taking the most direct route. We then use Monte Carlo in a curriculum experiment permuting World 1-1's six canonical segments across twelve conditions. Canonical ordering converges fastest, achieves the highest learning efficiency, and is the only condition with zero catastrophic failures; no random permutation matches all three criteria simultaneously. These results provide, to the best of our knowledge, the first empirical validation that World 1-1's canonical design encodes genuine pedagogical structure: one that measurably accelerates learning and cannot be replicated by chance.
Reinforcement learning with verifiable rewards (RLVR) has been extended from single-domain training to multi-domain reasoning suites spanning mathematics, programming, and science. However, the training curriculum (how often each domain is sampled) is typically fixed or hand-tuned, even though reasoning skills transfer unevenly across domains. Existing learnability-based curricula adapt to where the policy is currently improving, but are blind to whether a gradient step on the selected domain benefits the remaining domains. In this paper, we propose Transfer-Aware Curriculum (TAC), a bandit-style online curriculum that prioritizes domains whose updates broadly benefit the rest of the training suite. TAC repurposes signals already produced by RL training: per-domain advantages capture local learnability, and projected gradients, taken from the GRPO step being computed, estimate cross-domain transferability via gradient-geometry alignment, at negligible cost (<1% wall-clock overhead). Across a six-domain reasoning suite, TAC achieves the best macro-averaged accuracy on both Qwen3-1.7B and Llama3.2-3B, outperforming proportional random sampling, a hand-designed schedule, and a learnability-only bandit, and improving over the last of these by up to 2.8 points (10% relative). Ablations show performance degrades sharply when the transferability term is removed, and TAC remains robust on imbalanced training mixtures where learnability-only curricula over-commit to dominant domains. Our findings establish cross-domain transferability as a key signal for curriculum design in multi-domain RLVR.
Recently, world models have emerged as a promising paradigm for building intelligent agents by learning predictive models that estimate future environment states conditioned on observations and actions. In particular, JEPA-style latent world models provide an efficient alternative to pixel space prediction by learning action-conditioned dynamics in compact representation spaces. However, existing latent world models typically rely on one-step prediction and must be recursively rolled out for long-horizon planning, which leads to compounding errors and a mismatch between training objectives and downstream planning tasks. To address this limitation, we propose Variable-length Latent World Models (VLWMs), a framework that learns to predict future latent states conditioned on action sequences of variable lengths. Instead of training only on one-step transitions, VLWMs directly model temporally extended dynamics, allowing the same predictor to evaluate action plans over different horizons. We further introduce a curriculum training strategy that progressively expands the action horizon, stabilizing optimization from short-range dynamics to long-range prediction. At test time, we design planning methods tailored to VLWMs to better exploit their variable-length predictive capabilities. Experiments on long-horizon control tasks show that VLWMs significantly improve latent space world models, achieving 13\% average improvement over the state-of-the-art LeWM across different datasets, with especially large gains on tasks requiring extended planning. These results suggest that VLWM provides a simple yet effective paradigm for improving long-horizon prediction and planning in latent world models.
Safety is a core concern for deploying reinforcement learning (RL) agents in real-world domains such as robotics and autonomous driving. While benchmarks have been central to progress in RL, existing safety benchmarks with high-fidelity 3D physics remain computationally slow, limiting large-scale experimentation and rapid prototyping. To address this gap, we propose CRAX (Constrained RL Accelerated with JAX). Built on top of the MuJoCo XLA (MJX) physics engine with realistic 3D dynamics, CRAX leverages vectorized operations and hardware acceleration, yielding up to ~100x speedups over comparable CPU-based safety benchmarks. The benchmark features six environment suites and three agent-specific tasks, each spanning three difficulty levels. Evaluating six popular safe RL methods shows that no single approach dominates across all tasks, and reveals the trade-offs between performance and safety. We find that curriculum learning across difficulty levels and safety transfer can improve performance over direct training in harder settings.
Virtual training environments are software-intensive systems in which reinforcement learning (RL) agents learn, adapt, and demonstrate meaningful behavior. Virtual training environments offer a safe and cost-efficient alternative to training agents in real-world settings. However, to converge, most realistic RL problems require training in multiple, mostly similar but slightly different environments - i.e., families of environment variants. The typical development process of environment families is a labor-intensive and error-prone manual endeavor that does not scale well. To alleviate these issues, in this paper, we propose a model-driven approach for developing families of RL training environments. To obtain the family of environments, we develop an approach and prototype tool. In our approach, a hybrid genetic algorithm - a combination of population-based global search and heuristic local search - generates environment families. Mutations and constraints are expressed as model transformations and are operationalized into a search process by a state-of-the-art model transformation engine. We demonstrate the soundness of our approach in a wildfire mitigation scenario and curriculum learning - a particular learning paradigm that relies on environment families.
Reinforcement learning (RL) is a central approach for improving reasoning capabilities in large language models (LLMs), where training efficiency depends critically on how problems are sampled during optimization. Existing adaptive curriculum learning methods typically prioritize prompts of intermediate difficulty, treating problem selection as a standard bandit problem with independent arms and overlooking the structured, heterogeneous nature of the task space. In this work, we frame problem sampling as a manifold-structured bandit problem with endogenous non-stationarity: problems are related through the model's latent representation space, and sampling decisions can steer how learning signals evolve across that space. To operationalize this perspective, we introduce Bayesian Manifold Curriculum (BMC), a structure-aware framework that organizes problems into a hierarchical task tree and applies Bayesian learning to guide sampling. Empirically, we find that different sampling strategies induce non-trivial tradeoffs between productivity (learning signal), diversity (coverage of the task manifold), and utility (evaluation relevance). These results show that prioritizing difficulty alone is insufficient for strong downstream performance, highlighting the importance of incorporating structure and type-awareness into problem sampling.
Shivchander Sudalairaj, Kai Xu, Akash Srivastava +1cs.LG cs.AI cs.CL stat.ML
Standard Reinforcement Learning with Verifiable Rewards (RLVR) training allocates a fixed rollout budget to every query, without regard for what each query's difficulty means for the current policy. This leads to two symmetric failure modes: easy queries produce near-zero advantage because the policy already solves them, while unsolvable queries produce no signal because the policy never solves them. Both regimes waste training FLOPs without contributing to a learning gradient. We introduce sorted Group Policy Optimization (sGPO), a compute-efficient strategy that trades a small budget of inference FLOPs for a large reduction in wasted training FLOPs. The key insight is that cheap inference compute can serve as a single offline proxy for query difficulty. By generating a small batch of parallel samples per query under the initial policy, we obtain a model-aware empirical success rate. This motivates setting the training rollout group size to the inverse of this success rate, a practical rule that maximizes sample efficiency by extracting the most advantage per generated rollout. This single profiling pass simultaneously drives data filtering (removing trivial queries and sub-sampling unsolvable ones), adaptive group size allocation, and curriculum construction (scheduling queries from easy to hard). sGPO matches or exceeds baseline performance while reducing total training compute by a factor of three, with the upfront inference profiling cost included.
Group Relative Policy Optimization (GRPO) has demonstrated remarkable success in aligning text-to-image (T2I) flow models with human preferences. However, we have identified that the learning loop of current flow-based GRPO is fundamentally decoupled from the learner's current capability, suffering from critical blind spots at both prompt selection and advantage estimation: (i) Existing methods sample prompts randomly, overlooking the substantial impact of data selection on reinforcement learning (RL) efficacy--a factor proven crucial in GRPO for large language models; (ii) They evaluate sample quality solely relying on intra-group statistics, lacking a global perspective to accurately measure true policy improvement. To address these issues, we propose Adaptive GRPO (AdaGRPO), a novel capability-aware RL algorithm tailored for flow models. Specifically, AdaGRPO consists of two principal components: (i) Online Curriculum Filtering Strategy: Dynamically tracks the model's proficiency and adaptively selects prompts that best match its current learning boundary; (ii) Cross-Level Advantage Fusion: Synergistically integrates fine-grained intra-group advantages with macro-level global advantages, providing a comprehensive and unbiased policy evaluation. As a lightweight, plug-and-play module, AdaGRPO can be seamlessly integrated with existing frameworks such as Flow-GRPO, DanceGRPO, and Flow-CPS. Extensive experiments demonstrate that AdaGRPO consistently drives performance gains while significantly stabilizes GRPO training for flow models.
Xitai Jiang, Zihan Tang, Wenze Lin +3cs.LG cs.AI cs.CL
Reinforcement learning from verifiable rewards (RLVR) has shown strong promise for LLM reasoning, but outcome-based RLVR remains inefficient on hard problems because correct final-answer rollouts are rare and sample-level credit assignment cannot use partial progress in failed attempts. We introduce SCRL (Subproblem Curriculum Reinforcement Learning), a curriculum RL framework that derives verifiable subproblems from reference reasoning chains and fixes the final subproblem as the original problem. This turns partial progress on hard problems into verifiable learning signals. Algorithmically, SCRL uses subproblem-level normalization, which normalizes rewards independently at each subproblem position and assigns the resulting advantages to the corresponding answer spans, enabling finer-grained credit assignment without external rubrics or reward models. Our analysis shows that subproblem curricula lift hard problems out of gradient dead zones, with larger relative gains as the original problem becomes harder. Across seven mathematical reasoning benchmarks, SCRL outperforms strong curriculum-learning baselines, improving average accuracy over GRPO by +4.1 points on Qwen3-4B-Base and +1.9 points on Qwen3-14B-Base. On AIME24, AIME25, and IMO-Bench, SCRL further improves pass@1 by +3.7 points and pass@64 by +4.6 points on Qwen3-4B-Base, indicating better exploration on hard reasoning problems.
Andy Caen, Mark H. M. Winands, Dennis J. N. J. Soemerscs.AI
We present StratFormer, a transformer-based meta-agent that learns to simultaneously model and exploit opponents in imperfect-information games through a two-phase curriculum. The first phase trains an opponent modeling head to identify behavioral patterns from action histories while the agent plays a game-theoretic optimal (GTO) policy. The second phase progressively shifts the policy toward best-response (BR) exploitation, guided by a per-opponent regularization schedule tied to exploitability. Our architecture introduces dual-turn tokens -- feature vectors constructed at both agent and opponent decision points -- coupled with bucket-rate features that encode opponent tendencies across five strategic contexts. On Leduc Hold'em, a small poker variant with six cards and two betting rounds, we test against six opponent archetypes at two strength levels each, with exploitability ranging from 0.15 to 1.26 Big Blinds (BB) per hand. StratFormer achieves an average exploitation gain of +0.106 BB per hand over GTO, with peak gains of +0.821 against highly exploitable opponents, while maintaining near-equilibrium safety.