Reinforcement Learning

Reinforcement learning (RL) for reachability specifications is fundamental to sequential decision-making. Prior work establishes asymptotic convergence to optimal policies, but only through model-based methods that must explicitly estimate the transition probabilities of the underlying Markov Decision Process (MDP). We present Quasar, the first model-free algorithm with asymptotic guarantees for reachability on the fragment of MDPs free of non-terminal maximal end components (MECs), a building block to which every MDP reduces by the standard MEC quotient. Our algorithm follows the classical Q-learning approach, using temporal-difference updates to converge to an optimal policy without ever learning the transition probabilities. The resulting learner reduces the memory footprint from the O(|S|^2|A|) that model-based methods require to O(|S||A|). On the standardized Quantitative Verification Benchmark Set, our algorithm converges to the optimal policy with orders of magnitude fewer samples than the previous model-based state-of-the-art. Together these results are a concrete step toward the practical deployment of reachability learning and, with it, of specification-guided RL.

Primal-dual hybrid gradient (PDHG) methods solve large-scale linear programs (LPs) using GPU-friendly matrix-vector products and projections, but their practical performance depends on coordinating algorithm parameters, acceleration, and restarts. We introduce GALLOP, which uses reinforcement learning to jointly learn continuous algorithm parameters and discrete restart decisions without differentiating through the solver. Its generalized accelerated PDHG update combines separate primal and dual extrapolation, history corrections, and restart anchoring with independently adjustable coefficients. We train a dimension-agnostic feedback policy using a groupwise proximal policy optimization objective that clips likelihood ratios separately for different control groups and excludes inactive acceleration controls on restart transitions. We evaluate GALLOP on six LP families and a public item-placement benchmark. On the main evaluation settings across the six families, GALLOP reduces iteration counts by factors of $1.9$-$5.6$ and achieves up to a $16.0\times$ speedup in algorithm wall-clock time over MPAX. With one policy trained per family, the learned policies generalize without retraining to within-family LPs $3\times$-$400\times$ larger than the largest training instances, including Transport LPs with $10.24$ million variables.

Long-term dependencies remain a major challenge for sequential decision-making in the field of AI: RNNs suffer from vanishing gradients and the limited expressivity of vector-based hidden states, whilst Transformer-based models are limited by the quadratic scaling of attention. Recent work has proposed tackling this problem with the Test-Time Training (TTT) framework, which stores episodic memories in the parameters of a neural network through gradient descent at both train and test-time. This approach has seen success in the domain of Natural Language Processing, however, to the best of our knowledge it has not yet been applied to the domain of Reinforcement Learning (RL), nor has there been a study analysing how this memory practically functions. In this paper, we study the potential of the TTT framework for offline RL by augmenting a Decision Transformer with TTT layers, dubbed the Decision Titan. We analyse performance and properties of the model in the X-Maze environment, an extension of T-Maze designed to test sequential memory, and investigate how the memory mechanism learns by visualising gate values over time. Our key findings are that Decision Titan can learn long-term dependencies with ranges 20x longer than the context window, generalises to lengths 1.7x the training data, but crucially temporal generalisation depends on the time embeddings used, and the ability to learn long-term dependencies depends on how the relevant information is encoded.

Verifier-free reinforcement learning with probability-based rewards offers a promising way to train LLMs on general reasoning tasks where external verifiers are unavailable. Yet the reliability of these rewards, especially in long-horizon reasoning, remains underexplored. This work identifies a length-dependent failure mode of probability rewards, which we call the Posterior Concentration Phenomenon (PCP). We show that the probability of a reference answer conditioned on a reasoning trace often collapses to a low-variance interval as the trace becomes lengthy. This phenomenon results in nearly indistinguishable rewards, which, under GRPO-based settings, makes probability-based policy optimization unstable and inefficient. Motivated by this, we propose Reinforcement Learning with Concentration-aware Posterior Rewards (RLCPR), a verifier-free RL framework to explicitly account for PCP for better optimization stability and token efficiency. It has two components: uncertainty-aware data sampling, which reduces concentration-prone rollouts before generation, and concentration-aware regularization, which penalizes unnecessarily long traces when posterior rewards collapse. Extensive experiments show that, alongside higher token efficiency, RLCPR outperforms the state-of-the-art verifier-free RL baseline by up to 4.0% on six of seven benchmarks, including general-domain and mathematical reasoning challenges.

Reinforcement learning (RL) algorithms frequently compare probability distributions, such as state visitation distributions induced by policies and experts, action distributions from learned policies and offline datasets, or transition distributions from learned models and environments. However, commonly used divergences may become ineffective when these distributions overlap weakly, which is frequently encountered in imitation learning, offline RL, and deployment under distribution shift. Optimal transport (OT) offers an alternative by measuring the cost of \emph{moving} probability mass from one distribution to another under a ground cost that encodes task geometry. This survey covers how OT is used inside RL objectives and algorithms. For each method, we identify: the role OT plays, the distributions compared, the OT formulation used, and the treatment of temporal structure. Beyond categorising existing methods, we discuss the motivations behind different OT choices, practical considerations such as cost design and computational challenges, and highlight open problems including scalable trajectory-level transport, principled handling of mass mismatch, and theoretical analysis for OT-regularised RL.

Open multimodal reasoning models have benefited from large-scale reasoning supervision, yet reliable post-training remains challenging due to uneven data quality, inefficient supervision construction, imbalanced difficulty, and cross-domain interference. We introduce MMVistaReason (MVR), an open-data post-training recipe with three components: (1) broader capability coverage across complementary Analytical and Real-World reasoning groups, emphasizing structured reasoning versus visual perception and spatial grounding; (2) efficient SFT and RL data construction, standardizing heterogeneous open data through staged cleaning and annotation, combining difficulty-aware cascaded teacher distillation with answer-likelihood-based trajectory selection to construct MVR-SFT-528K, and applying scale-specific frontier filtering for MVR-RL-63K; and (3) specialize-then-integrate training, which trains complementary RL experts and consolidates their capabilities through multi-teacher on-policy distillation (MOPD). Our analyses reveal a capacity-dependent interaction between supervision difficulty, trajectory quality, and model capacity: smaller students benefit more from selected supervision, while larger students are robust to trajectory variation and mixed-domain interference. Mixed-domain RL introduces benchmark-level negative transfer, whereas MOPD provides consistent capability integration, with the preferred KL direction varying across model scales. Across 15 multimodal benchmarks, MVR-4B achieves an average score of 72.8, outperforming Qwen3.5-9B (Instruct) and MMFineReason-8B while using about 70% fewer samples than MMFineReason. Scaling to 9B improves the average to 74.4, surpassing Qwen3.5-35B-A3B (Instruct). Overall, MMVistaReason demonstrates that systematic open-data construction and capacity-aware post-training provide a practical and scalable path toward reliable multimodal reasoning.

Reinforcement learning for trading often struggles to balance upside participation with drawdown control. Profit-only policies can collapse toward passive long exposure on upward-drifting assets, while aggressively risk-penalized rewards can become too defensive during volatile periods. This paper proposes PPO-HRAP, a hybrid regime-aware policy that combines Proximal Policy Optimization with an interpretable regime prior. The agent observes both market features and portfolio-state variables, receives a reward combining portfolio log return, VIX-conditioned drawdown-increase penalty, target-exposure deviation, and turnover cost, and executes a blended action between the PPO actor output and a regime-derived target exposure. On the held-out 2020-2022 SPY test window, PPO-HRAP achieves 27.62% total return, 8.48% annualized return, 0.6447 Sharpe ratio, 0.8588 Sortino ratio, and 0.4592 Calmar ratio, while reducing maximum drawdown from 34.10% for Buy and Hold to 18.47%. Across five SPY seeds, PPO-HRAP remains stable with mean total return $0.2725 \pm 0.0109$ and mean Sharpe ratio $0.6219 \pm 0.0565$. Single-run cross-asset tests on QQQ and DIA further show that the proposed method ranks first on total return and Sharpe ratio for all three reported assets. These results suggest that blending learned actions with a volatility-aware regime prior is a practical way to improve risk-adjusted trading behavior, although the current policy still incurs high turnover and cross-asset robustness beyond SPY remains limited to single-run evidence.

Coordinated multi-humanoid loco-manipulation is promising yet challenging due to high-dimensional whole-body control, decentralized decision making, and scalability. While recent reinforcement learning methods have improved single-humanoid whole-body control, extending them to the multi-humanoid setting remains nontrivial and often requires substantial reward engineering or task-specific design. We propose MASkillBlender, a general multi-agent reinforcement learning framework to achieve decentralized multi-humanoid whole-body coordination. By learning a shared decentralized high-level policy over reusable pre-trained single-humanoid skills, MASkillBlender enables coordinated behaviors using only task-level rewards, without requiring task-specific motion references. To improve learning efficiency, we further introduce a permutation-based data augmentation strategy for homogeneous multi-humanoid systems, and theoretically show that the permuted samples preserve the policy-gradient direction of the original samples under the homogeneous Markov game formulation. We evaluate MASkillBlender on multiple multi-humanoid coordination tasks across two humanoid embodiments. Simulation results demonstrate that the proposed framework consistently achieves strong task performance and enables coordinated behaviors across different tasks and humanoid embodiments.

We connect the spurious-reward paradox to a model's reachability and propose random-reward reinforcement learning (RL) as a useful tool for the probing enterprise, addressing a decade-long debate over what probing performance actually reveals about a model. There are two prevailing explanations for the surprising finding that even random rewards can improve the performance of large language models (LLMs): one attributes the gains to particular mechanisms within RL training; the other to data contamination. Our results motivate a different view: spurious-reward RL can probe a model's reachability, or what further training can attain from its current state under specified constraints, beyond what is reflected in its current performance. Two OLMo checkpoints with the same accuracy on synthetic arithmetic (3.5%), for example, reach 8.5% and 55% in their best runs under the same correctness-rewarded RL. Examining OLMo checkpoints across pre-training and mid-training reveals three distinct regimes of training response: early on, RL produces little improvement even when correct answers are rewarded; later in pre-training, rewarding correct answers becomes effective while random rewards remain weak; and, upon entering mid-training, even random rewards can produce large gains. A similar ordering appears in a number-masked supervised fine-tuning (SFT) analysis of these checkpoints, suggesting that the pattern is not specific to a particular RL mechanism. Moreover, RL with random rewards offers a distinctive perspective on what training can make an LLM do, since its reward signal supplies no information about which answers are correct. By asking what training can attain without correctness feedback, it addresses the label-leakage side of a central problem in decodability-based probing: whether a successful probe reveals the model's capabilities or learns the task itself.

Training a single LLM agent jointly across diverse interactive environments has attracted increasing attention as a route to generalist agents. Existing curriculum and data-selection strategies often allocate training at the environment level or prioritize local reward-based signals, without explicitly considering relationships between current rollouts across environments for prompt-group selection. Meanwhile, as environments are learned at different rates, all-failure and all-success rollout groups can coexist within a batch, leaving those data without group-relative reward signals. Both challenges highlight limitations of relying solely on scalar rewards in multi-environment RL: they provide limited information about cross-environment relationships and no within-group reward contrast when rewards are identical. This motivates richer textual feedback, such as rubrics describing rollout behaviours, to guide learning. Beyond rubrics' usage as reward, we repurpose rubrics to guide both online data selection and policy supervision. An LLM judge tags each rollout using a predefined rubric vocabulary shared across environments. The resulting profiles guide the selection of data that aligns with the overall behavioural composition of the mixed-environment batch while limiting overlap with already-selected data. Available positive rubrics (describing desired behaviours) provide privileged context for an on-policy self-distillation teacher, supplying additional token-level supervision, while negative rubrics (describing undesired behaviours) guide subsequent rollout generation away from recurring failure modes. Together, these components form RISED. Across model backbones, RISED achieves the highest mean pass rate across environments and ranks first or second in every individual environment. Rubric-based analysis of RISED can further characterize the behavioural changes accompanying these gains.

Existing approaches to offline goal-conditioned reinforcement learning (GCRL) struggle with long-horizon tasks. Discounting shrinks value differences between distant states until they fall below the function approximation error, leaving the agent with no signal for ranking states. Temporal abstraction, which treats k environment steps as a single transition, restores this signal at long range, but no single fixed k suits all state-goal distances: large k preserves value differences across long temporal distances while collapsing distinctions between nearby states, and small k does the reverse. We make this trade-off explicit and introduce Generalized Implicit Temporal Abstraction (GITA), which conditions a single value function on k. GITA trains one policy by aggregating advantage-weighted supervision across multiple k values, so scales assigning larger positive advantages to a state-goal pair contribute more strongly to its update. GITA does not need to choose between local resolution and long-range signal; it retains both without committing to a single k. On OGBench, GITA outperforms a broad range of offline GCRL baselines, raising average success rate across all tasks by 25 percentage points (73% relative improvement) over HIQL. It also improves over the strongest fixed-k method, OTA, by 7 percentage points (14% relative).

Cyber attack agents are typically trained and evaluated within a single simulator, making it unclear whether learned policies transfer beyond the environments in which they were developed. This limitation hinders both deployment and fair comparison, as cyber simulators differ substantially in their state representations, observation models, and action spaces. In this paper, we study policy transfer across cyber environments and argue that simulator-to-simulator and simulator-to-real transfer can be viewed as instances of the same underlying alignment problem. We propose a framework that separates state alignment from action translation, enabling a policy trained in one environment to operate in another without retraining. We evaluate transfer across four cyber platforms, CyberBattleSim, NetSecGame, CyberWheel, and NASim, including emulated deployments in NASim. Our experiments show that zero-shot transfer is feasible, fully preserving source-policy performance in closely aligned environments and achieving 45.2% win rates when transferring policies whose source performance is 60.5%. In emulated virtual machine environments, transferred policies exhibit a Jensen-Shannon divergence of 0.085 from native policies, indicating strong behavioral similarity. Code and benchmarks are available at: https://anonymous.4open.science/r/RL-Transfer-between-env-4F47/.

By learning transferable rewards, inverse reinforcement learning (IRL) enables counterfactual evaluation of agents under modified environments. Such transfer places strict requirements on coverage since target environments affect agents' state occupancy. We propose a multi-task IRL method that pools data across multiple agents with different rewards in the same environment under a low-rank assumption. In addition to alleviating coverage requirements, so each task need not visit every state as long as others do, the method offers scalable evaluation of multiple tasks under new environments as computationally intensive planning scales with rank rather than the number of tasks. We provide finite sample guarantees on reward recovery and on policy learning in new environments. Experiments show our method is robust to limited coverage, recovers rewards on and off of each task's support, transfers to target environments at lower regret than baselines, with its computational advantage over per-task methods widening as tasks grow.

In partially observable reinforcement learning (RL), a later observation can make stored information obsolete or change what it implies for the next decision. Memory architectures and benchmarks for RL mostly test retention, the ability to keep information unchanged until it is needed. We formalize two further requirements. Rewriting sets the decision-relevant content to a value independent of the old one, and experience fusion transforms the old content by a rule that a later observation specifies. For tasks built from such updates, we count the memory states that a solution needs, and several baselines reach their lowest success rates on compositions that need more states. We introduce ALER (Adaptive Learnable Experience Rewriting), an agent that pairs an LSTM with a slot memory. An independently addressed Gumbel-Softmax write that concentrates its weight on one slot overwrites that slot, and a learned gate fuses the retrieved content with the recurrent state before the policy and value heads. We also introduce Rune-Mazes, three environments in which rune observations invert, cancel, reset, or repeat updates of a hidden cue under vector and pixel observations. Against seven baselines, ALER reaches a success rate of at least $0.82$ in all sixteen Endless T-Maze configurations and at least $0.99$ on all five Rune T-Maze compositions, and it has the highest mean success rate on four-branch Rune Multi-Corridor with an Invert rune. On pixel-based Rune MiniGrid Memory, it has a higher mean success rate than PPO-LSTM in eight of ten configurations. Project page: https://quartz-admirer.github.io/ALER-Adaptive-Learnable-Experience-Rewriting/.

Multi-reward reinforcement learning trains large language models to satisfy multiple behavioral objectives simultaneously. Reward-wise normalization, as used in GDPO, preserves reward-specific relative information within rollout groups, but different objectives can still exhibit uneven learning progress. We study this behavior through advantage energy, the sum of a reward's squared advantages over a batch. Under idealized GDPO normalization, we show that this energy is proportional to active-group density: the fraction of rollout groups in which the reward provides nonzero relative advantages. This reveals a residual batch-level signal imbalance and provides a basis for calibrating reward contributions. Based on this relation, we propose Density-Aware Reward Aggregation (DARA). We derive an inverse-square-root density correction that gives greater weight to signals from less frequently active rewards. DARA computes its weights from each rollout batch, adapting to changes in reward activity throughout training without modifying the underlying policy optimization objective. Experiments on tool calling and mathematical reasoning show that DARA learns the targeted behaviors faster than GDPO, reaching high format compliance in up to 26% fewer training steps on tool calling and near-saturated length compliance in up to 65% fewer steps on mathematical reasoning, while remaining competitive in final performance. Our code is available at https://github.com/zhaihaotian/DARA.

Training LLM agents with reinforcement learning (RL) is bottlenecked by environments, which must provide verifiable rewards, support long-horizon interaction, and scale cheaply. Existing approaches rely on costly human-curated data or on LLM-generated environments that risk hallucinations and benchmark contamination. We show that LLMs can instead be trained into capable search agents using synthetic environments generated entirely by rules, whose generation requires no LLM and has zero marginal cost. We build PhantomEnvironments, multi-turn RL environments from fictional worlds, where agents must search a corpus of templated articles to answer multi-hop questions. Despite sharing no facts with the real world, these strikingly simple environments yield agents that transfer to real-world multi-hop search benchmarks, often outperforming real-world training data on newer benchmarks. Trained agents generalize to unseen fictional universes, and Qwen models learn to scale their search budget roughly linearly with question difficulty, suggesting emergent search scaling from environment interaction alone. Ablating environment complexity reveals that hop count drives transfer more than constraints or comparisons: even the simplest rule-generated environments are a surprisingly effective, free resource for training generalizable LLM agents.

Long-term egocentric video enables personalized AI assistants to reason about daily life. However, as video histories grow to hundreds of hours spanning months or years, reprocessing raw clips for every query becomes computationally prohibitive. Memory systems offer a scalable alternative by compacting videos into text representations, but often fail on practical benchmarks: either the memory does not preserve key evidence, or the retriever fails to locate relevant entries due to retrieval competition in growing search spaces. To address these challenges, we introduce MemLife, a multimodal memory system that constructs entity-grounded, first-person text episodes and retrieves them via a time-indexed agentic reader. Without training or query-time video access, MemLife improves over the strongest training-free baseline by 4.6--12.0% across four long-horizon benchmarks. To further improve memory quality, we propose MemOpt, a reinforcement learning framework that optimizes the memory writer to produce faithful, informative, and retrievable memories. MemOpt consistently improves MemLife by 2.7--5.0% across different video and question distributions, with gains that generalize across writer and reader backbones and memory systems.

Reinforcement learning with verifiable rewards (RLVR) has become an important approach for improving reasoning during post-training. Recent work suggests that some difficult prompts remain resistant to learning even when they occasionally produce correct solutions. We revisit this unlearnability phenomenon and find that the affected prompts do improve, at roughly one third of the learnable rate, while the difficulty-defined set used to study them is much less reproducible than expected. These difficulty labels are estimated from a limited number of sampled responses. Combining them across seeds can further change which prompts are selected instead of simply reducing measurement noise. We develop a sampling-based framework for quantifying this instability and determining how much evaluation is required for difficulty assignments to reproduce reliably. We also revisit the gradient-similarity evidence proposed to explain unlearnability and show that part of the observed separation arises because difficult prompts provide fewer correct rollouts from which their gradients can be estimated. Matching this sample count weakens the gradient difference but does not remove it. Overall, the slow-learning phenomenon survives our reanalysis, while both the prompts used to define it and the evidence used to explain it require more careful measurement.

Exploratory reinforcement learning (RL) on an operating bus fleet is impractical,while policies trained only from historical data cannot acquire new experience. Hybrid Offline-and-Online (H2O) RL combines fixed target replay with simulator interaction, but the inexpensive online simulator can differ from the target in transition and event-duration dynamics. We study this cross-fidelity problem for multi-line bus holding and address a failure mode in which lower generalized passenger time coexists with incomplete passenger journeys.

Parameter-efficient reinforcement learning aims to improve reasoning with a compact trainable interface to a pretrained model. We introduce the Thalamic Router (T-Router), which concentrates adaptation on the reuse of completed computations. A compressed, addressable bank preserves block changes; a depth-recurrent controller conditions their selection and relative-scale writeback. This coupling gives thalamic context-dependent routing a concrete computational form: learn which earlier contributions a receiving layer uses, and with what influence. Correctness rewards train the interface while preserving backbone parameters and layer order. On an 8.95B-parameter backbone, T-Router allocates 41.73M parameters (0.466% of the backbone) and achieves 83.64 +/- 1.16 MathAvg after GSM8K RL, compared with 73.79 +/- 1.83 for full-parameter GRPO across three evaluation rounds. At a comparable parameter budget and with matched retries, it exceeds LoRA's 77.28 +/- 1.95 MathAvg, improving all three task families and raising mean AIME accuracy from 48.33 to 60.56. Capacity-controlled comparisons favor addressable block changes and recurrent context; separate search training extends the interface to tool-mediated reasoning. These results establish controlled computation reuse as an effective route to parameter-efficient reasoning reinforcement learning.

Inverse Reinforcement Learning (IRL) aims to recover a reward function that explains expert demonstrations. Existing IRL methods typically rely on a bi-level optimization procedure that alternates between reward learning and policy optimization, leading to substantial computational burden and training instability. In this work, we introduce a different route that eliminates policy optimization entirely by leveraging diffusion policies. Our key insight is that a diffusion policy encodes the action-gradient structure of the optimal soft Q function, enabling reward learning to be cast as a sequence of value recovery problems, thereby allowing us to bypass reward-policy loops inherent in prior IRL methods. Specifically, our method proceeds in three stages: (I) recovering the optimal soft Q function via action-gradient matching and estimating the corresponding soft value function (LogSumExp of Q values) in a way inspired by Gumbel regression; (II) calibrating these soft values by inferring a state-dependent offset; (III) extracting the reward by enforcing Bellman consistency. This leads to Loop-Free Inverse Reinforcement Learning (LFIRL), a fully offline algorithm that operates in a simple, loop-free, and sequential manner. LFIRL is simple to implement and significantly improves training efficiency while maintaining strong reward recovery performance. Empirically, across Maze, Franka Kitchen, Adroit Hand Pen, and Push-T benchmarks, LFIRL achieves 2-3x speedup over the fastest baselines, while matching or surpassing state-of-the-art methods in reward recovery quality.

Actor-critic methods achieve strong performance in continuous control, but their policies can produce highly oscillatory actions. A common remedy is to add auxiliary smoothness losses. However, their contribution can be negligible when their gradients are small relative to the native actor gradient. Moreover, existing methods often combine multiple auxiliary losses, complicating loss balancing without necessarily improving the return-smoothness trade-off. We introduce DAMPER (Direction-Aware Magnitude-Controlled Projection with Explicit Return Priority), which combines the native actor gradient with a temporal-consistency gradient through conflict-conditioned projection and adaptive magnitude control. It removes the auxiliary component opposing the actor gradient and scales the retained temporal direction relative to the actor gradient norm, preserving positive alignment with the native actor gradient. Experiments with TD3 and SAC on six continuous-control tasks show reduced action oscillation relative to the native agents in all 12 task-backbone pairs and the best oscillation score among the compared methods in eight, with task-dependent return trade-offs.

Scaling laws for optimization against reward models in AI alignment have pinned down how performance depends on optimization effort---measured by a KL-divergence budget relative to a reference policy. Beyond a certain budget, over-optimization (or reward hacking) can arise: because we optimize against a proxy reward model (distinct from true rewards), performance can plateau or degrade. Naturally, the proxy reward's accuracy depends on how much preference data (often in the form of pairwise comparisons) was used to train it. However, existing research does not cleanly identify how performance jointly scales with the amount of training data and the divergence budget. Our main contribution is to provide an empirically accurate and theoretically grounded scaling law in such context. Performance roughly scales as $Θ(\sqrt{\min\{\log(M),K\}})$, where $M$ is the number of comparisons in training data and $K$ is the policy's divergence budget. We develop an information-theoretic model to establish this upper bound and prove it is tightly achievable through a constructive procedure. Informed by this, we conduct extensive empirical evaluations using a real-world annotation setup, whereby a large 70B gold reward model generates feedback data and proxy reward models are trained from less capable models (0.6B to 4B). Our scaling law provides an excellent fit (R2 from 97% to 99%), outperforms alternative specifications, and remains robust across model sizes, noise, and optimization procedures (best-of-$N$ or policy tilting). Our evidence suggests that reward optimization is analogous to a surprisingly simple selection task: choosing from a sequence of IID Gaussian random variables using noisy preference feedback.

Real-time commentary for Multiplayer Online Battle Arena (MOBA) esports requires a vision-language model (VLM) to narrate a live match second by second, both fluently and accurately. Existing streaming VLMs sound natural but often miss key events such as kills and objectives. To address this limitation, we use game telemetry, which records exactly when each event occurs, as a supervision signal. We introduce MOBA-VL, a 9B-parameter model trained on this signal with event-localized multi-turn reinforcement learning, which rewards the turns that describe each event. We also collect MOBACast, 860 professional matches (about 460 hours) across three MOBA games with word-level timestamped commentary, and MOBACast-Bench, a benchmark from held-out tournaments. On MOBACast-Bench, MOBA-VL achieves the highest Overall score on full matches (63.25 vs. 55.12 for StreamingVLM) and clips (63.45 vs. 56.22 for DeepSeek-V4.1-Flash). Event-localized credit also raises event recall from 34.5 to 42.1 over supervised fine-tuning. Code and data will be released, and demos are available on an anonymous project page at https://moba-vl.github.io.

Training agents to follow arbitrary instructions is an important goal of multi-task reinforcement learning (RL). Linear temporal logic (LTL) provides a precise and structured formalism for specifying instructions to agents, and has been successfully adopted for training generalist multi-task policies. However, differences in implementations, task distributions, and evaluation protocols make existing methods difficult to compare, while high computational costs limit the scale and statistical reliability of experiments. We introduce Jaxolotl, a unified high-performance benchmark suite for multi-task LTL-RL to address these concerns. Jaxolotl provides a modular, end-to-end JAX implementation of six representative algorithms and four environments, together with newly curated task suites and a standardised, statistically robust evaluation protocol. By precompiling symbolic task representations into static arrays, Jaxolotl enables fully JIT-compiled training and evaluation, achieving end-to-end speedups of up to $220\times$ and supporting controlled comparisons at substantially greater experimental scale. We use this framework to systematically evaluate existing approaches, revealing complementary strengths and limitations: general methods capable of non-myopic reasoning struggle as the number of propositions grows, while methods with stronger scaling rely on environment-specific assumptions and suffer from myopia.

Recent approaches to reinforcement learning (RL) post-training for large language models increasingly remove the critic to reduce training instability and memory overhead. Even where a critic is trained, it is discarded once training ends, although it has learned to predict outcomes. We revisit this trend and show that a pretrained critic's ability to predict future outcomes can make it a valuable asset for efficient long-horizon reasoning. First, we find that instability in critic-based RL for long chain-of-thought reasoning is largely an optimization artifact: keeping policy updates small and low in variance restores stable convergence. Second, a well-pretrained critic estimates the posterior probability of eventual success from later trajectory states and unfinished prefixes. Its predictions provide outcome-derived, dense, per-prefix learning signals that, during policy optimization, require neither completed rollouts, step-level annotations, nor external reward labels. Building on this insight, we introduce Reward-Free Policy Optimization (RFPO), which repurposes a single calibrated, frozen critic as a rollout-level reward, a value baseline for generalized advantage estimation, and a success forecaster for unfinished prefixes. We further show that binarizing the debiased score stops the policy from exploiting the critic's length bias. Binarized, RFPO matches supervised PPO without a single label in the training loop, while cutting compute and memory overhead. This makes RFPO well suited to long-horizon reasoning tasks, where outcomes arrive late and generation dominates cost: because rollouts can be rewarded before they finish, training no longer has to pay for waiting on every trajectory to complete. Our findings challenge the prevailing critic-free paradigm and establish critic-based, reward-free optimization as a scalable and computationally efficient path for LLM post-training.

Production RL for language models lets the sampler fall behind the learner and repairs the resulting mismatch with a truncated importance weight. We ask how long the sampler can go without a refresh under that correction, and find a cliff: on Qwen2.5-Math-1.5B and GSM8K, importance-corrected GRPO refreshed every 192 updates learns well for 180 steps and then degrades severely in all three data seeds before the refresh arrives. Published remedies for staleness act on the update; we act on the sampler instead. Decoupled cooling draws samples at temperature 0.8 while the learner, the reference model and the importance weights stay at temperature 1, with the behaviour probability recorded from the tempered distribution, so the learner's objective is unchanged. All corresponding cooled runs are stable, and the longer interval keeps what the short one delivered: at the same update budget, a cooled sampler refreshed every 192 steps matches an uncooled sampler refreshed every 96 at the end of training (0.857 for both) and averaged over it (0.79), whereas lowering the learning rate to a safe value ends 3-7 points lower. On Qwen2.5-Math-7B the degradation points at interval 192 predict that an interval of 144 is fatal without cooling and survivable with it; on two data seeds the uncooled runs degrade before their first refresh and the cooled runs pass it and end at 92-93% against 68-81%, with one cooled run degrading transiently late in the second cycle. The benefit has a window: at three times the safe interval and in a high-mismatch MATH setting cooling delays degradation without preventing it, stronger cooling is not better, and cooling without the correction collapses. Sampling temperature is a control on staleness tolerance, and temperature and refresh interval should be chosen together.

GUI agents automate tasks on digital devices by grounding language instructions in visual interfaces. Existing group-relative reinforcement learning improves GUI action prediction by comparing the rewards of multiple responses sampled from the same GUI state. However, binary evaluation treats spatially different failed clicks as identical and provides no relative signal when all sampled clicks fail. To address these limitations, we propose Spatial Credit Assignment (SCA), which uses the screen coordinates of sampled clicks to refine group-relative credit. Specifically, SCA predicts each held-out response's reward from the other responses in groups containing both successes and failures, then uses the prediction residual to adjust credit. When all sampled clicks fail, SCA instead orders them by distance to the annotated target. These spatial references are used only to construct the training update; the deployed policy remains unchanged. We evaluate whether this correction improves the policy update itself by comparing its error and directional alignment with the exact return gradient in a controlled synthetic study. Across GUI grounding and offline action-prediction benchmarks, SCA improves grounding across professional domains and achieves the strongest results among reinforcement-fine-tuned models on most action-prediction metrics, with consistent gains across the reported GUI suites.

We propose STRAT, an auxiliary task that trains deep reinforcement learning (RL) agents to predict a short textual trace of their own state. Inspired by human spatial navigation, the description combines landmark, route, and survey knowledge, tracking the agent's position, inventory, goals, and immediate progress. Environment rules generate this text online without human labelling. Our method adds a single auxiliary head to a standard policy. Across 60 sparse-reward XLand-MiniGrid tasks, STRAT solves complex environments where standard RL fails outright, while compacting state representations and preventing rank collapse. Beyond performance gains, the predicted trace provides a readable account of agent beliefs at every step for no extra cost.

Self-rewarding reinforcement learning (RL) enables large language models (LLMs) to self-evolve without human labels. Existing ensemble-based methods construct reward references from rollout groups and assign rewards accordingly. However, a response's reward representation also depends on its randomly sampled group context, i.e., the other responses in its group. Using only one group-context realization may miss desired reward signals and provide unreliable guidance for policy optimization. To address this issue, we propose Group-Marginalized Advantage Estimation (GMAE), which aggregates reward realizations across possible contexts into a response-level distribution and estimates expected advantages. Experiments across eight benchmarks and four base models demonstrate strong performance and cross-domain generalization. GMAE also exhibits stable learning, low extra cost, and good applicability across training datasets and RL backbones.