Long-Horizon RL

Error-targeted learning gives a legible way to improve a model: identify specific weaknesses of the model, train the model to fix these weaknesses, and check whether the weaknesses are fixed. We study how to apply error-targeted learning to terminal agents, which solve long-horizon tasks specified in natural language by interacting with a command shell. Existing error-targeted methods are designed for single-turn tasks, and existing analyses of agent failures are used to evaluate and debug agents rather than to train them. We propose Misbehavior-driven RL (MiRL), which first profiles the errors of a policy to find generalizable misbehaviors: kinds of wrong steps that recur across many environments. MiRL then trains the policy with RL, starting rollouts at the steps where these misbehaviors occur and rewarding a rollout only if it passes the tests and avoids the misbehavior. On Qwen3.5-4B, eight misbehaviors account for 52.1% of wrong steps. After training with MiRL, the policy repeats the measured misbehaviors 43% to 57% less often on average on unseen prefixes. MiRL outperforms TMax-4B on Terminal-Bench Lite (51.8% vs. 47.4%) and matches it on Terminal-Bench 2.1 (21.3% vs. 20.6%), while using 35% of its rollouts. These results show that error-targeted learning can be applied to realistic, long-horizon terminal tasks.

With external tools, large language models (LLMs) can tackle complex tasks through sustained environmental interaction. LLM-based agents are therefore increasingly used to tackle complex long-horizon tasks in real-world environments. However, these tasks involve sequential, interdependent decisions and changes in environmental states. Early execution errors affect subsequent interaction histories and environmental states, and their effects accumulate along the decision chain. To address this challenge, we propose Reflection-Guided Policy Optimization (ReflectPO), a reinforcement learning framework for autonomous error recovery in long-horizon tasks. ReflectPO comprises two core components. The first is Reflection-Guided Sampling. We use branch differences and repeated visits in interaction trajectories to construct hints for error recovery. The second is Tree-Structured Credit Assignment. We organize sampled trajectories into trees and assign action-level credit using parent--child reward differences and recovery gains. Experiments over two long-horizon tool-use benchmarks show that ReflectPO outperforms multiple existing baselines in most domains. It also achieves the best overall performance on average. Further analyses show that ReflectPO effectively improves agents' ability to recognize their own deviations, recover from erroneous states, and continue making progress toward task completion.

Learning useful representations from continually changing value targets remains a challenge in deep reinforcement learning. We study the temporal horizon of this supervision: smaller discounts make these targets less sensitive to distant bootstrap changes, but using them for behavior changes the control objective. We introduce Short-to-Long (S2L), which supplies a long-horizon behavior learner with features trained by smaller-discount source networks. Detached connections prevent the behavior value loss from updating the sources, allowing each source to follow its own value objective while the behavior discount remains unchanged. Across Atari, online continuous control, and offline continuous control, the approach yields aggregate performance gains, improving the paired terminal median on 40 of 57 Atari games. Matched Atari ablations support the roles of feature transfer, smaller source discounts, and gradient isolation. Fixed-trajectory measurements further show reduced drift in source value targets with mixed discounts.

Long-horizon tasks are important for modern AI and robotics, yet pose a challenge for reinforcement learning. Historically, a popular approach has been to decompose a task into subgoals, and learn a subgoal-conditioned policy to execute each subtask in sequence. We introduce an alternative called Value Disaggregation (VaDar), which trains a single subgoal-independent policy to maximize a linear combination of per-subgoal critic values. Because subgoal information is needed only at training-time, VaDar removes the need for possibly costly or cumbersome subgoal-selection during policy deployment. Moreover, through careful experiments, we show that VaDar (1) is always competitive with, and frequently outperforms, natural baselines like goal-conditioning and (2) succeeds on tasks with non-sequential goal structure and multiple optimization objectives. In particular, VaDar is the first algorithm to solve challenging, long-horizon tasks in the RoboCasa suite, even when starting from a policy pretrained from behavior cloning with near-zero initial task success. Taken together, VaDar's successes suggest that subgoal information benefits actor-critic reinforcement learning by enhancing the efficacy of critic learning, whereas policy goal-conditioning is often unnecessary.

Long-horizon agent training, including software engineering, is advancing rapidly, but the recipe and infrastructure needed for a strong reinforcement-learning baseline remain difficult to reproduce. This makes gains from new algorithms or data hard to distinguish from improvements to an under-tuned baseline. We present Arctic-SWE, a fully asynchronous RL framework that establishes such a baseline through model-system co-design, using overfitting on a small task pool as the testbed. This testbed exposes failures that early reward gains conceal and guides the integration of established components: gated reward, importance-weight control, aligned training and inference engines, and consistent state across policy updates. No single component is new, yet together they form the missing foundation. On raw R2E-Gym data, without new algorithms or data work, Arctic-SWE trains Qwen3.5-4B to 62.0% pass@1 on SWE-bench Verified. This is comparable to concurrent FrogNano (61.5%), which relies on online task synthesis, after about one-sixth as many training rollouts. Building on this foundation, we further filter and refine R2E-Gym, SWE-rebench V2, and Scale-SWE. With this curated subset, the 4B model improves from 47.4%/25.0%/37.9% to 65.0%/38.3%/59.7% on SWE-bench Verified/Pro-v1/Pro-v2, and the recipe also improves Qwen3.5-9B from 56.2%/31.9%/48.8% to 65.7%/39.6%/70.2% on Verified/Pro-v1/Pro-v2. Controlled comparisons show that both curation and test strengthening improve held-out performance, although stronger tests reduce apparent training-task mastery. Arctic-SWE provides a documented starting point for studying better algorithms, data and environments for asynchronous agent RL.

Reinforcement learning with verifiable rewards has become a scalable post-training paradigm for large language models. However, training agents over long-horizon interactions presents two challenges: using only terminal rewards makes turn-level credit assignment sparse and high-variance, while sequential mini-batch updates on a fixed rollout batch introduce policy staleness as the current policy drifts from the behavior policy. Existing approaches obtain denser credit via learned critics, process reward models, or on-policy distillation, but they rely on a value network, step-level annotations, or a stronger external teacher that increase training complexity. Meanwhile, importance sampling and clipping mitigate policy drift, but they do not specify a finite target that stops sequential updates from overshooting. In this work, we introduce TreeOPSD, a critic-free, tree-aware posterior self-distillation framework for long-horizon agentic reinforcement learning. Treating each interaction turn as a tree node, TreeOPSD branches alternative continuations from shared prefixes and recursively backs up terminal rewards into implicit turn-level credit. It then maps each credit to a closed-form, bounded teacher distribution parameterized by the likelihood ratio relative to the frozen behavior policy. Minimizing the divergence between this teacher and the student policy recovers the policy-gradient direction as the tangent at the behavior policy while bounding updates toward a finite target across sequential mini-batches. Empirically, TreeOPSD improves agentic capabilities across several competitive benchmarks and model scales, especially for long-horizon tasks, e.g., raising the average accuracy of Qwen3-30B-A3B-Thinking-2507 by 4.97 points over GRPO on the Deep Research setting.

Long-horizon agents must coordinate reasoning, tool use, and environment feedback over extended interactions. Learning from sparse outcome rewards requires weighting trajectories of different lengths and updating the policy while rollouts are still being collected. We examine a single-rollout asynchronous recipe combining Muon, token-averaged loss, truncated importance sampling, and auxiliary length and tool-error penalties. Single-rollout sampling allows asynchronous learning without waiting for multiple trajectories for the same issue. We study optimizer choices and recipe components for repository-level issue resolution across two model families. The evaluated training runs show higher training success with the full recipe than with the baselines.

Long-horizon agents have drawn growing attention for their ability to work autonomously -- from hours to days -- on economically valuable tasks, a capability essential to automated discovery and recursive self-improvement (RSI). Yet open-source models still struggle on long-horizon tasks, largely for lack of both training data and a working recipe, and scaling both is hard: long, complex tasks are difficult to curate and verify, and their rewards are sparse. We address both. First, we introduce Tev-Gym, the first long-horizon agent training dataset with verifiable, dense, progressive rewards -- 1,170 verified task environments across 7 domains. It is built on a latent-world-first approach that first constructs a latent world: a complete and correct hidden specification of the task domain, workflow, and expected state after each step. Each task is then progressively rendered from this specification into an agent-facing environment, enabling controllable complexity and a natural progress metric. Second, we turn this metric into a training recipe: via progress-potential reward shaping (PPRS), we convert progress into a dense per-step reward that improves training efficiency and makes otherwise-intractable tasks trainable. Training with this recipe yields Tev-27B, which achieves substantial gains on the Agents' Last Exam computing and math sciences domains (ALE-CM), matching GPT-6 Astra and Claude Opus 5 at Pass@5. Despite training only on ALE-related data, it generalizes to the Terminal-Bench (TB) 3.0 and 4.0 subsets, surpassing GLM 5.2 and Gemini 3.7 Flash, and reaches Claude Opus 4.8-level performance on middle-horizon tasks such as TB 2.1.

Large language model agents increasingly operate in long-horizon environments where early mistakes can trigger cascading failures and trap agents in dead-end trajectories. Agents must therefore be able to proactively recover from such states and turn their exploratory experience into guidance for subsequent decisions. We introduce ReTRAIL, a framework that enables agents to rewind the environment to earlier states while preserving valid progress and carrying forward knowledge learned from abandoned exploration. The environment state moves backward while the agent's knowledge continues to move forward. ReTRAIL trains a shared policy with two complementary signals: State-Anchored GRPO compares alternative continuations from revisited states to improve execution, while a branch-advancement reward guides reflection through the progress of subsequent exploration. Experiments across four interactive benchmark MineSweeper, Sokoban, ALFWorld and ScienceWorld show that simply adding a rewind primitive provides limited benefit and can even degrade performance. In contrast, ReTRAIL enables agents to rewind from unproductive states and use insights from abandoned branches to guide subsequent exploration. These results demonstrate the value of coupling environment rewinding with experience reuse within an ongoing task for long-horizon task solving. The code is available at https://github.com/whi497/ReTRAIL.

Reinforcement learning (RL) has become a dominant paradigm for enhancing LLMs' reasoning capabilities. Yet long-horizon autoregressive rollouts introduce a fundamental limitation: local policy mismatch can compound into severe state distribution shift over trajectories. Existing LLM RL methods, such as GRPO and GSPO, control policy mismatch at the token or sequence level, but overlook this trajectory-induced shift, causing training instability and eventual collapse as the horizon grows. To close the state distribution gap, we propose Trajectory-Aware Policy Optimization (TAPO), a principled framework that theoretically derives the state-distribution correction from the off-policy policy gradient and incorporates it into the RL objective. TAPO further employs a geometric-mean estimator for variance reduction, together with a length-aware dynamic clipping that prevents overly deviated updates across the trajectory. Extensive experiments demonstrate that TAPO significantly surpasses existing LLM RL algorithms across eight competition-level benchmarks, achieving up to 48% and 12% improvement over GRPO on mathematical reasoning and algorithmic coding, with substantially enhanced training stability.

Training long-horizon agents to solve complex tasks requires effective supervision over extended interaction sequences. However, sparse terminal rewards obscure intermediate contributions, while on-policy distillation can lose informative teacher guidance as student-generated histories grow. To address this problem, we introduce SCAD, which organizes interactions into planning and bounded subtask execution, distills execution in local contexts, and refines planning credit through cross-rollout subtask prefix trees, with planning receiving full terminal credit and execution receiving positive terminal credit and teacher guidance. Across all evaluated benchmarks, SCAD improves macro-average accuracy over the strongest training baseline by 4.48 percentage points for text tasks and 4.19 points for multimodal tasks. SCAD effectively combines outcome-based credit assignment with teacher-guided distillation to improve planning and execution in long-horizon agents.

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).

Group-based reinforcement learning such as GRPO trains LLM agents by comparing rollouts sampled for each task, without a learned critic. In long-horizon settings, these rollouts revisit shared anchor states, offering cross-rollout evidence for step-level credit. Ideally, step-level credit should incorporate evidence beyond the realized suffixes observed at an anchor while aggregating alternative continuations according to their empirical frequencies. Visit-local averaging pools realized suffix returns at shared anchors and respects observed frequencies, but does not recursively propagate evidence across rollouts, whereas shortest-path estimators have global reach but allow a rarely observed route to dominate an anchor's value. We introduce Cross-Rollout Bellman Closure (CRBC), which merges each rollout group into a finite empirical process with absorbing success and failure boundaries and evaluates its behavior-policy Bellman fixed point with one linear solve. This fixed point uses the same empirical action and transition frequencies to propagate evidence through shared anchors and aggregate alternative continuations. Backing up the resulting state values through observed transitions yields action values, whose gain over the corresponding state value provides step-level credit. A corresponding finite-depth family recovers visit-local return averaging at zero depth and converges to the exact closure as depth increases. The normalized closure credit is combined with the trajectory-level group advantage for policy optimization, without additional environment rollouts. Across ALFWorld, WebShop, and Sokoban benchmarks with multiple model scales, CRBC consistently improves final performance and learning efficiency. For example, CRBC outperforms the strongest evaluated baseline by 5.59 percentage points on ALFWorld with Qwen2.5-1.5B-Instruct.

Large language model (LLM) agents increasingly undertake extreme-long (xlong) horizon tasks, where a single execution can span hours, hundreds of model--environment interactions, and nearly 1M tokens per rollout. Applying online reinforcement learning (RL) to such executions poses two fundamental challenges: (1) severe execution variance and prolonged rollout delays cause massive GPU idling; and (2) complex non-linear branching generates massive trajectory redundancy, crippling training efficiency. To address these, we presents QwenGyre, an end-to-end framework for xlong-horizon online RL. QwenGyre elastically reallocates GPUs between rollout and training without interrupting live executions, while its trajectory processor reconstructs branching histories, scores partial progress, and deduplicates redundant paths to bound training costs. Scaled to our flagship model, Qwen~3.8 2.4T, with 700K tokens per rollout, QwenGyre yields a 6.0% absolute gain on NL2RepoBench (52.5% $\to$ 58.5%) in 48 steps. Across our evaluations on diverse domains of training datasets, QwenGyre delivers up to $1.85\times$ and $1.78\times$ speedups over Colocate and Async, respectively.

Agent usage is shifting toward long-horizon tasks such as coding and scientific discovery, among which terminal tasks are especially important. We introduce T1, a Mixture-of-Experts model of 122B total trained with reinforcement learning, operating a real shell in a cloud sandbox for up to 300+ tool-call turns per task, rewarded by executing each task's own verifier. We provide a comprehensive recipe: First, an aggressively warm-started to stabilize actor-critic training, with a dense process reward scoring trajectories by the absolute number of passing verifiers. Second, stable optimization through TITO construction, training on the exact sampled token identifiers with drift repair at turn boundaries, and rollout routing replay, recording the sampler's per-token expert choices at every MoE layer and replaying them during training. Third, fully out-of-distribution training corpus: isolated seeds and synthesized tasks disjoint from Terminal-Bench 2.1 ensures gains reflect genuine capability transfer over benchmark overfitting. Together, TITO and R3 cut the training-to-inference log-probability difference from 0.021 to 0.013, with exactly aligned zero token drift in the loss region. On Terminal-Bench 2.1, our post-train pipeline raises initial base model from 43.8% to T1 with 64.0% resolved. On Long-Horizon Terminal Bench, T1 reaches 27.9% and surpasses GPT-5.4 and GLM-5.1.

Current paradigms for training language models via reinforcement learning rely heavily on sparse outcome rewards. However, as we pursue tasks that require longer and more complicated trajectories, such strategies result in slow learning. Prior work has attempted to address this problem by rewarding partial progress; however, naive formulations are often biased and converge to suboptimal policies. We show that a simple and unbiased dense reward formulation, which we term progressive point matching, scales exponentially more efficiently to long-horizon tasks by rewarding partial progress on a segment level, both theoretically and empirically via synthetic environments. We then show how progressive point matching can be practically instantiated using a single reference trajectory per task. On extremely hard math reasoning problems, sparse outcome rewards cannot make any progress, whereas segment-level rewards enable improvements at larger test-time token budgets when measured by success rate or pass@k.

Scaling the interaction horizon-the maximum number of environment interactions per episode-improves LLM agents on long-horizon tasks, and curriculum-based methods that progressively expand the horizon outperform fixed-horizon alternatives. However, existing schedules are open-loop: they monotonically increase the horizon until a manually specified maximum, with no mechanism to detect when further expansion stops helping. We propose the effective interaction frontier hypothesis: a dynamic boundary beyond which additional interactions yield diminishing returns while cost grows linearly. We then introduce Elastic Horizon, a closed-loop controller that tracks this boundary via the 90th percentile of successful trajectory lengths. On AppWorld and BFCL, fixed-horizon sweeps reveal clear saturation plateaus; Elastic Horizon stabilizes the horizon inside the saturation band from both under- and over-capacity initializations, attains the best success rates across 7B and 14B backbones, and saves up to 25% of per-step trajectory tokens. Our work shifts the paradigm from how to scale interaction horizons to when to stop scaling.

Group-based RLVR methods estimate advantages by repeatedly sampling multiple trajectories for each prompt, making long-horizon agent training expensive and discarding useful experience accumulated across iterations. We ask whether historical experience can replace these repeated within-iteration comparisons without directly optimizing on stale trajectories. We introduce Long-Short Term Advantage Estimator (LSTAE), a single-stream RL algorithm that uses history for advantage estimation while updating the policy only with the current rollout. LSTAE maintains a persistent tracker for each task anchor. At the trajectory level (long term), a drift-aware historical baseline tracks the anchor's moving success frontier and measures the relative contribution of each new trajectory. At the step level (short term), a recent state-experience buffer exploits recurrent states to estimate localized action advantages. This two-timescale design converts accumulated experience into multi-granular credit signals, requiring only one rollout per anchor. Across agentic and mathematical reasoning benchmarks, LSTAE matches or improves upon strong group-based baselines while substantially reducing rollout cost.

Scaling offline goal-conditioned reinforcement learning (GCRL) to long-horizon tasks is difficult because (1) long-range value learning depends on shorter-range estimates that may still be inaccurate, and (2) max-based value backups can amplify overestimation through repeated propagation. We propose DCRL (Divide-and-Conquer RL), which recursively decomposes each trajectory segment into a balanced binary tree and trains the values from leaves to root. Each parent is therefore updated only after its children, using an exact factorization of the observed route rather than selecting among noisy alternatives. Since this objective learns values along demonstrated routes that are not necessarily optimal, DCRL jointly propagates values across trajectories to discover shorter routes. Thanks to the balanced binary tree, DCRL reduces worst-case bootstrap depth from linear to logarithmic, and this shorter dependency structure empirically corresponds to much slower error accumulation. Across diverse goal-reaching tasks, DCRL substantially outperforms prior flat offline GCRL methods, and on the five most challenging long-horizon OGBench tasks, it improves the best prior average score from 55 to 64, surpassing all flat and hierarchical baselines.

Exploration in sparse-reward long-horizon tasks poses significant challenges for reinforcement learning. To address these challenges, we propose a two-level Hierarchical Reinforcement Learning (HRL) framework. The first level handles high-level strategic planning, while the low-level uses the continuous-control Soft Actor-Critic (SAC) algorithm, and they utilize entropy-regularized policy optimization. The proposed framework was trained and evaluated using the Search-and-Rescue-2 (SAR-2) dataset. HRL-SAC effectively addresses sparse-reward long-horizon search problems characterized by delayed rewards and continuous control, and its outperforming the flat SAC baseline reinforcement learning in terms of success rates, coverage efficiency, and convergence. These findings indicate that hierarchical entropy-regularized policies are a promising solution to tackle long-horizon sparse-reward reinforcement learning tasks.

Learning accurate value functions plays a decisive role for reinforcement learning (RL) agents to solve long-horizon, complex tasks. Conventional temporal-difference (TD) learning objectives suffer from value-estimation bias that accumulates over the horizon, while extended-horizon modeling methods, such as n-step TD backups and Q-chunking, adopt a rigid, fixed-horizon value-modeling recipe that is often not flexible enough to capture complex value structures in long-horizon, multi-stage tasks. In this paper, we show that enabling value updates with dynamic horizon composition can yield a strong offline policy learning scheme. Our method, Horizon Adaptive Offline Policy Learning via VAlue STitching (VAST), replaces fixed-horizon backups with recursive, horizon-adaptive value composition. Its key ingredient is to couple value optimization with a future state- and horizon-length-conditioned auxiliary value function that is learned through direct data supervision, and a stitching policy that optimally selects the reward-maximizing horizon length and future sub-goal to achieve horizon-adaptive value stitching. This design enables direct estimation and compositional "stitching" of variable-length returns grounded in actionable sub-goal states, providing an accurate and greedily exploitable value-supervision signal for offline policy optimization. Across 50 tasks on OGBench, VAST outperforms fixed-step, extended-horizon methods, and generative-value offline RL baselines, achieving strong performance particularly in high-complexity, long-horizon decision-making tasks.

Reinforcement learning problems typically define the goal as maximizing the expected value of a scalar reward function. But, pairwise preferences are often easier to specify than scalar rewards, and they express certain goals that scalar rewards cannot. Methods for reinforcement learning with pairwise preferences have thus received growing interest. Unfortunately, these methods are inefficient in problems with long time horizons, and they lack guarantees on the performance of Markov policies relative to history-dependent policies, which bridge the theory and practice of reinforcement learning. We therefore propose the Markov decision contest as a new problem model for reinforcement learning with pairwise preferences. We prove that stationary Markov policies are optimal among all history-dependent policies, that solving a Markov decision contest exactly is in P, and that a simple iterative algorithm converges to an optimal policy at a sublinear rate. Lastly, in a set of high-dimensional decision problems with long time horizons, we show that our approximate algorithm is significantly more learning-efficient than prior work.

Reinforcement learning from verifiable rewards (RLVR) is a promising paradigm for improving large language model (LLM) agents on long-horizon interactive tasks. However, in partially observable environments, incomplete observations cause agent beliefs to drift over time, while delayed rewards obscure the causal impact of intermediate decisions, exacerbating temporal credit assignment challenges. To address this, we propose ReBel (Reward Belief), a process-level reinforcement learning algorithm that explicitly models structured belief states to summarize interaction history and guide subsequent policy learning. ReBel introduces belief-consistency supervision, converting discrepancies between predicted beliefs and observed feedback into dense self-supervised signals without requiring external step-wise annotations or verifiers. It also employs belief-aware grouping to compare trajectories under similar belief states, yielding more robust and lower-variance advantage estimates. We evaluate ReBel on challenging long-horizon benchmarks, including ALFWorld and WebShop. ReBel improves task success by up to $20.4$ percentage points over the episode-level baseline GRPO and increases sample efficiency by $2.1\times$. These results suggest that belief-aware self-supervision is a promising direction for reliable long-horizon decision-making under partial observability. Code is available at: https://github.com/Fateyetian/Rebel.git.

Training long-horizon LLM agents with reinforcement learning is challenging because sparse outcome rewards reveal whether a task succeeds, but not which intermediate actions caused the outcome or how they should be corrected. Recent methods alleviate this issue by generating rewards or textual hints from turn-level action-output signals, or by using feedback-conditioned self-distillation. However, generating feedback at every turn is inefficient when many intermediate turns are already successful or neutral, and applying feedback at a fixed or misaligned turn often fails to supervise the actions that contributed to the failure. To bridge this gap, we propose HINT-SD, a targeted self-distillation framework that uses full-trajectory hindsight to select failure-relevant actions and applies feedback-conditioned distillation only on targeted action spans. Experiments on BFCL v3 and AppWorld show that our method improves over the dense per-turn feedback baseline by up to 18.80 percent while achieving 2.26$\times$ lower time per training step, suggesting that selecting where to distill is a key factor for both effective and efficient long-horizon agent training.

Model-based reinforcement learning (RL) offers a compelling approach to offline RL by enabling value learning on imagined on-policy trajectories. However, it often suffers from compounding errors due to repeated model inference on self-generated states. While geometric horizon models (GHM) alleviate this issue through direct prediction over a discounted infinite-horizon future, they remain challenged in accurately modeling distant future states. To this end, we introduce universal horizon models (UHM), a generalization of GHM that directly predicts future states under arbitrary horizons. Leveraging this flexibility, we propose a scalable value learning method that employs a winsorized horizon distribution to stabilize training by capping excessively large horizons. Experimental results on 100 challenging OGBench tasks demonstrate that the proposed method outperforms competitive baselines, particularly on tasks with highly suboptimal datasets and those requiring long-horizon reasoning. Project page: https://rllab-snu.github.io/projects/UHM/

In partially observable reinforcement learning (RL), a decision often depends on a cue seen many steps earlier, and training at such horizons is costly. Ideally, a policy trained on short horizons would remain optimal at arbitrarily long ones, making the training horizon a matter of convenience. We formalize this property as delay-horizon independence (DHI): optimality at every horizon, at a memory, computation and precision cost that is bounded in the horizon. We study agents that carry the cue in a recurrent memory of fixed size, whose cost does not grow with the delay. This paper characterizes DHI through the dynamics of that memory, in theory and on benchmarks. Although quantified over all horizons, DHI reduces to a property of a single map: a recurrent policy is DHI if and only if it admits a continuous readout of the memory, invariant under the idle dynamics and separating the cues. Monostable memory then precludes DHI at any parameter values, whereas multistable memory enables it. Monostability covers all contracting affine recurrences, hence state space models and gated linear recurrent neural networks (RNNs). Under arbitrarily small perturbations of the idle dynamics, multistability is the only mechanism supporting DHI at bounded memory. On the T-maze, the effective horizon of monostable models resists hyperparameter search: selected horizons fall short by up to $745\times$ when retrained. Multistable models trained on short horizons stay optimal up to $10^6$, on the T-maze and on MiniGrid. Current parallelizable RNNs thus trade horizon independence for scalability: parallelizable multistable architectures are the direction this points to.

While long-horizon agentic tasks require language agents to perform dozens of sequential decisions, training such agents with reinforcement learning remains challenging. We identify two root causes: credit misattribution, where correct early actions are penalized due to terminal failures, and sample inefficiency, where scarce successful trajectories result in near-total loss of learning signal. We introduce a milestone-guided policy learning framework, BEACON, that leverages the compositional structure of long-horizon tasks to ensure precise credit assignment. BEACON partitions trajectories at milestone boundaries, applies temporal reward shaping within segments to credit partial progress, and estimates advantages at dual scales to prevent distant failures from corrupting the evaluation of local actions. On ALFWorld, WebShop, and ScienceWorld, BEACON consistently outperforms GRPO and GiGPO. Notably, on long-horizon ALFWorld tasks, BEACON achieves 92.9% success rate, nearly doubling GRPO's 53.5%, while improving effective sample utilization from 23.7% to 82.0%. These results establish milestone-anchored credit assignment as an effective paradigm for training long-horizon language agents. Code is available at https://github.com/ZJU-REAL/BEACON.

Off-policy, value-based reinforcement learning methods such as Q-learning are appealing because they can learn from arbitrary experience, including data collected by older policies or other agents. In practice, however, bootstrapping makes long-horizon learning brittle: estimation errors at later states propagate backward through temporal-difference (TD) updates and can compound over time. We propose long-horizon Q-learning (LQL), which introduces a principled backstop against compounding error when learning the optimal action-value function. LQL builds on a prior optimality tightening observation: any realized action sequence lower-bounds what the optimal policy can achieve in expectation, so acting optimally earlier should not be worse than following the observed actions for several steps before switching to optimal behavior. Our contribution is to turn this inequality into a practical stabilization mechanism for Q-learning by using a hinge loss to penalize violations of these bounds. Importantly, LQL computes these penalties using network outputs already produced for the TD error, requiring no auxiliary networks and no additional forward passes relative to Q-learning. When combined with multiple state-of-the-art methods on a range of online and offline-to-online benchmarks, LQL consistently outperforms both 1-step TD and n-step TD learning at similar runtime.

Large language model (LLM) agents have recently demonstrated strong capabilities in interactive decision-making, yet they remain fundamentally limited in long-horizon tasks that require structured planning and reliable execution. Existing approaches predominantly rely on flat autoregressive policies, where high-level reasoning and low-level actions are generated within a single token sequence, leading to inefficient exploration and severe error propagation over extended trajectories. In this work, we propose HiMAC, a hierarchical agentic RL framework that explicitly decomposes long-horizon decision-making into macro-level planning and micro-level execution. HiMAC models reasoning as a structured blueprint generation process followed by goal-conditioned action execution, enabling robust long-horizon planning within LLM-based agents. To train this hierarchy efficiently, we introduce a critic-free hierarchical policy optimization paradigm that extends group-based reinforcement learning to bi-level structures through hierarchical relative advantage estimation. Furthermore, we propose an iterative co-evolution training strategy that alternates between planner exploration and executor adaptation, mitigating the non-stationarity inherent in hierarchical learning. Extensive experiments on ALFWorld, WebShop, and Sokoban demonstrate that HiMAC consistently outperforms strong prompting and reinforcement learning baselines, achieving state-of-the-art performance and substantially improved sample efficiency across both text-based and visually grounded environments. Our results show that introducing structured hierarchy, rather than increasing model scale alone, is a key factor for enabling robust long-horizon agentic intelligence.

Offline goal-conditioned reinforcement learning remains challenging for long-horizon tasks. While hierarchical approaches mitigate this issue by decomposing tasks, most existing methods rely on separate high- and low-level networks and generate only a single intermediate subgoal, leaving several structural limitations in long-horizon decision-making. To address this limitation, we draw inspiration from chain-of-thought reasoning and propose the Chain-of-Goals Hierarchical Policy (CoGHP), a novel framework that reformulates hierarchical decision-making as autoregressive sequence modeling within a unified architecture. Given a state and a final goal, CoGHP autoregressively generates a sequence of latent subgoals followed by the primitive action, where each latent subgoal acts as a reasoning step that conditions subsequent predictions. To implement this efficiently, we introduce an MLP-Mixer backbone, which supports cross-token communication and captures structural relationships among state, goal, latent subgoals, and action. Across challenging navigation and manipulation benchmarks, CoGHP consistently outperforms strong offline baselines, demonstrating improved performance on long-horizon tasks. Project page: https://wlsdn9350.github.io/projects/coghp/