NeurIPS 2026 Papers

Markov decision problems are most commonly solved via dynamic programming. Another approach is Bellman residual minimization, which directly minimizes the squared Bellman residual objective function. However, compared to dynamic programming, this approach has received relatively less attention, mainly because it is often less efficient in practice and can be more difficult to extend to model-free settings such as reinforcement learning. Nonetheless, Bellman residual minimization has several advantages that make it worth investigating, such as more stable convergence with function approximation for value functions. While Bellman residual methods for policy evaluation have been widely studied, methods for policy optimization (control tasks) have been scarcely explored. In this paper, we establish foundational results for the control Bellman residual minimization for policy optimization.

Behavioral Foundation Models (BFMs) are an emerging paradigm in reinforcement learning, playing a role analogous to large language models in natural language processing: they have shown remarkable versatility, enabling zero-shot performance, fast imitation, and online adaptation, all by exploiting the structure of a latent space. In this work, we investigate whether the latent behavioral space induced by BFMs can serve as an effective search space to discover large repertoires of behaviorally diverse and high-performing policies through Quality-Diversity (QD) methods. While QD methods generally search directly in high-dimensional policy parameter space, in this paper, we present BFM-QD, a framework that performs QD search in the compact latent space of a BFM. We further show that the BFM-QD framework provides a closed-form, gradient-free policy improvement operator that approximates a policy gradient update, but requires no critic training and no backpropagation. Across continuous-control benchmarks spanning dense locomotion, sparse navigation, and contact-rich manipulation, BFM-QD consistently outperforms parameter-space baselines, with particularly stark gains in sparse and deceptive settings, where all existing QD methods collapse to near-zero performance. These results show the effectiveness of the BFM-QD framework, benefiting from the synergy between dimensionality reduction of the search space and offline pretraining from diverse behavioral data. This positions BFMs as a general-purpose backbone for QD optimization, extending their utility beyond zero-shot task solving to the discovery of diverse behavioral repertoires.

Reward-robust RL typically models misspecification by specifying an uncertainty set that constrains the discrepancy of plausible rewards from a base reward. However, such reward space discrepancies can be behaviorally irrelevant: under potential-based reward shaping (PBRS), many distinct rewards preserve policy ordering. This can introduce substantial redundancy into standard uncertainty sets and degrade optimization performance. We propose **Shaping-Aware Reward-Robust RL**, which constructs uncertainty sets over PBRS equivalence classes by projecting each reward to a canonical representative, ensuring that the resulting set contains only rewards that induce behaviorally distinct policy rankings. We prove that this projection preserves the optimal robust value while shrinking the uncertainty set and improving empirical performance. Using the connection between robustness and regularization, we obtain a practical algorithm to solve the shaping-aware reward-robust RL problem and enjoy convergence guarantees under standard assumptions. Experiments on benchmarks spanning diverse task domains and levels of complexity show consistent improvements over representative robust RL baselines and exhibit improved robustness to reward perturbations.

Imitation Learning (IL) is a natural framework for learning in sequential decision-making systems and has emerged as the dominant paradigm through which we understand language model training. A central puzzle is that, while in theory offline IL can be horizon-free and optimal, in practice online methods such as on-policy distillation (OPD) often outperform offline methods such as supervised fine-tuning (SFT). We propose a noisy expert model to explain this gap, in which the learner only has access to a noisy version of the expert's policy, but wishes to compete against the reward achieved by a clean expert, motivated by the fact that in many applications, e.g. training language models to perform long chains of thought, the expert is often imperfect. In this setting, we show a sharp separation between offline and online IL. Offline learning from noisy trajectories is fundamentally hard: to compete with the clean expert, the sample complexity must grow exponentially, in contradistinction to the clean expert setting where no explicit horizon dependence exists. In contrast, we prove that online interaction with the noisy expert via a novel variant of OPD enables horizon-free guarantees in some settings and polynomial dependence on horizon in general. Our analysis leads to an alternative loss function form that is commonly considered empirically for LM training. We further provide algorithms and lower bounds, and extend our results to the more realistic setting of unknown corruption when the clean expert is deterministic, thereby providing a theoretical foundation for why on-policy distillation can outperform standard supervised fine-tuning when training language models from imperfect teachers. We complement our theoretical results with experiments on synthetic and natural-language tasks, showing that the OPD variant suggested by our theory outperforms both offline BC and existing OPD objectives under noisy expert feedback.

We trace factual sycophancy across three post-training pipelines (OLMo 3 7B Think and Instruct, Llama 3.1 8B Instruct, Tulu 3) on AMPS and MedQuAD with a dual-track evaluation: a GPT-4o-judged generative track and a log-probability track reporting $\Delta$LogOdds separately under \emph{in-context} rebuttals and \emph{preemptive} wrong-answer assertions. Decomposing by challenge type $\times$ context reveals three patterns. (1) \textbf{Challenge type:} the sycophantic shift is alternative-conditioned, so simple pushback with no asserted answer produces no shift, while ethos/justification/citation challenges produce substantial positive shifts. (2) \textbf{Context:} every base model's sycophantic shift concentrates preemptively, with weak or defensive in-context response. On computational, IC diverges into four pipeline-specific endpoints. On medical, the same four pipelines converge with no defensive IC developing on any recipe. (3) \textbf{Behavioral vs log-probability:} post-training produces a \emph{surface-predictive dissociation}: matched-subset behavioral flip rate drops significantly on identical items while preemptive $\Delta$LogOdds on those same items grows.

Reward models are central to aligning language models with human preferences via reinforcement learning (RL). As RL is increasingly applied to settings such as verifiable rewards and multi-objective alignment, RMs are expected to encode more complex and multifaceted preference distributions. However, classifier RMs remain static once trained, limiting their adaptability at test time. We propose Variational In-Context Reward Modeling (ICRM), a novel Bayesian reward modeling objective that enables test-time steerability via in-context preference demonstrations. ICRM casts reward modeling as amortized variational inference over a latent preference probability under the Bradley-Terry model using a conjugate Beta prior. We show that ICRM adapts to unseen preference distributions at test time for both single and multi-objective settings. With more demonstrations, ICRM improves RM-Bench accuracy from 60.5 to 70.8, achieves lower calibration error than a generative judge on moral dilemma preferences, and expands the attainable Pareto frontier under conflicting preferences. We further study the practical applicability of ICRM for RL training, showing that it can effectively encode verifiable rewards by outperforming a conventional RM in math reasoning. Finally, we provide theoretical guarantees that the variational objective admits a global interior optimum with finite confidence, and we analyze how KL regularization mitigates reward over-optimization.

Image captioning is one of the most fundamental tasks in computer vision. Owing to its open-ended nature, it has received significant attention in the era of multimodal large language models (MLLMs). In pursuit of ever more detailed and accurate captions, recent work has increasingly turned to reinforcement learning (RL). However, existing captioning-RL methods and evaluation metrics often emphasize a narrow notion of caption quality, inducing trade-offs across core dimensions of captioning. For example, utility-oriented objectives can encourage noisy, hallucinated, or overlong captions that improve downstream question answering while harming fluency, whereas arena-style objectives can favor fluent but generic descriptions with limited usefulness. To address this, we propose a more balanced RL framework that jointly optimizes utility-aware correctness, reference coverage, and linguistic quality. In order to effectively optimize the resulting continuous multi-objective reward formulation, we apply GDPO-style reward-decoupled normalization to continuous-valued captioning rewards and show that it improves performance over vanilla GRPO. Additionally, we introduce length-conditional reward masking, yielding a more suitable length penalty for captioning. Across LLaVA-1.5-7B and Qwen2.5-VL 3B and 7B base models, our method consistently improves caption quality, with peak gains of +13.6 DCScore, +9.0 CaptionQA, and +29.0 CapArena across different models.

Aligning language models for both helpfulness and safety typically requires complex pipelines---separate reward and cost models, online reinforcement learning, and primal-dual updates. Recent direct preference optimization approaches simplify training but incorporate safety through ad-hoc modifications such as multi-stage procedures or heuristic margin terms, lacking a principled derivation. We show that the likelihood ratio of the optimal safe policy admits a closed-form decomposition that reduces safety alignment to a density ratio matching problem. Minimizing Bregman divergences between the data and model ratios yields **Bregman Safety Optimization (BSO)**, a family of single-stage loss functions, each induced by a convex generator, that provably recover the optimal safe policy. BSO is both general and simple: it requires no auxiliary models, introduces only one hyperparameter beyond standard preference optimization, and recovers existing safety-aware methods as special cases. Experiments across safety alignment benchmarks show that BSO consistently improves the safety--helpfulness trade-off.

Modern data-centric applications increasingly require language agents capable of operating over live, stateful database environments, where successful problem resolution depends not merely on initial SQL generation, but on reasoning about evolving database states, interacting with execution feedback, and repairing state-mutating operations. While agentic reinforcement learning (RL) has emerged as a promising paradigm for training small language models (SLMs), existing frameworks are predominantly tool-centric and struggle with data-centric environments. Specifically, applying tool-centric frameworks to stateful tasks like SQL debugging introduces severe spatial inefficiencies since proper environment isolation typically requires a separate database container per rollout. Naively reusing databases without tracking evolving states across multi-turn interactions causes trajectory contamination and cross-trajectory interference, which severely destabilizes policy updates. To overcome these bottlenecks, we introduce **BIRD-RL**, a novel four-stage agentic RL curriculum that alternately enhances foundational agent reasoning and trajectory-adaptive on-policy exploration to circumvent the instability inherently associated with direct end-to-end learning. Crucially, to support this curriculum, BIRD-RL is driven by a **Trajectory-scoped Persistent Execution Infrastructure**, which enables safe database replica reuse while preserving trajectory isolation. This design improves spatial RL efficiency by **12.8x**, successfully enabling scalable agentic RL for complex data-centric tasks without needs of Kubernettes. Empirical evaluations on the BIRD-CRITIC-SQLite benchmark demonstrate that our 7B and 14B models achieve Success Rates of **44.40%** and **48.00%**, respectively, performing on par with or exceeding strong proprietary model-based agents such as Claude-Opus-4.6 Agent (48.20%). Furthermore, BIRD-RL successfully trains unified SLMs capable of both advanced SQL debugging and generation, highlighting its broader potential for multi-objective optimization across heterogeneous, real-world data-centric tasks.

Constrained preference-conditioned MORL typically assumes full task observability, treating preferences and safety budgets as stationary task signals. In real-world deployment, however, these signals are often unreliable proxies: intent may drift, safety tolerances may shift with context, and exposed descriptors may be noisy, delayed, or incomplete. We therefore formulate constrained preference-conditioned MORL as a partially observed task-specification problem, where the agent must navigate a fundamental conflict between unreliable external signals and latent interaction dynamics. We propose \textbf{BECON}, a belief-conditioned framework for constrained MORL with drifting preferences and budgets, which infers latent task context from recent histories to estimate preferences and safety budgets. These estimates are fused with the exposed task signal via uncertainty-dependent gates, enabling the policy to defer to observations under high epistemic uncertainty while correcting them when history is informative. The fused context jointly conditions preference optimization and context-adaptive constraint enforcement. Experiments on diverse multi-objective control tasks demonstrate that BECON consistently improves over state-of-the-art MORL baselines, achieving stronger robustness and constraint satisfaction under task drift.

Recent research-level physics-reasoning benchmarks for LLMs reveal a failure mode that lies not in knowledge or execution, but in modeling the world being reasoned about. When faced with unseen problem setups, models often silently alter given quantities, fabricate laws, or inject unstated assumptions to force the problem into familiar patterns, and subsequent reasoning then proceeds within this corrupted world. We define this premise-level divergence as modeling drift: the gap between a model's internal axiomatic world model (AWM) and the true physical world specified in the problem. Although RLVR and PRM have yielded substantial gains in mathematics and code, their reward shapes do not directly supervise world modeling in axiomatic domains such as physics. We propose Reinforcement Learning with Axiomatic World Modeling (RLAWM), which optimizes the policy by penalizing divergence between its inferred axiomatic world model and the true physics world. RLAWM probes physics reasoning at two hierarchical levels (modeling and solving), each scored by a physically grounded reward. The modeling reward targets abstract knowledge formulation, evaluating whether the model captures the true axiomatic world before attempting calculation. The solving reward targets instantiated knowledge reasoning, checking whether the model's concrete derivation remains consistent with the axiomatic world. This two-level structure separates what world the model believes it is reasoning in from how it reasons within that world. The framework operates exclusively during training, with no extra cost during inference. RLAWM improves performance by up to $+10.8$ points on PhysReason and $+5.2$ on PHYSICS over the baseline. RLAWM also exhibits strong zero-shot generalization, yielding a $2.45{\times}$ gain over the strongest baseline on unseen physics problems.

Open multi-agent systems, where only a subset of agents are controllable, are central to real-world domains such as smart grids, yet lack a principled foundation for reinforcement learning algorithm design. We study this setting through n-agent ad hoc teamwork (NAHT), a recent framework for learning in open multi-agent environments. We propose an axiomatic framework that derives value function learning from the Shapley axioms (Efficiency, Symmetry and Linearity), treating them as structural constraints rather than heuristic design choices. This formulation builds on a novel NAHT decomposition, which characterises the fundamental difference between open and fully controllable multi-agent systems, and establishes a cooperative game-theoretic foundation for learning. We further show that enforcing these axioms on learning individual value functions recovers the Shapley value for Dec-POMDPs, providing a principled bridge between reinforcement learning and classical cooperative game theory. Building on this framework, we introduce Shapley Machines and Banzhaf Machines, two generic algorithmic templates that can be instantiated with standard reinforcement learning methods. When applied to strong baselines such as IPPO and POAM, our methods consistently improve learning efficiency and generalisation to unseen agent types and conventions across NAHT benchmark tasks.

We study policy optimization for infinite-horizon, discounted constrained Markov decision processes (CMDPs). While existing theoretical guarantees typically hold for the mixture policy, deploying such a policy is computationally and memory intensive. This leads to a practical mismatch where a single (last-iterate) policy must be deployed. Recent theoretical works have thus focused on proving last-iterate convergence, but are largely limited to the tabular setting or to algorithmic variants that are rarely used in practice. To address this, we use the classic inexact augmented Lagrangian ($\texttt{AL}$) method from constrained optimization, and propose a general framework with provable last-iterate convergence for CMDPs. We first focus on the tabular setting and propose to solve the $\texttt{AL}$ sub-problem with projected Q-ascent ($\texttt{PQA}$). Combining the theoretical guarantees of $\texttt{PQA}$ and the standard $\texttt{AL}$ analysis enables us to establish global last-iterate convergence. We generalize these results to handle log-linear policies, and demonstrate that an efficient, projected variant of $\texttt{PQA}$ can achieve last-iterate convergence with comparable guarantees as prior work. Finally, we demonstrate that our framework scales to complex non-linear policies, and evaluate it on continuous control tasks.

Neuro-symbolic systems typically couple a neural perception module with a discrete symbolic solver, where exact constraint inference is intractable at training time and a discrete solver must be invoked at inference time, precluding end-to-end optimization of the model. We introduce AS2 (Attention-Based Soft Answer Sets), a fully differentiable neuro-symbolic architecture that replaces the discrete solver with a continuous approximation of the Answer Set Programming (ASP)immediate-consequence operator $T_P$. AS2 maintains per-position probability distributions over a finite symbol domain throughout the forward pass and trains end-to-end by minimizing the fixed-point residual of a probabilistic lift of $T_P$, thereby differentiating through the constraint check without invoking an external solver during either training or inference. On spatial constraint-satisfaction tasks, AS2 replaces conventional positional embeddings entirely, and problem structure is encoded through constraint-group membership embeddings derived directly from the declarative ASP specification, making the model agnostic to arbitrary position indexing. On Visual Sudoku, AS2 achieves 99.89\% cell accuracy and 100\%constraint satisfaction, without invoking any external solver. On CLEVR-Hans, AS2 achieves 99.94% on CLEVR-Hans3 and 87.77% on CLEVR-Hans7. These results demonstrate that a soft differentiable fixpoint operator, combined with constraint-aware attention and declarative constraint specification, can match or exceed pipeline and solver-based neuro-symbolic systems while maintaining full end-to-end differentiability.

Reinforcement learning (RL) is increasingly used to improve the reasoning, coding, and tool-use capabilities of large language models, but agentic RL remains prohibitively expensive. Scaling RL to agentic LLMs requires supporting complex workloads, including multi-policy collaborative training, while efficiently using elastic, heterogeneous, and cross-region compute resources. Existing LLM RL systems support some of these capabilities, but each new extension often requires dedicated system engineering. This burden arises from trainer-centered control architectures and the lack of principled abstractions for RL system components. To address these limitations, we propose AstraFlow, a dataflow-oriented RL system that replaces conventional trainer-centered control with principled component abstractions. In AstraFlow, rollout services, dataflow management, and training are decoupled into autonomous components, enabling the system to natively support complex multi-policy agentic RL workloads and efficiently exploit diverse compute resources. We evaluate AstraFlow across math, code, search, and AgentBench workloads, showing that the same system supports multi-policy training, elastic scaling, heterogeneous cross-region execution, and composable data algorithms without system-level code changes. In multi-policy collaborative training, AstraFlow achieves comparable or better accuracy than existing RL systems while speeding up training time by 2.7x.

We propose a new framework for low-precision neural networks based on angular geometry and randomized low-bit estimators. Rather than approximating Euclidean linear operations under limited precision, we reinterpret neural computation in terms of directional similarity and construct quantized random-feature estimators of cosine interactions. Our approach introduces \textit{Angular Layers}, which replace standard linear transformations with low-bit projections that estimate angular similarity in the forward pass, while gradients are computed with respect to the underlying continuous cosine geometry. This decoupling enables stable optimization without straight-through estimators or heuristic surrogate gradients, even under aggressive quantization of both weights and activations. On the theory side, we introduce \emph{G-Gradient} as a gradient proxy for angular layers and show that, in a one-layer planted model, a sufficiently small \emph{G}-gradient can guarantee exact recovery of a target binary solution. We further prove uniform approximation and convergence guarantees that provide a rigorous path from tractable continuous optimization to exact recovery in the original discrete model. Empirically, we instantiate these ideas in \textit{Angular Nets}, including low-precision variants of ResNet, Vision Transformers, and BERT-style encoders, and obtain strong performance across vision and language tasks at substantially reduced precision. Overall, our results suggest that preserving angular structure provides a principled foundation for low-bit deep learning. Our full implementation is available at: \url{https://github.com/GGM2026/GGM}.

Modern foundation models are trained through multistage pipelines, typically beginning with unsupervised pretraining, followed by supervised fine-tuning (SFT) on step-by-step solutions, and reinforcement learning (RL) with bulk feedback. Empirically, the design of these stages, particularly the compute allocated to each, strongly affects performance. Yet our theoretical understanding of multistage training remains limited. Here, we introduce a simple, analytically tractable model of multistage training. The model reproduces several qualitative phenomena: SFT and RL can be complementary, pretraining quality imposes a performance ceiling with power-law scaling, optimal compute allocation varies with data quality and pretraining level, and RL can selectively amplify task-relevant pretrained skills. Our model distills the complex behaviors into key ingredients, allowing clearer understanding of how and where they arise. Overall, our model provides a theoretical starting point for explaining the phenomenology of multistage training pipelines in the compute-limited regime.

In structurally constrained molecular optimization, state-of-the-art methods restart an expensive oracle-driven search from scratch for every new input structure, scaling poorly to settings with many starting structures or expensive oracles. While amortized approaches that learn a transferable policy could in principle remove this bottleneck, existing methods struggle to generalize to diverse structural constraints at inference time. We present AMORTIX, an amortized Graph Transformer model that natively supports such constraints, optimizing molecular structures in a single forward pass with zero inference-time oracle calls. A central challenge for amortized training in this domain is that optimization difficulty varies drastically across starting structures. We show that, under this heterogeneity, standard reinforcement learning methods fail to stabilize training, and address this by normalizing rewards within groups of completions sharing the same starting structure. We evaluate on structurally constrained single- and multi-target kinase inhibitor design, and on a few-shot prodrug case study. AMORTIX outperforms both amortized and instance-optimization baselines on goal-directed scaffold decoration and ranks first among amortized methods on the PMO benchmark; the prodrug case study further demonstrates transfer of a learned modification rule to unseen drug structures.

Formulaic alpha discovery is a core challenge in quantitative trading, as identifying alphas that work well together remains difficult. Recent reinforcement learning (RL) methods formulate this task as a Markov decision process (MDP), but two important issues remain unresolved. First, as the alpha pool evolves, the reward function changes accordingly, making the MDP inherently non-stationary. Second, most existing methods optimize a single objective, typically predictive power, while ignoring other important properties of a high-quality alpha pool. Motivated by these challenges, we propose AlphaPareto, an RL method for formulaic alpha discovery. To address non-stationarity, AlphaPareto augments the state to include both the alpha under construction and the current alpha pool, and applies a large language model (LLM) to encode the pool. This design allows the agent to adapt to the evolving search environment. To overcome the limitation of single-objective reward design, AlphaPareto replaces the scalar reward with a multi-objective vector-valued reward that simultaneously captures predictive power, temporal stability, perturbation robustness, and diversity, and optimizes these objectives through a Pareto-regularized learning procedure. Empirical applications to real-world datasets show that our AlphaPareto method outperforms its competitors.