Robust PAC Learning of Concurrent Stochastic Games

We introduce the first Probably Approximately Correct (PAC) learning framework for general-sum concurrent stochastic games (CSGs) with transition uncertainty, while addressing the challenge of Nash equilibrium (NE) existence. Our algorithm maintains data-driven $L^1$ confidence sets over transition kernels and solves a robust CSG to compute a social-welfare optimal $\varepsilon$-NE, using a robust MDP-based exploration mechanism to drive joint state-action coverage. Crucially, we introduce a Nash margin characterisation that enables principled reasoning about equilibrium existence: the framework either returns an $\varepsilon$-approximate NE whose social-welfare value is $\varepsilon$-close to optimal, or provides a sound certificate that no exact NE exists. Under a minimum reachability condition $p_{\mathrm{reach}}>0$ over relevant state-action pairs, the algorithm terminates after a polynomial number of trajectory samples, with sample complexity $\widetilde{O}\left( {R_{\max}^2 H^4 |S|^2 |A| / (p_{\mathrm{reach}} \varepsilon^2)} \right)$. Empirical results on benchmark CSGs demonstrate near-optimal performance, correct handling of equilibrium (non-)existence, and sample complexity consistent with theory.

Sequential Beats Joint: On the Interplay between On-Policy Distillation and RLVR

Reinforcement learning with verifiable rewards (RLVR) and on-policy distillation (OPD) have emerged as two dominant methods for post-training reasoning LLMs. Prior work uses OPD's dense token-level supervision to complement the sparse RL reward, fusing the two signals within a single step: either as a \emph{weighted-additive combination} or a \emph{teacher-modulated rescaling} of the RL advantage. In this paper, we show that a simple two-stage scheme, OPD-then-RL, consistently outperforms pure OPD, pure RLVR, and all such joint baselines across logic and math reasoning benchmarks. Beyond the empirical results, we further provide a systematic understanding of this through pass@$k$ behavior, learning dynamics, and parameter updates, yielding a consistent explanation: OPD expands the student's coverage of teacher-supported solutions and RL sharpens within that support, while jointly optimizing the two signals causes them to interfere.To provide a practical recipe, we find that the OPD validation score is the key signal for when to switch to RL, and that OPD is a better cold start for RL than SFT. Together, our results establish OPD-then-RL as a simple yet strong way to combine the two methods, turning two entangled signals into complementary stages.

Subspace Inference Enables Efficient Active Reward Learning from Preferences

Reinforcement learning from human feedback (RLHF) has emerged as a powerful yet sample-inefficient approach for learning reward models from human preferences, making active learning a critical component in synthesizing informative preference queries. However, effective uncertainty quantification required for active learning remains a key challenge for large neural network reward models. In this paper, we introduce PreferenceEKF, a sample-efficient approach that tracks reward model uncertainty by framing active preference learning as a sequential Bayesian filtering problem. Instead of relying on computationally prohibitive posterior inference over the full neural network parameter space, our method performs sequential inference via an extended Kalman filter within a low-dimensional parameter subspace, continuously updating the reward model posterior as new preference queries arrive. Our approach enables scalable sampling of neural network parameters to efficiently compute acquisition functions for active reward learning. Experiments on the D4RL and V-D4RL benchmarks demonstrate that our approach achieves better sample efficiency, runtime, scalability, and calibration compared to other Bayesian deep learning approaches, and the learned reward models lead to competitive offline reinforcement learning policy performance. This highlights the potential of scalable Bayesian methods for preference-based reward modeling in RLHF. Our code is available at https://github.com/yutaizhou/bnn_pref.

Spurious Advantage Hidden in GRPO

Group Relative Policy Optimization (GRPO) is widely studied for reinforcement learning with verifiable rewards, where its advantage estimator assigns each rollout a magnitude from within-group reward statistics. In the common case, this magnitude rewards rollouts that reach the correct answer through reasoning. Yet, an overlooked case shares the same surface: a rollout may land on it by guessing, and the formula still assigns a high magnitude, which we identify as the spurious advantage. This arises in three cases: bounded-answer tasks with a small candidate set; open-answer sets hosting bounded sub-cases; and search agents whose budget opens many paths to the same answer. In all three, this misleads the policy toward guess-like behaviors. We propose SIGNBALANCE, whose magnitude is composition-free: it keeps the verifier sign, uses a global scale, and restores zero-mean balance via a stop-gradient per-class rescaling. Across math and search agent benchmarks at different scales, SIGNBALANCE matches GRPO on open-answer math and improves on bounded-answer math and search agents. Code will be released.

The Dually Flat Geometry of Planning as Inference

We present an alternative characterization of the occupancy measure of reinforcement learning, obtained by embedding the planning criterion into the dynamics through a resetting planning process. Its stationary measure, which we term visitation measure, is the object on which the information geometry of decision making is most naturally expressed. The achievable visitation measures form a dually flat statistical manifold whose two affine charts are the visitation probabilities and the log-policies, dual under the conditional entropy. This structure makes planning-as-inference generalize from linear rewards to nonlinear functionals of the visitation, each iterate solved by one natural-gradient step, and gives the temporal-difference error the interpretation of a marginal-utility estimate. We develop the geometry and its consequences for reinforcement learning and theoretical neuroscience.

Headroom-Drift Replay: A Primitive for Principled Replay Control in GRPO

RL-based post-training for reasoning models is increasingly bottlenecked by repeated fresh rollout generation, particularly in agentic settings where environment interaction dominates wall-clock cost. Replay can reduce this burden by reusing past trajectories, but existing methods typically embed it within larger training pipelines involving exploration, experience restructuring, or mixed-policy optimization. This makes replay's own contribution difficult to isolate. We ask a focused question: how far can principled replay selection alone go? We introduce Headroom-Drift Replay, a group-level replay control primitive for GRPO that separates reuse into two decisions. Headroom ranks stored groups by remaining learning value, while Drift gates them by compatibility with the current policy. The fresh on-policy stream remains unchanged, and the method adds no auxiliary generation or training machinery. Across mathematical reasoning, multimodal reasoning, and Agentic Search benchmarks, this single intervention outperforms naive replay and matches or exceeds broader replay methods on Avg Mean@32. In Agentic Search, where environment interaction dominates cost, it delivers comparable quality at materially lower wall-clock time.

Multi-step Proximal Policy Improvement in Offline Reinforcement Learning

Offline reinforcement learning (RL) must reconcile two competing requirements: policy updates should stay near dataset-supported actions to keep value estimates reliable, yet meaningful gains often require moving beyond the behavior distribution. We develop a geometric view of offline actor updates by modeling policies as a probability manifold endowed with a chosen metric geometry. Under this lens, a broad class of offline actor objectives can be interpreted as a single proximal policy improvement step (SPI), i.e., an implicit discretization of a manifold gradient flow induced by a critic-defined energy. Building on this insight, we propose multi-step proximal policy improvement (MPI), a plug-in refinement mechanism that composes sequential re-centered proximal steps. MPI enables controlled policy improvement beyond dataset support while retaining proximal control at each refinement. The framework accommodates multiple policy geometries and admits practical instantiations for deterministic and diagonal-Gaussian policies. Experiments on D4RL benchmarks show that small numbers of MPI refinements improve strong offline baselines, including TD3+BC, ReBRAC, and IQL, on many tasks. Focused diagnostics further distinguish re-centered refinement from fixed-objective update scheduling and characterize limitations under critic error.

Out-of-Distribution Generalisation with Sequence Models in Offline Multi-Agent Reinforcement Learning

Generalising to unseen tasks remains a fundamental challenge in offline multi-agent reinforcement learning (MARL). In this work, we present a principled analysis of zero-shot task generalisation in the offline setting and conduct an extensive empirical investigation into the scaling behaviour governing task diversity, dataset size, and network capacity. To facilitate this study, we extend offline sequence modelling architectures to handle multi-task observation and action spaces alongside variable agent counts across tasks. Our primary finding is that scaling task diversity---rather than sheer dataset size is the dominant factor in achieving robust zero-shot transfer. Through large-scale experiments across four challenging environments (Connector, RWARE, SMAX, and LBF), we demonstrate that our multi-task approach achieves a mean improvement of 3.2x on held-out test tasks compared to single-task models and consistently outperforms strong behaviour cloning baselines. These results suggest that the development of generalisable MARL agents should prioritise the diversity of the training distribution with varying numbers of agents, providing a roadmap for scaling offline MARL effectively.

Local Updates, Global Learning (LUGL): Playing Games with non-incremental Learners

The dominance of Neural Networks (NNs) in RL is partially due to their incremental learning capability, which naturally suits the online, non-stationary nature of self-play training. However, gradient-boosted trees like LightGBM are widely recognised as the state of the art for tabular data in supervised learning, often outperforming NNs in accuracy and efficiency. Game states are inherently tabular---discrete actions, categorical card identities, structured board positions---which makes them an ideal candidate for tree-based methods. We introduce LUGL (Local Updates, Global Learning), a framework that decouples data collection from model fitting, enabling non-incremental learners such as GBTs to operate in RL settings where they would otherwise fail due to distributional shift. LUGL alternates between a local updates phase, where the agent plays self-play games and accumulates tabular updates (Q-values, V-values, policies, or regret values) in a finite table, and a global learning phase, where the table is used to train a function approximator that generalises to unseen states before the table is reset. We test our approach in four standard perfect-information games (Tic-tac-toe, Connect-4, Othello, and Hex) and five imperfect-information games (Kuhn's poker, Leduc Hold'em, Liar's Dice, Goofspiel, and Flop5 Hold'em), and show that our results are competitive with or superior to DQN and DeepCFR. Our experiments demonstrate that the community's strong bias towards NNs in game-playing may be unwarranted, since LightGBM-based agents achieve competitive or superior performance across all tested benchmarks.

From Prior-Guided Heuristics to Deployable Agents: Accelerating Demonstration-Driven Reinforcement Learning for Deadline-Constrained Network Control

Timely delivery of delay-sensitive information over dynamic, heterogeneous networks is essential for NextG interactive applications, yet providing strict End-to-End (E2E) peak latency guarantees remains an open challenge. Two obstacles limit the adoption of learning-based network control in this setting: traditional volume-based routing metrics, while highly effective for general traffic management, are not designed to capture traffic urgency; and Deep Reinforcement Learning (DRL) controllers trained from scratch suffer from sample inefficiency, long training times, and early-stage exploration volatility. This paper introduces a deployment-focused network control framework that addresses both obstacles. First, we present Effective Congestion (EC), a deadline-aware metric family that quantifies interface congestion by packet urgency and proactively filters non-viable traffic, coupled with a Uniform Path Grouping (UPG) distribution heuristic promoting robust load-balancing; the resulting policies are embedded into Multi-Agent Deep Reinforcement Learning Effective Congestion ($p^*$) (MADRL EC ($p^*$)), a hybrid architecture combining a distributed scheduler with a centralized RL-based router. Second, we introduce a unified training objective that generalizes existing policy-learning paradigms---behavioral cloning, offline Reinforcement Learning (RL), online RL, and offline-to-online schemes---as special cases, combining a live-reward term, a pre-collected-reward term, and a policy-imitation term. From this objective, we derive the Model-Guided Annealed Reinforcement Learning (MGA-RL) protocol, instantiated on a Deep Deterministic Policy Gradient (DDPG) backbone: a deployment-oriented, demonstration-driven training approach that generalizes conventional Offline-to-Online (O2O) schemes, in which trajectories from a lightweight [...]

Gradients Know What Outcomes Don't: Unlocking Reinforcement Learning for LLM Reasoning with Gradient-Aligned Rewards

Reinforcement learning from verifiable rewards (RLVR) drives chain-of-thought reasoning in large language models, yet its binary outcome reward cannot distinguish among correct trajectories. Existing dense reward alternatives, from surface heuristics to process reward models, either ignore the expert solutions already present in training corpora or require expensive offline annotation. We propose Gradient-Aligned Reward (GAR), which operates in the policy's own gradient space: truncated backpropagation through the output projection layer extracts a compact gradient vector for each rollout, and cosine similarity with an expert-anchor gradient yields a dense, reasoning-aware reward with less than 9% wall-clock overhead. We prove that this cosine admits a multiplicative decomposition into prediction-error and activation-pattern factors, providing a concrete characterization of what the alignment signal measures. On Qwen3-4B and Qwen3-8B, GAR consistently improves over GRPO and other baselines on competition-level math benchmarks and transfers to GPQA Diamond and MMLU-Pro without domain-specific data. Code and data are available at https://github.com/LQgdwind/GAR.

DE-Venus: A Data-Efficient RLVR Framework for Large Language Models

Reinforcement learning with verifiable rewards (RLVR) improves large language model reasoning, but its practical scaling is constrained by expensive on-policy rollouts and the cost of obtaining reliable targets at scale. Existing methods address sample selection, incomplete supervision, or noisy labels separately, often entangling supervision logic with distributed training and hindering controlled comparison and reuse. We present DE-Venus, a unified framework for data-efficient RLVR that treats supervision as evolving state across data preparation and policy optimization. It organizes this lifecycle into three modules: Active Data Selection allocates training and annotation budgets; Weak Supervision Construction derives learning signals from unlabeled examples; and Training-Time Supervision Refinement filters or corrects unreliable supervision. DE-Venus supports seven representative methods and a data-selection pipeline by expressing method-specific decisions as offline dataset transitions or online transformations of targets, rewards, batches, and advantages while preserving verl's distributed execution contracts. Across public benchmarks and three business scenarios, separate configurations preserve or improve model quality with only 10% of labels or as little as 13% of relevant data; selected business configurations also reduce observed convergence steps by 63%--75%. DE-Venus thus reduces annotation and training costs without sacrificing scalable RL execution.

FlowBalance: Verifier-Grounded Self-Improvement from On-Policy Reasoning Experience

A reasoning model can improve from its own on-policy experience, but this inner loop is fragile: terminal verifiers provide reliable yet sparse supervision, while dense same-model guidance can reinforce false confidence or overconcentrate learning on a narrow solution mode. We introduce FlowBalance, a verifier-grounded self-improvement method that learns a normalized distribution over complete responses. For each on-policy trajectory, a frozen training-time view of the same policy uses privileged context to produce token-level log-probability gains, which are aggregated into a trajectory-level self-guidance score. FlowBalance calibrates this score with the verifier-derived group advantage: guidance is retained on positive-advantage trajectories, reversed on negative-advantage trajectories, and disabled when the rollout group provides no outcome preference. The resulting energy exponentially reweights a reference policy, and profiled trajectory balance fits the normalized target with one log-partition estimate per rollout group. This realizes outcome-calibrated self-guidance via trajectory balance, without a separate token-level imitation loss. Our analysis establishes within-group contrast preservation, a minimum-change reverse-KL characterization, monotonic verifier control of target reward, and an exact correction against false-positive self-guidance on rejected responses. On mathematical reasoning, FlowBalance improves average performance over FlowRL on both Qwen3-4B and Qwen3-8B, while also improving training speed and stability, avoiding direct OPSD's response-length collapse, and exhibiting higher correct-strategy diversity in a controlled AIME24 diagnostic.

Cliff: Learning Process Rewards from the First Mistake

Reinforcement learning with verifiable rewards (RLVR) has emerged as a powerful paradigm for large language model (LLM) post-training, but its reliance on coarse outcome rewards leads to limited guidance on intermediate reasoning processes. Existing approaches such as process reward modeling and on-policy distillation introduce additional constraints, such as reliance on a specialized reward model or assuming identical reasoning patterns between teacher and student. Nevertheless, we observe that once a reasoning process first goes wrong, evaluating the subsequent reasoning provides limited additional information, as it is already conditioned on an invalid prefix. Therefore, we propose Cliff, a reward shaping strategy that utilizes an off-the-shelf LLM as a teacher to identify the first mistake in each rollout. As a result, the rollout is naturally decomposed into two parts: a correct prefix and an incorrect suffix. Cliff then converts this signal into token-level advantages, assigning positive advantages for the correct prefix and negative feedback afterward. Experiments across 12 different scenarios demonstrate that Cliff consistently improves reasoning performance, outperforming on-policy distillation by 15% and standard GRPO by 7%, even with teachers of modest capability. Furthermore, we analyse the role of ``ground truth'' in Cliff and investigate its training dynamics. These results establish Cliff as a simple, general and effective approach for improving RLVR with richer, fine-grained supervision.

Tail-Likelihood Reinforcement Learning

Reinforcement learning typically optimizes average reward. For generative policies, the average can hide an important distinction: two policies can achieve the same mean reward while having very different chances of producing a rare but high-reward rollout. This matters as sampling increases during training and inference, since its benefit depends on retaining probability mass on high-reward outcomes. We propose to optimize this coverage directly. Rather than considering only expected reward, we consider all of its upper tails: for each reward threshold, how likely is the policy to exceed it? This turns a continuous reward into a family of binary success events. We introduce Tail-Likelihood Reinforcement Learning (TailRL), which maximizes the log-probability of exceeding a randomly chosen reward threshold. Its gradient gives more weight to rare, high-reward rollouts and can be interpreted as a mixture of Best-of-(k) gradients. TailRL requires only a simple modification to the advantage function, making it compatible with existing reinforcement learning pipelines. Across object localization, maze navigation, GUI grounding, and code optimization, TailRL leverages rare high-reward training samples to avoid suboptimal solutions and yields models that benefit more from additional samples at inference time.

Coverage, Not Targeting: A Structural Regime in Multi-Turn Agent Credit Assignment

Multi-turn agentic RL increasingly treats credit assignment as a targeting problem: given a terminal verifiable reward, per-turn methods localize credit onto the turns that mattered. We identify the structural quantity that predicts when this is the right move, the verifier information density V_d = k/C (the fraction of an agent's C-step causal chain whose per-turn correctness the verifier exposes), and show that terminal-state verifiers sit deep in a low-V_d regime where targeting is the wrong axis. In controlled shared-rollout comparisons on tau^2-bench that separate reward density from credit geometry, a continuous dense reward spread uniformly beats the sparse binary outcome reward (net-harmful on 4/5 seeds), while concentrating the same advantage on progress turns or on random turns is equally harmful: targeting is second-order. The mechanism is coverage: terminal-state verification collapses the observable signal to a single final-write turn (k=1 in 98% of rollouts) while success requires a 5-8 step chain of prerequisite tool calls. A synthetic phase boundary places the crossover at V_d* ~ 0.8, whereas measured V_d is ~0.15 on tau^2-bench and ~0.4 on BFCL V3; uniform also wins on BFCL, where a matched-concentration shuffled control is negative on 8/8 seeds. The effect reproduces across model families on ToolACE-2-8B (Delta = -0.048 over 32 pre-registered seeds; an independent 20-seed replication is itself significant), and a pre-registered matched-budget breadth sweep traces a monotone dose-response whose deficit vanishes only at full chain coverage, with a reward-to-go arm reaching full-coverage parity. Uniform redistribution is the zero-information coverage default that per-turn schemes must beat; we contribute the matched-concentration shuffled control that any targeting claim should clear.

Recursive Value Learning for Long-Horizon Offline Goal-Conditioned RL

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.

PGPO: Potential-Guided Policy Optimization for Multi-Turn Agentic Tasks

Group-based reinforcement learning (RL) has become an effective paradigm for LLM post-training, but in multi-turn agentic tasks with sparse terminal rewards, it often provides coarse credit for intermediate actions. To obtain more fine-grained credit assignment, recent work such as GiGPO introduces step-level advantages for intermediate actions. However, these step-level signals still rely on the final outcome of each individual trajectory. As a result, actions within failed trajectories can remain poorly differentiated, so effective actions can receive the same unfavorable credit as erroneous ones. In this work, we propose Potential-Guided Policy Optimization (PGPO) for multi-turn agentic tasks. PGPO estimates empirical state potentials from anchor-state-group return statistics within each rollout group. It then derives action advantages from potential differences between adjacent states, enabling cross-trajectory credit propagation. This provides finer-grained step-level credit assignment, especially within failed trajectories. Experiments on ALFWorld and WebShop show strong overall performance relative to recent group-based RL methods. Further analysis provides evidence that PGPO yields more informative failure-side credit signals with negligible training overhead.

Posterior Tempering Explains Variance Inflation in Linear and Generalized Linear Thompson Sampling

We study a variant of the Thompson Sampling (TS) algorithm, called $α$-TS, for solving stochastic generalized linear bandit problems. Existing analyses of TS require inflating the posterior variance to derive near-optimal regret guarantees. We formalize the idea of variance inflation by introducing $α$-TS that uses a fractional or $α$-posterior instead of the standard posterior. Our main contribution is to identify general regularity conditions on the prior and reward distributions that enable a regret analysis of $α$-TS without assuming any tractable approximation of the posterior distribution, unlike previous works. For a specific choice of $α\propto d^{-1}$, our general regret bound yields the best known regret bound of $O(d^{3/2}\sqrt{T}\log T)$ for both the exponential and sub-Gaussian families of reward distributions. We further provide an $α$-dependent lower bound showing that the regret constant depends on the product $αd$, and that when $α\propto d^{-1}$ the regret scales as $Ω(d^{3/2}\sqrt{T})$, explaining the origin of the $d^{3/2}$ factor in the upper bound. Our proof technique adapts and combines recent advancements in the analysis of linear bandit problems with first- and second-order posterior concentration theory from the Bayesian statistics literature.

Reinforcement learning to choose optimizers

No single optimization method is uniformly best for all problems, and the most suitable optimizer choice can change during a run. Existing approaches that change optimizer during execution typically predetermine part of the strategy: the portfolio is restricted to one algorithm class, the switch occurs once at a fixed time, or the frequency of decisions is treated as a hyperparameter rather than a learned one. We introduce "Reinforcement Learning to Choose Optimizers", which formulates the optimization algorithm choice as a sequential decision-making problem. At each decision, a recurrent policy reads the current run state and decides both which optimizer should be used next and for how long. The portfolio includes both gradient-based and derivative-free optimizers, and each switch passes on the current best solution and a representative step size. A context proxy conditions a gating network over expert heads, and training employs a decoupled actor-critic whose return is expressed in the same empirical runtime distribution metric used at evaluation. Training tasks and portfolio are designed jointly so that no optimizer dominates. On unseen problems, the learned policy outperforms every portfolio optimizer at all but the smallest budgets, and it remains robust under distribution shift.

Pooling and Drift in Delayed Bandits

A system often has to act long before it learns whether the act worked: a recommender sees a click in seconds and a purchase in days. With $K$ actions and a delay of $d$ rounds, the best rate known for this setting is $\widetilde{O}(\sqrt{(K+d)T})$ over $T$ rounds, so a longer menu is always more expensive to learn from. It need not be: if the outcome depends on the action only through the state it produced, then one late outcome informs every action that could have produced the observed state, and the price is set by how many genuinely different states the actions produce rather than by how many actions there are. We measure this using an effective dimension $v_t$ between $1$ and the number of states, and prove $\widetilde{O}(\sqrt{(d+1)V\log K})$ for a rotating algorithm and $\widetilde{O}(\sqrt{V^{-}}+\sqrt{dT})$ for the single-copy algorithm used in practice, for any budget fixed in advance; merging similar states lowers the price further, at an explicit bias. Even when given the exact losses from $d$ rounds ago, no algorithm escapes $Ω(\sqrt{dE\min\{1+\log J,T/d\}})$, where $J$ counts the drifting directions and $E$ bounds how far losses move while the learner waits. On generated data, the state channel cuts regret by up to 79 percent against action-level weighting and, on the funnel family, by 32 to 68 percent against a tuned minimax-optimal method.

Scaling Near-Optimal SFT-RL Annotation Budget Allocation from Small to Large LLMs

How to divide a fixed annotation budget between supervised fine-tuning (SFT) and reinforcement learning (RL) during LLM post-training remains an open problem. Existing work characterizes only broad trends (e.g., SFT dominates in low-data regimes), lacks a principled allocation framework, and does not examine whether the optimal ratio transfers across model sizes. We frame this problem in terms of near-optimality: rather than seeking a single optimal SFT-RL ratio, we characterize the near-optimal region, the set of allocations within a specified tolerance of peak performance. Empirically, this region is wide even for small tolerances (2-10%), widens with model scale, and transfers reliably from small proxy models to large target models. This yields a practical strategy: small proxy-model experiments suffice to identify a transferable near-optimal region, eliminating the need for exhaustive large-scale search. Our results hold consistently across tasks, model families, and both preference-based off-policy and reward-supervision on-policy RL methods. We further analyze how the asymmetry in annotation costs between SFT and RL data shifts the near-optimal region.

Selective Agent Guidance via Entropy: Learning Autonomous Policies from Imperfect VLM Teachers

Vision-Language Models (VLMs) provide useful priors for interactive decision-making, but using them directly as policies is expensive and brittle: they must be queried at every step, do not improve from environment interaction, and can repeat systematic errors. We study how to learn a cheap autonomous policy from an online, expensive, and imperfect but informative VLM teacher. We propose SAGE (Selective Agent Guidance via Entropy), a framework that queries a VLM only when the learner is uncertain, executes the suggested action during training, and distills guidance into a lightweight Reinforcement Learning (RL) policy. Because VLM advice is not always reliable, SAGE can weight teacher-action distillation using environment-derived advantages rather than treating all suggestions as equally useful. Across sparse-reward visual reasoning and navigation tasks, SAGE learns policies that act without VLM guidance at evaluation time and improves over unguided RL in several environments, including settings where the learned policy exceeds its VLM teacher. The results show that selective guidance is most beneficial when the VLM can help the agent discover high-reward trajectories, and less useful when unguided exploration already succeeds or teacher actions do not lead to informative experience. SAGE also reduces VLM usage by prompting the teacher only on a fraction of training steps and requiring no VLM calls at deployment. Overall, our results suggest that VLMs don't need to be used as fixed policies to be useful; they can instead act as temporary, imperfect sources of guidance whose value is tested and internalized through interaction.

NashDreamer: Model-Based Reinforcement Learning for Zero-Sum Imperfect-Information Games

Model-based reinforcement learning (MBRL) has achieved remarkable results in single-agent domains, yet its extension to competitive imperfect information games (IIGs) remains underexplored. In multi-agent settings, opponent-induced non-stationarity complicates the learning process, and decentralized model learning faces severe identifiability barriers, which we argue make centralized model learning a mathematical necessity. Building on this analysis, we propose NashDreamer, a principled MBRL framework for two-player zero-sum IIGs. It introduces a centralized Multi-Agent Recurrent State-Space Model (MARSSM) that decouples environment dynamics from the effect of players' strategies on their individual observations. NashDreamer is designed to use arbitrary policy gradient algorithms and inherits their convergence guarantees towards Nash equilibria under an idealized model. Empirical evaluations across four benchmark games demonstrate that NashDreamer substantially improves sample efficiency over model-free baselines early in the training. Finally, we theoretically analyze the architecture's optimization landscape, identifying the vulnerability of the Dreamer family of algorithms to posterior collapse in stochastic environments. We leave it as an open challenge.

From Rollouts to Recipes: Self-Contained Post-Training for LLMs

Post-training large language models usually applies a single training recipe to all samples, even though the model's own rollouts reveal different sample-level learning states. We propose Self-Routing, a behavior-conditioned post-training framework that uses rollout correctness and confidence to decide how each sample should be optimized. Depending on its behavior state, a sample is routed to GRPO, on-policy self-distillation, regularization, or skipping, allowing training to adapt without external teachers, extra annotations, or additional sampling. Experiments on mathematical reasoning across Qwen3 and Qwen3.5 backbones show that Self-Routing consistently improves over uniform GRPO, uniform OPSD, fixed mixtures, and simpler routing baselines. Further analyses show that the routing distribution changes over training and reduces unnecessary updates on low-signal or already stable samples.

Provably Safe Sim-to-Real Transfer

To mitigate the sample complexity of real-world reinforcement learning (RL), a common practice is to first train a policy in a simulator, where samples are cheap, and then deploy the learned policy in the real world with the hope that it generalizes effectively. Such direct sim-to-real transfer is not guaranteed to succeed: simulator-trained policies can be suboptimal in the real world due to sim-to-real mismatch. Correcting this mismatch requires collecting data from the real system, but in many applications, such as robotics and healthcare, this data-collection process is itself subject to safety constraints. This gives rise to the problem of safe sim-to-real transfer: how can an agent exploit an imperfect simulator while ensuring safe real-world data collection and learning a near-optimal feasible policy for the target system? We address this problem by formulating safe sim-to-real transfer within the framework of reward-free safe RL. We design a computationally efficient algorithm that exploits simulator information to provably reduce real-world interaction while ensuring safe exploration and enabling the computation of a near-optimal feasible policy for any potential reward function. Our real-world sample complexity bound characterizes the benefit of using the simulator in terms of the sim-to-real mismatch.

Bandits in Prod: Hyperparameter Optimization at Inference Time

Many production systems can assess a configuration only by using it on live requests and observing noisy feedback. Modern agentic systems are a prominent example, with inference-time choices such as model selection, retrieval depth, prompting strategy, and decoding temperature, yet often with no representative validation data. We formalize this setting as Online Hyperparameter Optimization (OHPO) and cast it as an infinitely many-armed bandit over mixed and conditional search spaces. We introduce IMABO, a general framework that combines any bandit policy for choosing among already sampled configurations with any oracle for proposing new ones. We instantiate it with IMOSS, a restart-free anytime policy whose active set grows as $t^β$, and prove an expected cumulative quantile-regret bound of $O(p_ρ^{-1/β} + T^{(1+β)/2})$, where $β\in(0,1)$ controls active-set growth and $p_ρ$ lower-bounds the probability that a proposed configuration falls in the top-$ρ$ fraction of the search space. We combine IMOSS with three practical oracles: a Tree-structured Parzen Estimator, an incumbent-mutation oracle driven by a per-coordinate bandit, and a pretrained tabular foundation model, all three improving over the uniform random oracle baseline. IMABO obtains the lowest cumulative regret across diverse OHPO settings, from tuning classical machine-learning models to configuring LLM-based agents.

From Base Rollouts to RL Reasoning: A Budgeted Search Perspective

Reinforcement learning with verifiable rewards (RLVR) improves language-model reasoning, but how these gains relate to inference-time decoding and search remains unclear. Does RL create reasoning the base model lacks, or shift the rollout distribution toward trajectories it can already reach but rarely samples? We study this behaviorally with a Unified Decoding Framework (UDF), which expresses token-level sampling, beam-like search, tree search, and sequence-level resampling as executable policies over a shared budgeted operating space, scored post hoc with pass@$k$, self-consistency, best-of-$N$, and first-finish success. Using paired Base/RL checkpoints from SimpleRL-Zoo, we ask whether an RL default-policy curve can be approximated by a structured path of Base operating points. On Math500, AIME, GPQA, and IFEval, the pass@$k$ recovery path follows a Budgeted Operating-Point Transition Rule (BOPTR), $N_{\mathrm{Base}} \approx αN_{\mathrm{RL}}^β$, with benchmark-conditioned exponents. On Qwen2.5-7B, BOPTR gives the lowest transfer error among the non-oracle rules we test, 3.41 pp (95% CI [2.32, 5.53]); a three-seed replication gives 3.07 $\pm$ 0.39 pp. The rule extends to ten models across four families (3.28 to 4.87 pp on checkpoints added after fitting), to four benchmarks it was never fitted on (5.03 pp vs. 4.44 pp in fit), and holds without an RL checkpoint for the target model (4.19 pp) or without RL supervision of any kind (5.08 pp). These results support a qualified internalized-search reading: under the recipe we test, much of the measured RL gain corresponds to a change in sampling efficiency toward operating points the base model can already reach under search. We treat the scaling patterns as descriptive of this recipe and cohort, report where they break down, and use UDF and BOPTR as behavioral diagnostics rather than evidence of parameter-level equivalence.

Explore More, Drift Less: Outcome-Only Reinforcement Learning Can Suffice for Long-Horizon Interactive Agents

Reinforcement learning is a natural way to post-train LLM agents for long-horizon interactive tasks judged only by end-of-task verification, yet a shared belief holds that outcome-only RL soon hits a ceiling on small open models. Recent work therefore compensates around the training with denser rewards, SFT priors, skill libraries, curated memory, or multi-agent orchestration. We argue the ceiling is an artifact of two failures of common practice. Signal starvation: group-relative RL with sparse outcome-only rewards yields a gradient only when a task's rollout group mixes successes and failures, so under-scaled exploration silences exactly the hardest, most instructive tasks. Policy drift: squeezing many updates out of a small task pool degrades the policy itself, as an unanchored objective lets the sampling distribution collapse exactly when saturation has already made informative groups rare. We present CANOPY (Coverage-ANchored On-PolicY RL), a minimalist protocol attacking both directly: scale same-task exploration until the natural signal reappears, keep every update on-policy, KL-anchored, and confined to the agent's own action tokens, then cash in an enlarged interaction budget at test time. On AppWorld, a long-horizon interactive coding benchmark, a Qwen3-14B policy trained with CANOPY through environment interaction alone--without task-specific supervision, auxiliary credit signals, or elaborate agent scaffolding--topped the public leaderboard (Feb. 2026; Test-Normal TGC 86.9, Test-Challenge 67.6), and the same design principles lift Qwen3.5-9B on SWE-bench Verified by 16.6 points. Agentic RL alone thus internalizes long-horizon capability directly into a small open model; we plan to release the complete training stack at https://github.com/AlibabaResearch/SignalCoverageRL.

Accelerating Reinforcement Learning via MPC Solver-Gradient Guidance for Weights-varying MPC

In Model Predictive Control (MPC), cost-function weights shape closed-loop behavior, yet changing conditions often make fixed parametrizations suboptimal and motivate context-dependent online adaptation. Learning such policies is difficult because behavior depends implicitly on numerical MPC solutions, producing nonlinear, potentially nonsmooth, long-horizon dependencies on policy parameters. This creates a bias-variance tradeoff: Reinforcement Learning (RL) optimizes realized closed-loop return from environment samples but is sample-inefficient, whereas Gradient-Based Policy Learning (GB-PL) uses low-variance solver gradients from differentiable MPC to optimize surrogate losses on predicted trajectories but can be biased under model mismatch. We propose Solver-Gradient Guided Reinforcement Learning (SG-RL), a solver-sensitivity augmentation for RL-based online MPC cost-weight adaptation. SG-RL keeps sampled closed-loop return as the objective and uses bounded solver-derived gradients as auxiliary guidance to improve stability and sample efficiency. We instantiate SG-RL in Proximal Policy Optimization (PPO) with four modular algorithms that inject solver-gradient guidance into actor-update scaling, policy loss, advantage estimation, and value-function learning. On two full-scale autonomous racing platforms with intentional model mismatch, SG-RL reaches PPO's best closed-loop return with up to 70.6% fewer samples, outperforms GB-PL baselines by at least 54% in closed-loop return, and generalizes zero-shot to unseen environments.