Agentic reinforcement learning (RL) often requires repeated tool calls in task-specific environments. A training job may create thousands of these environments in bursts while sharing a cluster with other jobs. We present Sandman, a sandbox service built and operated at Amazon for agent tool execution and evaluation. It serves multiple production agentic RL workloads on shared Kubernetes. A training framework supplies a task image and uses commands and file operations in the returned sandbox. Files and processes persist across calls until the framework releases the environment. Sandman manages creation, readiness and cleanup. Each sandbox is a Kubernetes pod with a small daemon mounted into the unmodified image. In a scale test, Sandman held 11,858 concurrent tiny sandboxes. Four production SWE-bench Verified training campaigns created 3.1 million sandboxes in October 2026. We report the design trade-offs and operational lessons from handling creation bursts, preparing task environments, reclaiming abandoned sandboxes, and running evaluation under controlled conditions. We will open-source Sandman's daemon, provider and pool.
https://arxiv.org/abs/2610.39711
Deep search agents extend language models by interleaving reasoning with external retrieval. However, effective search-agent training requires addressing two challenges beyond final-answer optimization. First, the capability frontier of agents is largely determined by training questions, whereas fixed or labeled task collections cannot adapt as agents improve. Second, outcome-only reinforcement learning treats all successful trajectories equally, even when some correct answers rely on redundant searches, creating an inherent tension between answer accuracy and tool efficiency. To address these issues, we introduce \textsc{ZEST-Search}, a zero-label and tool-efficient framework for search-agent training via heterogeneous co-evolution. Starting from unlabeled reference questions, \textsc{ZEST-Search} constructs validated search tasks online through an answer-first and evidence-path-guided generation process. A heterogeneous proposer adaptively constructs training tasks around the solver's evolving capability boundary, while the solver learns search-augmented reasoning through reinforcement learning. To jointly optimize task difficulty and search efficiency, \textsc{ZEST-Search} employs an intermediate-difficulty reward for the proposer and a task-local tool-aware reward for the solver, encouraging informative tasks and correct answers with fewer redundant searches. Experiments on seven general-domain and multi-hop question answering benchmarks demonstrate that \textsc{ZEST-Search} consistently improves search-agent performance while achieving higher tool efficiency without labeled search-training data or expert search trajectories. Further analyses show that heterogeneous generation, adaptive difficulty control, and tool-aware optimization enable more effective search-agent training.
https://arxiv.org/abs/2610.39682
Asynchronous reinforcement learning (RL) is becoming a mainstream paradigm for post-training large language models (LLMs), as it improves training efficiency by updating the model as rollouts arrive. Recent work argues that group-wise sampling in GRPO does not naturally fit asynchronous RL training because rollout lengths follow a long-tailed distribution, and proposes Single-rollout Asynchronous Optimization (SAO) to improve stability and off-policy behavior, especially on agentic tasks. However, SAO relies on a closed-source value model obtained from scaling value pretraining. In this paper, we analyze GRPO and LiSAO, our lightweight reproduction of SAO without the pretrained value model, on single-turn reasoning and multi-turn agentic tasks. We find that GRPO outperforms LiSAO on reasoning tasks, while the reverse holds on agentic tasks. Since the value model of LiSAO is not yet well trained , LiSAO lags behind GRPO substantially in early training steps. To address this issue, we propose Li$^{2}$SAO, which Lifts Light Single-rollout Asynchronous Optimization with group-relative actor-critic bootstrapping: while the critic is cold, a group-relative advantage trains the actor and a group-centered return trains the critic, after which training switches to single-rollout GAE. Experiments show that Li$^{2}$SAO catches up with or surpasses GRPO in early training and further raises the later performance ceiling. Code is available at this https URL.
https://arxiv.org/abs/2610.40726
Label-free test-time reinforcement learning adapts vision--language models using rewards derived from their own predictions. However, misinterpreted visual evidence and sensitivity to textual formulation can produce a consistent but incorrect consensus that majority voting reinforces. Cross-view aggregation can expose such errors, but image and text transformations may themselves degrade task-relevant evidence to different extents. We introduce \method, a reliability-aware harmonic consensus framework for multimodal test-time reinforcement learning. \method constructs a $2\times2$ grid combining original and perturbed images with direct-solving and reframing modes, selects pseudo-labels through weighted harmonic aggregation, and adapts modality-level weights using batch-averaged, temporally smoothed shifts in pseudo-label confidence as a heuristic reliability signal. We formulate consensus as a weighted $\chi^2$-barycenter problem whose unique minimizer is the normalized weighted harmonic aggregate, without requiring correct-answer invariance. An exact support--dispersion decomposition characterizes when harmonic aggregation preserves or corrects arithmetic rankings, while a sensitivity analysis establishes how modality reweighting changes pairwise ranking margins, informing interpretation of the heuristic updates. Across six benchmarks and three Qwen3-VL model scales, \method outperforms TTRV in 16 of 18 benchmark--model settings on adaptation instances and 17 of 18 settings on held-out instances under matched estimation and optimization rollout counts. These results demonstrate improved target-task adaptation and transfer to unseen instances without further updates.
https://arxiv.org/abs/2610.39439
Many applications of multi-objective reinforcement learning (MORL) require policies that balance conflicting objectives while satisfying safety constraints. We study safe MORL with zero constraint violation throughout learning, covering both cumulative and stepwise constraints. A key challenge is to explore sufficiently under unknown dynamics and constraint costs without violating the constraints. For a given preference over objectives, we develop an algorithm to learn a safe Pareto optimal policy by combining optimistic reward estimates with pessimistic cost bounds. With high probability, every policy executed over $T$ episodes incurs zero constraint violation. The algorithm returns a safe Markov policy induced by the averaged occupancy measure and achieves an $\widetilde{O}(1/\sqrt{T})$ suboptimality gap under smooth Tchebycheff scalarization. We further develop a preference-free algorithm that first explores safely without a prespecified preference and then computes a safe policy for any given preference without further interaction. Over $T$ exploration episodes and $K$ planning iterations, it retains the same safety guarantee and achieves an $\widetilde{O}(1/\sqrt{T}+1/\sqrt{K})$ suboptimality gap. Both algorithms require knowledge of a policy that strictly satisfies the constraints and its costs. We then relax these requirements, incurring at most constant cumulative violation. To our knowledge, we provide the first sample-efficient MORL algorithms that guarantee safety for every executed policy.
https://arxiv.org/abs/2610.39409
Reinforcement learning with verifiable rewards (RLVR) makes a language model solve more problems on the first try and fewer when given many tries: it raises pass@1 while the base model overtakes it at large sampling budget k. Is this a failure of RL to add reasoning, or a transient that more training removes? We settle the question with a theorem. The reversal is a price, and we compute its exact rate. Modeling RLVR as an exponential tilt of a base policy over strategies shared across prompts, we prove that under exclusive specialization every update that raises pass@1 strictly lowers the success of some prompt; a strictly positive price on prompts (Stiemke duality) is the exact condition, and being merely the best strategy on a prompt is provably not enough. When the loss reaches the hardest prompts, it forces a pass@k crossover, and the number of crossings is at most the sign variation of the shift in per-prompt success, a totally positive bound that is tight and that recovers the known single-crossover result as its order-preserving case. The crossover is not a bug to patch: a constrained update traces the exact pass@1 versus pass@k frontier, and removing the crossover entirely costs the entire pass@1 gain. The same tilt identity yields entropy collapse and the entropy-performance law with an identifiable exponent, unifying two literatures under one mechanism. Reinforcement cannot widen the reasoning frontier; it can only move along it, at a price we make measurable by a diagnostic that reads the bound, the order-preserving test, and the price from any evaluation log. There is no free lunch, only a price.
https://arxiv.org/abs/2610.39295
Multi-image composition (MICo) is a critical yet challenging capability for large-scale image editing models, where consistency degrades rapidly as the number of reference images increases. While supervised fine-tuning (SFT) can equip models with basic MICo ability, it provides only implicit supervision on the composed image and often fails to learn reliable object-level correspondence across multiple references. We propose DeCoRL, a reinforcement-learning (RL) framework that improves MICo consistency by decomposing holistic MICo consistency into object-level consistency. DeCoRL first establishes instruction-relevant object correspondences across reference images and localizes the corresponding regions in the generated image. It then uses a VLM-based reward model trained on single-object consistency annotations to produce fine-grained, object-wise feedback, which is aggregated into a multi-object consistency reward to guide RL post-training. We further introduce DeCo-Bench, a benchmark covering compositions from 2 to 6 reference images. Experiments on DeCo-Bench and the public MICo-Bench demonstrate consistent improvements in MICo consistency.
https://arxiv.org/abs/2610.39265
While frontier vision-language models demonstrate strong capabilities in user interface (UI) navigation, their high inference costs prohibit everyday use. Conversely, smaller models trained via supervised fine-tuning (SFT) or offline reinforcement learning often memorize static trajectories, leading to brittle execution and an inability to recover from errors. To address these limitations, we propose a novel online reinforcement learning framework that trains UI navigation agents directly on live iOS applications. Our framework decouples the agent into two specialized components: a Planning agent and a UI Grounding model. We rely on an LLM-as-a-Judge to provide comprehensive reward signals, combining dense, step-level feedback to evaluate intermediate progress with a terminal reward for overall task completion. To effectively leverage this dual reward structure, we optimize the agent using Proximal Policy Optimization (PPO) with step-level advantage estimation. Furthermore, we introduce GiGPPO, a novel neighbor-conditioned value estimation method that improves critic stability by leveraging reward signals from visually similar states across concurrent trajectories. To support this online training paradigm at scale, we introduce an efficient infrastructure that orchestrates hundreds of concurrent virtual iOS devices. Evaluations on rigorous benchmarks, including UINavBench, iOSWorld, and AndroidWorld, demonstrate that our online RL trained agents substantially outperform both SFT and terminal-only RL baselines while accelerating training convergence. Notably, our 8B RL agents achieve nearly a sevenfold improvement over the SFT baseline in out-of-distribution generalization to Android environments, while outperforming Gemini-3.5-Flash and tying with Gemini-3.1-Pro on real iOS applications.
https://arxiv.org/abs/2610.39264
Large language models (LLMs) are increasingly described as acquiring "reasoning" skills after reinforcement learning with verifiable rewards. However, whether these gains reflect genuine reasoning or more superficial adaptations remains underexplored. In this work, we probe LLMs trained in a finite and exhaustively analyzable logical domain, namely Tic-Tac-Toe, and trace how internal representations evolve across reinforcement learning (RL) with Group Relative Policy Optimization (GRPO). Quantitatively, RL yields high accuracy and robustness across prompt variations, suggesting the emergence of game reasoning. Mechanistic interpretability, however, paints a different picture: features extracted with sparse autoencoders (SAEs) reveal that models primarily adapt to rely more heavily on information already explicit in the prompt, such as whose turn it is, game progression and board occupancy. In comparison, high-level concepts like board symmetries and strategic forks remain weakly represented, raising concerns that reasoning benchmarks overestimate model abilities. This suggests that RL-driven "reasoning" may conflate task-specific adaptations to input information with reasoning ability. We provide, for the first time: (i) a systematic interpretability pipeline tracing representation dynamics across RL training in small-scale LLMs; (ii) an extension of SAE-based feature discovery to hypothesis-driven testing in a finite logical domain; and (iii) an interpretability-based demonstration that RL post-training neither adds nor removes concept information but reorganizes which features dominate the representation, with causal interventions locating the decision downstream of it, in the late-layer state.
https://arxiv.org/abs/2610.39182
Self-evolving personal agents act for users and learn from user feedback. However, if an agent obeys an instruction that an untrusted third party hides in content, the third party gains control of the agent. Such indirect prompt injection (IPI) poses severe risks. We investigate whether self-evolution degrades the robustness of personal agents to IPI. To study this question, we design a controlled two-phase methodology. In the adaptation phase, the user asks the agent to read external content and complete the task described in it, a common request in daily use. The agent then learns from the user's feedback and improves itself as designed. In the test phase, a third party writes a similar task into new external content, but the user's test request does not authorize the injected task. Using this methodology, we build multiple tasks with diverse test instances in different domains for a real personal agent. Our extensive experiments reveal that self-evolution substantially degrades robustness to IPI. Specifically, compared with the base agent, which does not evolve from user feedback, the average attack success rate rises by 14.0--48.8 percentage points under skill evolution and by 3.0--39.3 percentage points under reinforcement learning, posing safety risks. The code is available at this https URL
https://arxiv.org/abs/2610.39122
Balatro, a 2024 roguelike deckbuilder, presents three difficulties that have historically derailed reinforcement learning methods: a 3,000-action state-dependent action space, horizons of several hundred decisions with sparse rewards, and pervasive stochasticity in both card draws and shop generation. Published RL results on the game remain scarce. We introduce an end-to-end pipeline comprising (i) a high-throughput Rust simulator that is automatically state-diffed against the live game client via BalatroBot, (ii) a condensed observation-action interface with dynamic per-step masking of legal moves, and (iii) a multi-agent PPO architecture that decomposes play into a tactical blind policy and a strategic shop policy that share the full game state but act in disjoint phases. Long-horizon credit assignment is partially addressed by per-agent reward routing with explicit cross-agent credit. On the main joint run, training metrics show a sharp phase transition in which the first-blind clear rate converges above 99% and mean episode return increases by roughly an order of magnitude, plateauing at a mean maximum ante of 3 out of 8; single-agent baselines under identical rewards oscillated between greedy and hoarding failure modes and did not stably clear the first blind. These results establish the two-policy decomposition as a strong reactive baseline for Balatro and localise the remaining gap to long-horizon strategic planning rather than tactical blind play.
https://arxiv.org/abs/2610.39049
Autoresearch agents can now attempt long-horizon AI research end-to-end, i.e., self-improvement. However, best results are still obtained by research agents interacting with human researchers, and improving AI's ability to perform this co-research will only reinforce this effect---a process termed co-improvement (Weston and Foerster, 2025). Further, aligning with human expectations is likely a safer path for research agents, especially given recent agent reward hacking phenomena (OpenAI, 2026b). In this work we address these issues in four ways: (i) we empirically study the role of humans in directing autoresearch agents, focusing on the domain of benchmark creation, and find humans still play a pivotal role particularly in the ideation phase; (ii) we also develop a benchmark, HackBench, that shows current autoresearch agents are not aligned and are unable to achieve hack localization sufficiently; (iii) we present a method to train agents for improved human interaction by using human simulators as a proxy during reinforcement learning (RL); and finally (iv) we develop a method to improve model text generation, and hence agent communication, by RL with rubrics aligned with human experts. Together, our training and evaluation recipes provide a path toward more capable and aligned (co-)research agents.
https://arxiv.org/abs/2610.38882
In many settings where LLM post-training is desirable, high-quality answers are recognizable but difficult to score with explicit rewards. Reinforcement learning with verifiable rewards (RLVR) is limited to tasks where an explicit correctness signal is available. Prior adversarial approaches to training reasoning LLMs either complement verifiable rewards with co-trained critics or require reference reasoning traces. We ask whether a co-trained LLM judge can turn reference answers alone into the sole reward for on-policy post-training of reasoning LLMs. We call this method Reinforced Adversarial Learning (RAL). We first validate RAL on three verifiable tasks (integer multiplication, code-based arithmetic-expression synthesis, and SMILES-to-formula translation), using the verifiers only for evaluation. With sufficiently capable judges and enough training, RAL matches direct RLVR. We then apply RAL to scientific abstract generation in two settings. In the first setting, RAL guides the generator to produce abstracts in the scientific domain of the reference abstracts, even though the prompt leaves that domain unspecified. In the second setting, we generate abstracts for U.S. National Institutes of Health grant proposals conditioned on the grant title. Human scientists and an ensemble of LLM judges find our generations harder to distinguish from real abstracts than those of frontier-LLM baselines. These results suggest a path toward post-training reasoning models in scientific and other high-value domains, where increasingly capable judges infer hard-to-specify reward functions from example answers.
https://arxiv.org/abs/2610.38851
Automated jailbreak discovery aims to find prompts that elicit prohibited behaviors from safety-trained language models, helping developers identify vulnerabilities before deployment. One class of approaches uses reinforcement learning to train an investigator model to generate prompts that elicit a specified behavior from a target model. However, training directly against a safety-trained target is difficult because nearly all prompts are refused, leaving the investigator with a sparse reward signal. Prior work addresses this with the propensity bound (PRBO), a proxy reward estimated by sampling responses from a more compliant target, and then adjusting for how likely those responses would have been under the original target. We introduce Curriculum of Models (CoM), an alternative method that trains the investigator against a sequence of modified versions of the target, progressing gradually from a version that readily exhibits the specified behavior to the original target. For jailbreak discovery, training begins against a target version that rarely refuses harmful requests, and advances to the next, harder version once the investigator reliably elicits the behavior from the current one. We evaluate CoM on elicitation tasks involving CBRN materials, explosives, and illicit drugs, using two open-weight targets, gemma-4-31b-it and gpt-oss-120b. We compare against PRBO and direct training on the original target without a curriculum. When the investigator is trained to elicit a single behavior, CoM finds successful jailbreaks more reliably than either baseline. When trained on multiple behaviors simultaneously, the CoM-trained investigator can elicit held-out behaviors, though PRBO-trained investigators achieve higher success rates. Our results suggest that a simple curriculum over target models offers a promising approach for addressing sparse rewards in rare-behavior elicitation.
https://arxiv.org/abs/2610.38833
Clinical practice guidelines encode evidence-based recommendations as conditional decision flows, which makes them a natural source of process supervision for training reasoning models. Two properties of clinical reasoning make this supervision difficult to use. A decision flow consistent with a guideline does not by itself determine the correct answer for a given patient, which we call the path--answer gap, and several valid decision flows can support the same clinical decision, which we call path multiplicity. Current training approaches address parts of this problem. Answer rewards supervise the final decision, and process rewards computed against a reference flow supervise one valid decision flow per case. Supervised fine-tuning on annotated flows teaches guideline-consistent reasoning but constrains the model to one trajectory per case and can reduce answer accuracy. We introduce GUIDER, a method that jointly optimizes a decision flow controller and a reasoning policy. The controller learns to generate plausible decision flows from guideline-derived supervision, and the policy learns to generate a decision flow and a final answer for each patient case. GUIDER computes the process reward for the policy over several controller-generated flows, which accounts for path multiplicity, and gates this reward on answer correctness, which addresses the path--answer gap. Joint training allows the process supervision to evolve with the policy. On MedGUIDE, GUIDER with Qwen3-14B achieves 82.5 weighted accuracy and 73.5 guideline adherence, 3.3 and 3.1 points above the strongest clinical reinforcement learning baseline. With Qwen3-14B and Gemma4-12B backbones, GUIDER also improves over CRPO, MRPO, and FaithMed on the out-of-domain benchmarks AMEGA-LLM, RealMedQA, and CancerGUIDE.
https://arxiv.org/abs/2610.38709
Autonomous far-range rocket landing is a challenging control problem because navigation, descent-rate regulation, attitude management, and fuel use must be coordinated in the presence of uncertain atmospheric and vehicle dynamics. This paper presents a curriculum-driven proximal policy optimization (PPO) framework for three-dimensional rocket landing in a stochastic environment incorporating altitude-dependent aerodynamic drag, wind shear, temporally correlated turbulence, discrete gusts, uncertain propulsion and aerodynamic parameters, thrust-vector misalignment, engine lag, actuator-gain variation, noisy observations, and command latency. Learning is organised into far-range approach, soft descent, and integrated landing stages. Policy transfer, critic warm-up after reward changes, rehearsal of earlier tasks, and progressive expansion of weather severity are used to support learning across these coupled phases. Across 100,000 evaluation episodes, the policy achieves 96,656 successful landings, corresponding to a success rate of 96.656\% and a 95\% Wilson confidence interval of 96.543--96.766\%. Success decreases from 98.84\% under zero-disturbance conditions to 88.07\% in the highest weather-severity band. Successful touchdowns exhibit small miss distances and low residual horizontal and vertical velocities. An exploratory logistic-regression analysis identifies mean wind speed as the strongest measured correlate of success, with initial distance, initial altitude, initial vertical velocity, and wind-shear exponent also associated with outcomes. The results quantify both the effectiveness of the learned policy over the evaluated disturbance distribution and the degradation that occurs under severe compound atmospheric conditions.
https://arxiv.org/abs/2610.38636
There is a fundamental contradiction between the desire for models that can generalize, and models that can continuously adapt to recent input with changing statistics. These conditions, captured in few-shot and continual learning settings, can bias or disrupt learned representations. This harms generalization to a broader context, leaving the model unable to overcome input variance. This paper proposes a solution based on the Complementary Learning System architecture (CLS), in which a Short-Term Memory (STM) delegates generalization to a slow, statistical Long-Term Memory (LTM). Delegation is achieved by working in a space of robust, generalized perceptions produced by the LTM. With this separation, the STM can focus on memorizing recent input and avoiding interference between memories. We show that on an image classification task, the resulting CLS model is more resistant to forgetting in a domain-incremental continual learning setting than a baseline ResNet LTM, and generalizes more effectively in a few-shot setting than other continual learners. In the continual setting, overall accuracy is slightly worse than existing continual learning models, but with a different mix of performance characteristics. Results analysis suggests that the model is limited by the representations and representational plasticity of the LTM. In future work, we will seek to address this by replaying STM memories to the LTM.
https://arxiv.org/abs/2610.38577
Rubric-based reinforcement learning (RL) offers interpretable, fine-grained supervision for aligning large language models (LLMs) on open-ended generation tasks. However, static rubric criteria may become saturated or remain beyond the policy's exploration, rendering the reward signals insufficiently discriminative. While recent efforts seek to guide sampling exploration or evolve rubrics, they fail to explicitly factor in how rubric difficulty should track the evolving policy's capabilities, resulting in a persistent mismatch between the optimization objective and the policy's current capability frontier. In this paper, we propose \textbf{Co}-Evolving Policy and Rubric via \textbf{C}apability \textbf{A}wareness (\textbf{CoCA}), a closed-loop framework that jointly adapts the rubric and policy through criterion-level diagnosis. Specifically, CoCA contrasts query-only and rubric-guided rollouts to characterize each criterion relative to the current policy, recalibrates criteria with mismatched difficulty, and identifies guidance-revealed capability gaps for frontier-based learning. Based on this insight, CoCA either expands rubric-conditioned frontiers through guided optimization or transfers qualified gains through on-policy self-distillation. As the policy updates, CoCA improves the capability diagnosis and enables more reliable distillation, thereby completing the co-evolution loop. Extensive experiments across diverse benchmarks and LLMs demonstrate that CoCA consistently improves performance over rubric-based RL methods. Moreover, CoCA promotes the internalization of guidance-revealed capabilities into query-only behavior while mitigating capability degradation.
https://arxiv.org/abs/2610.38566
Outcome-based reinforcement learning provides coarse supervision for long-horizon LLM agents: failed trajectories may contain correct steps, while successful trajectories can contain errors. Trajectory-level skills can also shift teacher preferences at unrelated steps, introducing off-target distillation signals. We introduce SCOPE, a framework for Selective Critical-Step On-Policy Self-Distillation. After a supervised warm-up, the policy analyzes its own trajectories, generates step-specific hindsight skills, and distills their guidance only at selected error steps. A bounded signed teacher-student coefficient stabilizes auxiliary updates while preserving positive reinforcement and negative correction. A success-relative pairwise length reward further encourages efficient task completion. Experiments on ALFWorld and WebShop demonstrate consistent improvements across multiple model backbones. With Qwen2.5-3B, SCOPE achieves 97.7% success on ALFWorld and 85.2% on WebShop, outperforming SEED by 5.9 and 6.3 percentage points, respectively. On unseen ALFWorld tasks, SCOPE reaches 89.6% success, improving over GRPO by 23.2 percentage points with 46.7% fewer interactions. Scaling to Qwen3-32B, SCOPE achieves 99.2% success on seen ALFWorld tasks and 94.0% on unseen tasks.
https://arxiv.org/abs/2610.38391
Bisimulation metrics offer a principled notion of task-relevant state similarity in reinforcement learning, but existing constructions and methods are largely confined to discounted MDPs, where contraction arguments ensure well-defined fixed points and downstream guarantees. We develop a unified foundation for bisimulation metrics in undiscounted settings, that is total- and average-reward problems, by replacing the standard operator-centric view with a game-centric one: we interpret prior metric operators as Bellman-Shapley operators of zero-sum turn-based games and define metrics as the corresponding game value functions, yielding unique definitions even when $\gamma=1$. This game-theoretic foundation facilitates transfer of dynamic-programming theory and algorithms. We also use this game-centric perspective to characterize how metric finiteness depends on structural properties of the underlying MDP and motivate certain directed metrics that remain finite in weakly communicating MDPs. We further introduce an abstract framework for modifying the games' action spaces, allowing general transition coupling sets, that recovers many existing metrics and guides new constructions. Finally, we prove that these metrics bound total-reward and, when the optimal gain is state-independent, optimal relative value differences. We also provide error and suboptimality guarantees for aggregation-based planning in total- and average-reward settings.
https://arxiv.org/abs/2610.38313