Model-Based Planning

World models such as DINO-WM and LeWM specify the goal with an image, which is difficult to obtain in advance for novel tasks. We present the Grounded World Model (GWM), a latent world model that enables zero-shot planning in the real world from language goals alone. Given a candidate action sequence and the current observation, GWM predicts the future in the visual space of a pretrained video-language embedding model. The frozen readout of this embedding model maps this imagined future and the task description into the same embedding space, where their negative cosine similarity serves as the planning cost. Training GWM requires only offline and task-agnostic video-action pairs and no language labels. In simulated experiments on WISER, planning with GWM, which executes the candidate action of lowest cost, solves 87% of 288 tasks with unseen instructions and visual signals, while ten fine-tuned VLAs average 22%. We then scale GWM up with real robot data, and use it for zero-shot planning in realistic simulation and real scenes. In the IsaacSim evaluation, planning with GWM completes all 70 trials across 14 tasks that require reasoning over referring expressions, matching a modular planner grounded by a frontier VLM, while pi0.5 reaches 37/70. Deployed on a real Franka, the same stack completes 55/60 separately evaluated pick-and-place sub-tasks, comparable to the modular planner's 52/60, with the full system running locally on a single consumer GPU. Project website: https://quanyili.github.io/gwm-wiser/.

Humans effortlessly navigate the physical world by predicting how objects behave under gravity and contact forces, yet how such judgments support sequential physical planning under resource constraints remains poorly understood. Research on intuitive physics debates whether prediction relies on the Intuitive Physics Engine (IPE) or fast, cue-based heuristics; separately, decision-making research debates deliberative lookahead versus myopic strategies. These debates have proceeded in isolation, leaving the cognitive architecture of sequential physical planning underspecified. How physical prediction mechanisms and planning strategies jointly adapt under limited cognitive resources remains an open question. Here we show that humans exhibit a dual transition under resource pressure, simultaneously shifting both physical prediction mechanism and planning strategy to match cognitive budget. Using Overhang Tower, a construction task requiring participants to maximize horizontal overhang while maintaining stability, we find that IPE-based simulation dominates early stages while CNN-based visual heuristics prevail as complexity grows; concurrently, time pressure truncates deliberative lookahead, shifting planning toward shallower horizons: a dual transition unpredicted by prior single-mechanism accounts. These findings reveal a hierarchical, resource-rational architecture that flexibly trades computational cost against predictive fidelity. Our results unify two long-standing debates (simulation vs. heuristics and myopic vs. deliberative planning) as a dynamic repertoire reconfigured by cognitive budget.

Automated planning algorithms require an action model specifying the preconditions and effects of each action, but obtaining such a model is often hard. Learning action models from observations is feasible, but existing algorithms for numeric domains are offline, requiring expert traces as input. We propose the Reinforcement learning, Action Model learning, and Planning (RAMP) strategy for learning numeric planning action models online via interactions with the environment. RAMP simultaneously trains a Deep Reinforcement Learning (DRL) policy, learns a numeric action model from past interactions, and uses that model to plan future actions when possible. These components form a positive feedback loop: the RL policy gathers data to refine the action model, while the planner generates plans to continue training the RL policy. To facilitate this integration of RL and numeric planning, we developed Numeric PDDLGym, an automated framework for converting numeric planning problems to Gym environments. Experimental results on standard IPC numeric domains show that RAMP significantly outperforms PPO, a well-known DRL algorithm, in terms of solvability and plan quality.

Goal-oriented conversational systems require making sequential decisions under uncertainty about the user's intent, where the algorithm must balance information acquisition and target commitment over multiple turns. Existing approaches address this challenge from different perspectives: structured methods enable multi-step planning but rely on predefined schemas, while LLM-based approaches support flexible interactions but lack long-horizon decision making, resulting in poor coordination between information acquisition and target commitment. To address this limitation, we formulate goal-oriented conversation as an uncertainty-aware sequential decision problem, where uncertainty serves as a guiding signal for multi-turn decision making. We propose a Conversation Uncertainty-aware Planning framework (CUP) that integrates language models with structured planning: a language model proposes feasible actions, and a planner evaluates their long-term impact on uncertainty reduction. Experiments on multiple conversational benchmarks show that CUP consistently improves success rates while requiring fewer interaction turns. Further analysis demonstrates that uncertainty-aware planning contributes to more efficient information acquisition and earlier confident commitment.

Large foundation models enable powerful reasoning for autonomous systems, but mapping semantic intent to reliable real-time control remains challenging. Existing approaches either (i) let Large Language Models (LLMs) generate trajectories directly - brittle, hard to verify, and latency-prone - or (ii) adjust Model Predictive Control (MPC) objectives online - mixing slow deliberation with fast control and blurring interfaces. We propose Agentic Fast-Slow Planning, a hierarchical framework that decouples perception, reasoning, planning, and control across natural timescales. The framework contains two bridges. Perception2Decision compresses scenes into ego-centric topologies using an on-vehicle Vision-Language Model (VLM) detector, then maps them to symbolic driving directives in the cloud with an LLM decision maker - reducing bandwidth and delay while preserving interpretability. Decision2Trajectory converts directives into executable paths: Semantic-Guided A* embeds language-derived soft costs into classical search to bias solutions toward feasible trajectories, while an Agentic Refinement Module adapts planner hyperparameters using feedback and memory. Finally, MPC tracks the trajectories in real time, with optional cloud-guided references for difficult cases. Experiments in CARLA show that Agentic Fast-Slow Planning improves robustness under perturbations, reducing lateral deviation by up to 45% and completion time by over 12% compared to pure MPC and an A*-guided MPC baseline. Code is available at https://github.com/cjychenjiayi/icra2026_AFSP.

Partially Observable Markov Decision Processes (POMDPs) provide a principled mathematical framework for decision-making under uncertainty. However, the exact solution to POMDPs is computationally intractable. In this paper, we address the computational intractability by introducing a novel framework for adaptive open-loop simplification with formal performance guarantees. Our method adaptively interleaves open-loop and closed-loop planning via a topology-based belief tree, enabling a significant reduction in planning complexity. The key contribution lies in the derivation of efficiently computable bounds which provide formal guarantees and can be used to ensure that our simplification can identify the immediate optimal action of the original POMDP problem. Our framework therefore provides computationally tractable performance guarantees for macro-actions within POMDPs. Furthermore, we propose a novel framework for safely skipping replanning during execution, supported by theoretical guarantees on multi-step open-loop action sequences. To the best of our knowledge, this framework is the first to address skipping replanning with formal performance guarantees. Practical online solvers for our proposed simplification are developed, including a sampling-based solver and an anytime solver. Empirical results demonstrate substantial computational speedups while maintaining provable performance guarantees, advancing the tractability and efficiency of POMDP planning.

Robotic reproduction of oil paintings using soft brushes and pigments requires force-sensitive control of deformable tools, prediction of brushstroke effects, and multi-step stroke planning, often without human step-by-step demonstrations or faithful simulators. Given only a sequence of target oil painting images, can a robot infer and execute the stroke trajectories, forces, and colors needed to reproduce it? We present IMPASTO, a robotic oil-painting system that integrates learned pixel dynamics models with model-based planning. The dynamics models predict canvas updates from image observations and parameterized stroke actions; a receding-horizon model predictive control optimizer then plans trajectories and forces, while a force-sensitive controller executes strokes on a 7-DoF robot arm. IMPASTO integrates low-level force control, learned dynamics models, and high-level closed-loop planning, learns solely from robot self-play, and approximates human artists' single-stroke datasets and multi-stroke artworks, outperforming baselines in reproduction accuracy. Project website: https://impasto-robopainting.github.io/

Planning long duration robotic manipulation sequences is challenging because of the complexity of exploring feasible trajectories through nonlinear contact dynamics and many contact modes. Moreover, this complexity grows with the problem's horizon length. We propose a search tree method that generates trajectories using the spectral decomposition of the inverse dynamics equation. This equation maps actuator displacement to object displacement, and its spectrum is efficient for exploration because its components are orthogonal and they approximate the reachable set of the object while remaining dynamically feasible. These trajectories can be combined with any search based method, such as Rapidly-Exploring Random Trees (RRT), for long-horizon planning. Our method performs similarly to recent work in model-based planning for short-horizon tasks, and differentiates itself with its ability to solve long-horizon tasks: whereas existing methods fail, ours can generate 45 second duration, 10+ contact mode plans using 15 seconds of computation, demonstrating real-time capability in highly complex domains.

We present a novel LLM-informed model-based planning framework, and a novel prompt selection method, for object search in partially-known environments. Our approach uses an LLM to estimate statistics about the likelihood of finding the target object when searching various locations throughout the scene that, combined with travel costs extracted from the environment map, are used to instantiate a model, thus using the LLM to inform planning and achieve effective search performance. Moreover, the abstraction upon which our approach relies is amenable to deployment-time model selection via the recent offline replay approach, an insight we leverage to enable fast prompt and LLM selection during deployment. Simulation experiments demonstrate that our LLM-informed model-based planning approach outperforms the baseline planning strategy that fully relies on LLM and optimistic strategy with as much as 11.8% and 39.2% improvements respectively, and our bandit-like selection approach enables quick selection of best prompts and LLMs resulting in 6.5% lower average cost and 33.8% lower average cumulative regret over baseline UCB bandit selection. Real-robot experiments in an apartment demonstrate similar improvements and so further validate our approach.

We want a multi-robot team to complete complex tasks in minimum time where the locations of task-relevant objects are not known. Effective task completion requires reasoning over long horizons about the likely locations of task-relevant objects, how individual actions contribute to overall progress, and how to coordinate team efforts. Planning in this setting is extremely challenging: even when task-relevant information is partially known, coordinating which robot performs which action and when is difficult, and uncertainty introduces a multiplicity of possible outcomes for each action, which further complicates long-horizon decision-making and coordination. To address this, we propose a multi-robot planning abstraction that integrates learning to estimate uncertain aspects of the environment with model-based planning for long-horizon coordination. We demonstrate the efficient multi-stage task planning of our approach for 1, 2, and 3 robot teams over competitive baselines in large ProcTHOR household environments. Additionally, we demonstrate the effectiveness of our approach with a team of two LoCoBot mobile robots in real household settings.

Learned action policies are increasingly popular in sequential decision-making, but suffer from a lack of safety guarantees. Recent work introduced a pipeline for testing the safety of such policies under initial-state and action-outcome non-determinism. At the pipeline's core, is the problem of deciding whether a state is safe (a safe policy exists from the state) and finding faults, which are state-action pairs that transition from a safe state to an unsafe one. Their most effective algorithm for deciding safety, TarjanSafe, is effective on their benchmarks, but we show that it has exponential worst-case runtime with respect to the state space. A linear-time alternative exists, but it is slower in practice. We close this gap with a new policy-iteration algorithm iPI, that combines the best of both: it matches TarjanSafe's best-case runtime while guaranteeing a polynomial worst-case. Experiments confirm our theory and show that in problems amenable to TarjanSafe iPI has similar performance, whereas in ill-suited problems iPI scales exponentially better.

Long-horizon indoor mobile manipulation (MoMa) requires robots to execute extended navigation-manipulation sequences whose feasibility depends on state changes induced by preceding skills. Vision-language models (VLMs) can decompose instructions into plausible skill sequences, but they do not reliably track such cumulative embodiment constraints or revise a plan when execution deviates from expectation. We present MoMaStage, a map-light framework for state-consistent planning and closed-loop execution in long-horizon indoor MoMa. MoMaStage couples a frozen VLM with robot execution through three mechanisms: (i) a hierarchical library of grounded, executable skills and a topology-only projection of a Skill-State Graph (SSG) that constrains the VLM's planning space; (ii) an SSG verifier that propagates scene-region and gripper-occupancy state to reject infeasible plans before execution; and (iii) an event-driven monitor that triggers graph-grounded repair only when an observed outcome invalidates the remaining plan. The SSG captures the compact embodiment state needed for skill sequencing without requiring a dense scene map, while geometric and contact-level conditions remain within the underlying controllers. Experiments in physics-rich simulation and on a real mobile manipulator show that MoMaStage improves planning validity and long-horizon execution survival over the evaluated baselines, while reducing latency and model token consumption.

This paper bridges some of the gap between optimal planning and reinforcement learning (RL), both of which share roots in dynamic programming applied to sequential decision making or optimal control. Whereas planning typically favors deterministic models, goal termination, and cost minimization, RL tends to favor stochastic models, infinite-horizon discounting, and reward maximization in addition to learning-related parameters such as the learning rate and greediness factor. A derandomized version of RL is developed, analyzed, and implemented to yield performance comparisons with value iteration and Dijkstra's algorithm using simple planning models. Next, mathematical analysis shows: 1) conditions under which cost minimization and reward maximization are equivalent, 2) conditions for equivalence of single-shot goal termination and infinite-horizon episodic learning, and 3) conditions under which discounting causes goal achievement to fail. The paper then advocates for defining and optimizing truecost, rather than inserting arbitrary parameters to guide operations. Performance studies are then extended to the stochastic case, using planning-oriented criteria and comparing value iteration to RL with learning rates and greediness factors.

Generalized planning studies the construction of solution strategies that generalize across families of planning problems sharing a common domain model, formally defined by a transition function $γ: S \times A \rightarrow S$. Classical approaches achieve such generalization through symbolic abstractions and explicit reasoning over $γ$. In contrast, recent Transformer-based planners, such as PlanGPT and Plansformer, largely cast generalized planning as direct action-sequence prediction, bypassing explicit transition modeling. While effective on in-distribution instances, these approaches typically require large datasets and model sizes, and often suffer from state drift in long-horizon settings due to the absence of explicit world-state evolution. In this work, we formulate generalized planning as a transition-model learning problem, in which a neural model explicitly approximates the successor-state function $\hatγ \approx γ$ and generates plans by rolling out symbolic state trajectories. Instead of predicting actions directly, the model autoregressively predicts intermediate world states, thereby learning the domain dynamics as an implicit world model. To study size-invariant generalization and sample efficiency, we systematically evaluate multiple state representations and neural architectures, including relational graph encodings. Our results show that learning explicit transition models yields higher out-of-distribution satisficing-plan success than direct action-sequence prediction in multiple domains, while achieving these gains with significantly fewer training instances and smaller models. This is an extended version of a short paper accepted at ICAPS 2026 under the same title.

Diffusion models have shown promising capabilities in trajectory generation for planning in offline reinforcement learning (RL). However, conventional diffusion-based planning methods often fail to account for the fact that generating trajectories in RL requires unique consistency between transitions to ensure coherence in real environments. This oversight can result in considerable discrepancies between the generated trajectories and the underlying mechanisms of a real environment. To address this problem, we propose a novel diffusion-based planning method, termed as Diffusion Modulation via Environment Mechanism Modeling (DMEMM). DMEMM modulates diffusion model training by incorporating key RL environment mechanisms, particularly transition dynamics and reward functions. Experimental results demonstrate that DMEMM achieves state-of-the-art performance for planning with offline reinforcement learning.

Language Model (LM) agents have demonstrated remarkable capabilities in solving tasks that require multiple interactions with the environment. However, they remain vulnerable in environments where a single error often leads to irrecoverable failure, particularly under strict feasibility constraints. We systematically analyze existing agent frameworks, identifying imperfect planning and stochastic execution as the primary causes. To address these challenges, we propose Tool-guided Adaptive Planning with constrained Execution (TAPE). TAPE enhances planning capability by aggregating multiple plans into a graph and employing an external solver to identify a feasible path. During execution, TAPE employs constrained decoding to reduce sampling noise, while adaptively re-planning whenever environmental feedback deviates from the intended state. Experiments across Sokoban, ALFWorld, MuSiQue, and GSM8K-Hard demonstrate that TAPE consistently outperforms existing frameworks, with particularly large gains on hard settings, improving success rates by 21.0 percentage points on hard settings on average, and by 20.0 percentage points for weaker base models on average. Code and data available at here.

Planning-based reinforcement learning for continuous control is bottlenecked by two practical issues: planning at primitive time scales leads to prohibitive branching and long horizons, while real environments are frequently partially observable and exhibit regime shifts that invalidate stationary, fully observed dynamics assumptions. We introduce I-TAP (In-Context Latent Temporal-Abstraction Planner), an offline RL framework that unifies in-context adaptation with online planning in a learned discrete temporal-abstraction space. From offline trajectories, I-TAP learns an observation-conditioned residual-quantization VAE that compresses each observation-macro-action segment into a coarse-to-fine stack of discrete residual tokens, and a temporal Transformer that autoregressively predicts these token stacks from a short recent history. The resulting sequence model acts simultaneously as a context-conditioned prior over abstract actions and a latent dynamics model. At test time, I-TAP performs Monte Carlo Tree Search directly in token space, using short histories for implicit adaptation without gradient update, and decodes selected token stacks into executable actions. Across deterministic MuJoCo, stochastic MuJoCo with per-episode latent dynamics regimes, and high-dimensional Adroit manipulation, including partially observable variants, I-TAP consistently matches or outperforms strong model-free and model-based offline baselines, demonstrating efficient and robust in-context planning under stochastic dynamics and partial observability.

Reactive motion generation in dynamic and unstructured scenarios is typically subject to essentially static perception and system dynamics. Reliably modeling dynamic obstacles and optimizing collision-free trajectories under perceptive and control uncertainty are challenging. This article focuses on revealing tight connection between reactive planning and dynamic mapping for manipulators from a model-based perspective. To enable efficient particle-based perception with expressively dynamic property, we present a tensorized particle weight update scheme that explicitly maintains obstacle velocities and covariance meanwhile. Building upon this dynamic representation, we propose an obstacle-aware MPPI-based planning formulation that jointly propagates robot-obstacle dynamics, allowing future system motion to be predicted and evaluated under uncertainty. The model predictive method is shown to significantly improve safety and reactivity with dynamic surroundings. By applying our complete framework in simulated and noisy real-world environments, we demonstrate that explicit modeling of robot-obstacle dynamics consistently enhances performance over state-of-the-art MPPI-based perception-planning baselines avoiding multiple static and dynamic obstacles.

We explore how different types and uses of memory can aid spatial navigation in changing uncertain environments. In the simple foraging task we study, every day, our agent has to find its way from its home, through barriers, to food. Moreover, the world is non-stationary: from day to day, the location of the barriers and food may change, and the agent's sensing such as its location information is uncertain and very limited. Any model construction, such as a map, and use, such as planning, needs to be robust against these challenges, and if any learning is to be useful, it needs to be adequately fast. We look at a range of strategies, from simple to sophisticated, with various uses of memory and learning. We find that an architecture that can incorporate multiple strategies is required to handle (sub)tasks of a different nature, in particular for exploration and search, when food location is not known, and for planning a good path to a remembered (likely) food location. An agent that utilizes non-stationary probability learning techniques to keep updating its (episodic) memories and that uses those memories to build maps and plan on the fly (imperfect maps, i.e. noisy and limited to the agent's experience) can be increasingly and substantially more efficient than the simpler (minimal-memory) agents, as the task difficulties such as distance to goal are raised, as long as the uncertainty, from localization and change, is not too large.

Previous Vision-Language-Action models face critical limitations in navigation: scarce, diverse data from labor-intensive collection and static representations that fail to capture temporal dynamics and physical laws. We propose NavDreamer, a video-based framework for 3D navigation that leverages generative video models as a universal interface between language instructions and navigation trajectories. Our main hypothesis is that video's ability to encode spatiotemporal information and physical dynamics, combined with internet-scale availability, enables strong zero-shot generalization in navigation. To mitigate the stochasticity of generative predictions, we introduce a sampling-based optimization method that utilizes a VLM for trajectory scoring and selection. An inverse dynamics model is employed to decode executable waypoints from generated video plans for navigation. To systematically evaluate this paradigm in several video model backbones, we introduce a comprehensive benchmark covering object navigation, precise navigation, spatial grounding, language control, and scene reasoning. Extensive experiments demonstrate robust generalization across novel objects and unseen environments, with ablation studies revealing that navigation's high-level decision-making nature makes it particularly suited for video-based planning.

Planning requires a transition model that predicts how each action changes the current state. When a large language model (LLM) plays this role, every next state is generated token by token, which makes searching over many possible futures slow and expensive. Existing alternatives either still query an LLM at every step or require a symbolic model of the domain. We propose EmbedPlan, a transition model built on frozen text embeddings: it embeds natural language descriptions of the state and the action with a frozen LLM, predicts the embedding of the next state with a lightweight learned network, and returns the closest real state. Because this network can be trained on top of any encoder, EmbedPlan also provides a controlled way to compare text representations for learning transitions. We evaluate it on 9 classical planning domains, under six settings that hold out progressively more of the data, from transitions to entire domains, and against baselines ranging from predicting no change to learning symbolic action rules. On planning problems seen during training, EmbedPlan almost always ranks the true next state among its top five guesses, still does so for most queries even when every observed state is a candidate, and retains 92-99% of its single-step accuracy when predicting several steps ahead from its own outputs. Given the same candidate states as GPT-5.4, it picks the true next state more often while taking about 0.17 ms per transition with cached embeddings. Accuracy is lower on unseen problems and near chance on unseen domains, and the controlled comparison traces this limit to the state representation rather than to the learned transition.

Recent advances in world models have shown promise for modeling future dynamics of environmental states, enabling agents to reason and act without accessing real environments. Current methods mainly perform single-step or fixed-horizon rollouts, leaving their potential for complex task planning under-exploited. We propose Imagine-then-Plan (ITP), a unified framework for agent learning via lookahead imagination, where an agent's policy model interacts with the learned world model, yielding multi-step ``imagined'' trajectories. Since the imagination horizon may vary by tasks and stages, we introduce a novel adaptive lookahead mechanism by trading off the ultimate goal and task progress. The resulting imagined trajectories provide rich signals about future consequences, such as achieved progress and potential conflicts, which are fused with current observations, formulating a partially observable and imaginable Markov decision process to guide policy learning. We instantiate ITP with both training-free and reinforcement-trained variants. Extensive experiments across representative agent benchmarks demonstrate that ITP significantly outperforms competitive baselines. Further analyses validate that our adaptive lookahead largely enhances agents' reasoning capability, providing valuable insights into addressing broader, complex tasks. Our code and data will be publicly available at https://github.com/loyiv/ITP.

Mobile GUI agents have shown strong potential in real-world automation and practical applications. However, most existing agents remain reactive, making decisions mainly from current screen, which limits their performance on long-horizon tasks. Building a world model from repeated interactions enables forecasting action outcomes and supports better decision making for mobile GUI agents. This is challenging because the model must predict post-action states with spatial awareness while remaining efficient enough for practical deployment. In this paper, we propose MobileDreamer, an efficient world-model-based lookahead framework to equip the GUI agents based on the future imagination provided by the world model. It consists of textual sketch world model and rollout imagination for GUI agent. Textual sketch world model forecasts post-action states through a learning process to transform digital images into key task-related sketches, and designs a novel order-invariant learning strategy to preserve the spatial information of GUI elements. The rollout imagination strategy for GUI agent optimizes the action-selection process by leveraging the prediction capability of world model. Experiments on Android World show that MobileDreamer achieves state-of-the-art performance and improves task success by 5.25%. World model evaluations further verify that our textual sketch modeling accurately forecasts key GUI elements.

MuJoCo is a powerful and efficient physics simulator widely used in robotics. One common way it is applied in practice is through Model Predictive Control (MPC), which uses repeated rollouts of the simulator to optimize future actions and generate responsive control policies in real time. To make this process more accessible, the open source library MuJoCo MPC (MJPC) provides ready-to-use MPC algorithms and implementations built directly on top of the MuJoCo simulator. However, MJPC relies on finite differencing (FD) to compute derivatives through the underlying MuJoCo simulator, which is often a key bottleneck that can make it prohibitively costly for time-sensitive tasks, especially in high-DOF systems or complex scenes. In this paper, we introduce the use of Web of Affine Spaces (WASP) derivatives within MJPC as a drop-in replacement for FD. WASP is a recently developed approach for efficiently computing sequences of accurate derivative approximations. By reusing information from prior, related derivative calculations, WASP accelerates and stabilizes the computation of new derivatives, making it especially well suited for MPC's iterative, fine-grained updates over time. We evaluate WASP across a diverse suite of MJPC tasks spanning multiple robot embodiments. Our results suggest that WASP derivatives are particularly effective in MJPC: it integrates seamlessly across tasks, delivers consistently robust performance, and achieves up to a 2$\mathsf{x}$ speedup compared to an FD backend when used with derivative-based planners, such as iLQG. In addition, WASP-based MPC outperforms MJPC's stochastic sampling-based planners on our evaluation tasks, offering both greater efficiency and reliability. To support adoption and future research, we release an open-source implementation of MJPC with WASP derivatives fully integrated.

Collaborative Combat Aircraft (CCAs) are envisioned to enable autonomous Intelligence, Surveillance, and Reconnaissance (ISR) missions in contested environments, where adversaries may act strategically to deceive or evade detection. These missions pose challenges due to model uncertainty and the need for safe, real-time decision-making. Robust Markov Decision Processes (RMDPs) provide worst-case guarantees but are limited by static ambiguity sets that capture initial uncertainty without adapting to new observations. This paper presents an adaptive RMDP framework tailored to ISR missions with CCAs. We introduce a mission-specific formulation in which the CCA alternates between movement and sensing states. Adversarial uncertainty is represented by finite threat prototypes defining observation, exposure, and state-action transition models. Our approach incrementally refines policies by eliminating inconsistent threat models, allowing the CCA to move from worst-case protection toward more efficient mission policies while maintaining robustness. We establish fixed point stability, agreement with nominal planning as credible sets identify the true node-specific threat prototypes, and a conservative expected value guarantee while those prototypes remain credible. Experiments under Gaussian and non-Gaussian threat models across diverse network topologies show higher mission rewards and fewer exposure events compared to nominal and static robust planners.

Current evaluations of Large Language Model (LLM) agents primarily emphasize task completion, often overlooking resource efficiency and adaptability. This neglects a crucial capability: agents' ability to devise and adjust cost-optimal plans in response to changing environments. To bridge this gap, we introduce CostBench, a scalable, cost-centric benchmark designed to evaluate agents' economic reasoning and replanning abilities. Situated in the travel-planning domain, CostBench comprises tasks solvable via multiple sequences of atomic and composite tools with diverse, customizable costs. It also supports four types of dynamic blocking events, such as tool failures and cost changes, to simulate real-world unpredictability and necessitate agents to adapt in real time. Evaluating leading open-sourced and proprietary models on CostBench reveals a substantial gap in cost-aware planning: agents frequently fail to identify cost-optimal solutions in static settings, with even GPT-5 achieving less than 75% exact match rate on the hardest tasks, and performance further dropping by around 40% under dynamic conditions. By diagnosing these weaknesses, CostBench lays the groundwork for developing future agents that are both economically rational and robust.

We study reinforcement learning (RL) with transition look-ahead, where the agent may observe which states would be visited upon playing any sequence of $\ell$ actions before deciding its course of action. While such predictive information can drastically improve the achievable performance, we show that using this information optimally comes at a potentially prohibitive computational cost. Specifically, we prove that optimal planning with one-step look-ahead ($\ell=1$) can be solved in polynomial time through a novel linear programming formulation. In contrast, for $\ell \geq 2$, the problem becomes NP-hard. Our results delineate a precise boundary between tractable and intractable cases for the problem of planning with transition look-ahead in reinforcement learning.

This paper addresses conservatism, limited numerical accuracy, and high computational effort in existing methods ensuring safety by design in online model-based motion generation. The presented method employs a novel captivity-escape zero-sum differential game to adapt the planning model's performance so that resulting reference trajectories are trackable within a prescribed safety margin by a jointly synthesized safety controller. A numerical example demonstrates orders-of-magnitude faster computation and improved numerical accuracy compared to the state of the art.