Belief-Space Planning

Coordinating multiple autonomous agents to explore and serve spatially heterogeneous demand requires jointly learning unknown spatial patterns and planning trajectories that maximize task performance. Pure model-based approaches provide structured uncertainty estimates but lack adaptive policy learning, while deep reinforcement learning often suffers from poor sample efficiency when spatial priors are absent. This paper presents a hybrid belief-reinforcement learning (HBRL) framework to address this gap. In the first phase, agents construct spatial beliefs using a Log-Gaussian Cox Process (LGCP) and execute information-driven trajectories guided by a Pathwise Mutual Information (PathMI) planner with multi-step lookahead. In the second phase, trajectory control is transferred to a Soft Actor-Critic (SAC) agent, warm-started through dual-channel knowledge transfer: i) belief state transfer supplies spatial uncertainty, and ii) replay buffer seeding provides demonstration trajectories generated during LGCP exploration. A variance-normalized overlap penalty enables coordinated coverage through shared belief state, permitting cooperative sensing in high-uncertainty regions while discouraging redundant coverage in well-explored areas. The framework is instantiated in two scenarios: multi-Unmanned Aerial Vehicle (UAV) wireless service provisioning, and mobility-on-demand sensing over measured New York City taxi demand. In the wireless scenario it achieves 10.8% higher cumulative reward and takes 38% fewer episodes to reach the reward level of the baselines, with ablation studies confirming that dual-channel transfer outperforms either channel alone; the taxi scenario yields consistent gains with all algorithmic components unchanged.

In the real world, planning is often challenged by distribution shifts. As such, a model of the environment obtained under one set of conditions may no longer remain valid as the distribution of states or the environment dynamics change, which in turn causes previously learned strategies to fail. In this work, we propose a theoretical framework for planning under partial observability using Partially Observable Markov Decision Processes (POMDPs) formulated using causal knowledge. By representing shifts in the environment as interventions on this causal POMDP, the framework enables evaluating plans under hypothesized changes and actively identifying which components of the environment have been altered. We show how to maintain and update a belief over both the latent state and the underlying domain, and we prove that the value function remains piecewise linear and convex (PWLC) in this augmented belief space. Preservation of PWLC under distribution shifts has the advantage of maintaining the tractability of planning via $α$-vector-based POMDP methods.

We present POMDPPlanners, an open-source Python package for empirical evaluation of Partially Observable Markov Decision Process (POMDP) planning algorithms. The package integrates state-of-the-art planning algorithms, a suite of benchmark environments with safety-critical variants, automated hyperparameter optimization via Optuna, persistent caching with failure recovery, and configurable parallel simulation -- reducing the overhead of extensive simulation studies. POMDPPlanners is designed to enable scalable, reproducible research on decision-making under uncertainty, with particular emphasis on risk-sensitive settings where standard toolkits fall short.

Vision-language-action models must enable agents to execute long-horizon tasks under partial observability. However, most existing approaches remain observation-driven, relying on short context windows or repeated queries to vision-language models (VLMs). This leads to loss of task progress, action repetition under perceptual aliasing, and high inference latency. While semantic grounding is important, long-horizon manipulation fundamentally requires persistent, action-conditioned state representations. Current VLAs lack such representations and exhibit limited temporal and physical reasoning, making them ill-suited for multi-stage control. This paper introduces RB-VLA, a belief-centric architecture trained with self-supervised world-model objectives that maintains a compact latent state encoding task-relevant history, dynamics, and object interactions. Queried once per task, the VLM provides high-level intent, while the belief tracks task progress and enables phase-aware, causally grounded control under partial observability without storing raw observations or scaling memory with time. The belief and intent jointly condition a diffusion policy for robust closed-loop execution. RB-VLA outperforms prior VLAs on long-horizon benchmarks, achieving 52.5 percent and 37.5 percent higher success rates on multi-stage pick-and-place and stacking tasks, respectively, compared to pi_0. It also reduces inference latency by up to five times relative to baselines and eliminates memory growth across timesteps observed in existing VLAs. Ablations show the belief module is the primary driver of performance, increasing success rates from 32.5 percent without belief to 77.5 percent with belief.

Autonomous driving in complex traffic requires reasoning under uncertainty. Common approaches rely on prediction-based planning or risk-aware control, but these are typically treated in isolation, limiting their ability to capture the coupled nature of action and inference in interactive settings. This gap becomes especially critical in uncertain scenarios, where simply reacting to predictions can lead to unsafe maneuvers or overly conservative behavior. Our central insight is that safe interaction requires not only estimating human behavior but also shaping it when ambiguity poses risks. To this end, we introduce a hierarchical belief model that structures human behavior across coarse discrete intents and fine motion modes, updated via Bayesian inference for interpretable multi-resolution reasoning. On top of this, we develop an active probing strategy that identifies when multimodal ambiguity in human predictions may compromise safety and plans disambiguating actions that both reveal intent and gently steer human decisions toward safer outcomes. Finally, a runtime risk-evaluation layer based on Conditional Value-at-Risk (CVaR) ensures that all probing actions remain within human risk tolerance during influence. Our simulations in lane-merging and unsignaled intersection scenarios demonstrate that our approach achieves higher success rates and shorter completion times compared to existing methods. These results highlight the benefit of coupling belief inference, probing, and risk monitoring, yielding a principled and interpretable framework for planning under uncertainty.