Risk-Sensitive Planning

Robust partially observable Markov decision processes model agents that act under partial observability while adversarial environment resolves uncertainty in the transition probabilities. Reward objectives such as discounted-sum, long-run average and cumulative reward under finite and infinite horizons allow quantifying the utility of an agent. We consider the problem of solving RPOMDPs under all four reward objectives, where the goal is to decide whether the value of a risk measure with respect to a reward objective exceeds a given threshold. We consider different risk measures, such as (1)~expected value, (2)~mean-variance (MV), (3)~conditional value-at-risk (CVaR), and (4)~entropic risk (ERisk). Our results can be summarized as follows. First, we formalize the class of law-invariant risk measures, that subsume all four risk measures above. Second, we propose a unified framework for solving RPOMDPs with discounted-sum, long-run average and cumulative reward objectives under any law-invariant risk measure, by reducing the problem to solving partially observable stochastic games (POSGs). Our unified framework applies to (s,a)-rectangular RPOMDPs with polytopic uncertainty sets, which we show to be {\em equivalent} to POSGs, for each of the four reward objectives and any law-invariant risk measure. We prove equivalence by designing logspace reductions between the RPOMDP and POSG models, that map strategies to strategies and preserve the distribution of the reward objective, up to a constant rescaling factor. Third, as a corollary, we derive new computational complexity results for R(PO)MDPs and POSGs. In particular, we show that solving (s,a)-rectangular RMDPs is as hard as solving simple stochastic games.

Monte-Carlo Tree Search (MCTS) typically stores only scalar mean estimates, which makes it poorly suited for tail-risk objectives such as conditional value-at-risk (CVaR). We introduce Categorical Thompson Sampling with Optimism (CATSO) and Particle Thompson Sampling with Optimism (PATSO), two distributional MCTS algorithms that maintain finite-support empirical backup laws at Q-edges. CATSO represents Q-edge laws with categorical atoms and Dirichlet Thompson sampling, while PATSO represents them with adaptive particles. Both algorithms select actions using the CVaR of a Thompson-sampled Q-edge law plus a polynomial optimism bonus, and propagate scalar continuation values through visit-weighted averages of child Q-edge CVaR scores. For the finite-depth nested CVaR planning target, we prove an $O(n^{-1/2})$ bound on the root value error after $n$ rollouts, which upper-bounds the risk-sensitive simple regret. CATSO adds a fixed-grid discretization bias, while capped PATSO adds a tunable Wasserstein compression bias. Experiments on stochastic planning benchmarks show that distributional Q-edges improve lower-tail return and reduce catastrophic outcomes when mean-optimal and risk-sensitive behavior differ.

Signal Temporal Logic (STL) specifies robot tasks with spatio-temporal requirements, and its robustness semantics allow planning by trajectory optimization. In practice, robots estimate their state from noisy measurements, and when the information gained from a measurement depends on the state, the robot can actively reduce its uncertainty by planning in the belief space. The resulting problem is, however, generally non-convex, for which gradient-based methods are neither complete nor globally optimal. In this paper, we consider Risk STL (RiSTL) planning in Gaussian belief space and show that an information-form parameterization of the belief, together with a convex relaxation of the belief dynamics, yields a mixed-integer convex program (MICP). We prove that the MICP is sound and complete, and that the relaxation preserves the globally optimal input trajectories. We validate the effectiveness of our method in numerical simulations.

Safe navigation in dynamic environments requires robots to plan under obstacle predictions whose errors are uncertain, non-stationary, and can induce rare but safety-critical failures. Existing control-barrier-function safety filters can reject immediately unsafe controls, but they provide little guidance on when the current finite-horizon planning mode itself is becoming unsafe as prediction uncertainty evolves. We propose Conformal Event-Triggered Risk-Certified Replanning (CERT-Replan), a framework that uses calibrated barrier risk as an early-warning signal for replanning. CERT-Replan calibrates horizon-indexed obstacle-prediction residuals online and uses the resulting uncertainty radii to evaluate dynamic-obstacle safety margins. A one-step safety filter protects the next applied control, while a horizon-level risk monitor evaluates the upper-tail CVaR of predicted barrier-violation losses along the current MPC rollout. When this risk exceeds an allocated budget, CERT-Replan rejects the current planning mode and selects a lower-risk alternative, such as a different speed profile, corridor, or homotopy class, rather than repeatedly correcting the same nominal plan. In a non-stationary benchmark, CERT-Replan achieves an $83.3\%$ collision reduction relative to the safety-filter-only baseline \textcolor{black}{and a $77.8\%$ reduction relative to simple replanning triggers}, while reducing average safety-filter intervention by $32.4\%$. \textcolor{black}{With Trajectron++, CERT-Replan achieves $96\%$ collision-free operation. Hardware experiments and onboard runtime profiling demonstrate computational feasibility.}

Risk-aware planners score paths on uncertain elevation maps using the path cost's mean and standard deviation. Modeling rigid contact, however, requires computing a maximum over several uncertain cells. First-order propagation loses accuracy here by differentiating at only a single cell, while Monte Carlo sampling requires a full path evaluation per draw. We compute the moments of that contact maximum in closed form using Clark's pairwise recursion. By tracking each contact's covariance against the shared map cells, we propagate the smooth remainder using exact Gaussian quadratic-form identities. A contest-depth calibration, fitted once on two design traverses, closes the aggregate standard-deviation shortfall that remains. On 317 held-out rover path segments, scored against a Monte Carlo reference from the same belief, every pre-registered criterion was met. The corrected Clark fold cuts the median error of the mean from linearization's 2.3% to 0.19% and attains the lowest error in the conditional value at risk (CVaR) at the 90% level of every method tested. A benchmark plan costs just 5.5 microseconds on a GPU. These accuracy gains concentrate at contested contacts. While they seldom change which path is chosen on this terrain, the fold still selects the reference-best path in 98% of decisions against linearization's 93 to 96%. On a second dataset the mean transfers, though the risk number does not.

Agile flight in unknown, cluttered, and dynamic environments requires a planner that knows where and when danger will appear, not only that a trajectory is dangerous. One-stage learning-based planners trained with differentiable privileged costs are fast and expert-free, but the only signal reaching their encoder is a scalar trajectory cost with no spatial or temporal structure, so avoidance degrades into late reactive maneuvers. We present RiskFly, a one-stage planner that predicts risk in the same space in which it acts. A dual-stream observation pairs a short depth sequence with a frustum-aligned inverted spherical range-map sequence, whose angular cells match the end-state proposals one to one. An auxiliary head regresses a frustum-aligned spatio-temporal risk field, supervised by a privileged closest-point-of-approach (CPA) target. This self-predicted field is queried differentiably along the instantiated quintic trajectory at its own arrival times, and also enters the training objective, so representation supervision and planning gradients meet in a single space. Privileged signals are discarded at deployment, and the planner runs map-free from onboard depth and proprioception. Extensive simulation and zero-shot real-world flights on resource-constrained platforms show higher success rates at comparable end-to-end latency.

Online POMDP planners optimize the expected cumulative cost, which can mask dangerous states when the belief places significant mass on high-cost states. Existing risk-averse methods apply static or dynamic Conditional Value at Risk (CVaR) to the value function, capturing trajectory-level risk, but share two gaps: (i) by retaining the immediate cost as an expectation of a state-dependent cost over the belief, the risk within the belief is left unaddressed; and (ii) by modifying the value function, they require new tailored algorithms rather than reusing existing expectation-based planners. We instead apply CVaR to the immediate cost over the belief at each step, directly targeting per-step uncertainty about the current state. The standard expected cumulative return is retained as the objective, so the resulting problem has a standard MDP structure: any expectation-based POMDP planner can be made risk-sensitive by changing only the cost computation. We inherit finite-time guarantees for policy evaluation and sparse sampling---with estimation error independent of the risk level---and, as our central theoretical result, prove a finite-time bound on the gap between the particle belief MDP surrogate and the original POMDP, which together yield an end-to-end guarantee from the true POMDP value to the algorithmic estimate. In the risk-neutral limit, the formulation recovers standard expectation-based planning.

Hazardous robotic exploration requires robots to map spatial risks, such as unsafe terrain, radiation, fire, mines, or structural damage, while operating where collecting information can itself cause failure. A highly informative path may expose the robot to hazards, terminate execution, and prevent future observations. Hazardous exploration therefore requires deciding not only where uncertainty is largest, but when reducing it is worth the risk. This paper introduces a valuation-layer view of this problem. We keep the belief update, sensor model, physical risk model, and finite-horizon informative planner fixed, and change only the scalar objective used to rank feasible paths. Within this framework, we introduce a risk-augmented Behavioral Information objective based on Prelec probability weighting, yielding an interpretable family of conservative-to-aggressive information-risk valuations. Theoretically, we show that valuation parameters create switching boundaries between high-information/high-risk and lower-information/lower-risk paths, and induce a transformed Pareto-frontier structure over feasible exploration policies. Large-scale failure-truncated grid-world experiments show that valuation alone reshapes the information-risk frontier. Shannon information planning remains a strong raw-information baseline, while risk-aware objectives can reduce hazard exposure and robot losses by avoiding failures that truncate future sensing. Risk-augmented Behavioral valuation is Pareto-competitive with standard risk-aware baselines and provides interpretable conservative and intermediate regimes. These results support a framework in which robots reason not only about how much uncertainty an action reduces, but whether that reduction is worth the risk required to obtain it.

Interactive medical diagnosis dynamically acquires patient information through multiple rounds of questioning, supporting accurate, efficient, and safe clinical decisions under incomplete evidence. Existing methods commonly guide information acquisition with predictive uncertainty or label ambiguity, but overlook the asymmetric clinical risk of missing severe diseases and lack unified long-horizon planning over whether to continue asking questions or commit to a diagnosis. To address these limitations, we propose Severity-Aware Conformal Clinical Planning, which formulates interactive diagnosis as a risk-sensitive sequential decision problem. The framework maintains complementary diagnostic, safety, and masked-evidence beliefs; calibrates turn-specific diagnostic prediction sets and severity-weighted differential-diagnosis risk on held-out diagnostic trajectories; and introduces the calibrated clinical risk into Monte Carlo Tree Search to jointly evaluate long-horizon Ask and Commit trajectories. Experiments on DDXPlus and MediQ show that our method achieves more accurate diagnoses with fewer questions across multiple large language models, while improving differential-diagnosis quality and reducing high-risk errors in severe cases. These findings validate the value of using clinical risk, rather than predictive uncertainty alone, as a planning signal and demonstrate the effectiveness of the proposed framework for information acquisition and risk-aware diagnostic decision making. They also motivate future work on clinical-risk-oriented interactive diagnosis and information-acquisition methods.

How cautious should an agent be while it is still learning its environment? We propose RATTL (Risk-Adversarial Total-Reward Learning), which ties caution to epistemic uncertainty: the agent holds a Bayesian posterior over unknown dynamics and plans against a Wasserstein ambiguity set whose radius is a monotone function of that posterior. The radius contracts with evidence, so behaviour interpolates continuously between worst-case robustness and risk-neutral total-reward maximization. The design follows the duality underlying the Entropic Value-at-Risk, which converts the choice of a risk level into the choice of an ambiguity radius. We show the resulting planning problem is well posed under transience and compactness conditions, and prove a Safety Sandwich: the RATTL value lies between the uninformed robust value and the full- knowledge optimum, with a gap that vanishes as the posterior concentrates. In a canonical binary-hazard instance, the induced criterion reduces to Conditional Value-at-Risk at a level set by the posterior entropy. A worked example shows the agent deferring the efficient action until a sharp identification threshold. RATTL targets runtime safety for agents, including LLM-based systems, acting under uncertainty.

For autonomous space exploration, robotic agents need to perform motion planning in which environmental interactions may be unknown. Learning these interactions, such as terrain mechanics for wheeled robots, can introduce uncertainties that lead to risky motion plans and potentially hazardous operations or mission failures. Moreover, uncertainties induced by perception-based systems can exacerbate the problem of safe motion planning. In this letter, we address the problem of performing cost-optimal kinodynamic motion planning with risk awareness. We approach this in two steps. First, a sampling-based planner (AO-RRT) generates a dynamically feasible, risk-aware, and asymptotically cost-optimal trajectory. Second, we formulate motion planning as a nonlinear optimization problem and solve it using sequential convex programming (SCP), using the AO-RRT trajectory as an initial solution. By quantifying risk using conditional value-at-risk (CVaR), we demonstrate a reduction in risk by over $\sim$97% across trajectories in simulation and hardware experiments.

We study finite-horizon MDP planning under root-based (resolute) risk objectives that apply a rank-dependent functional to the distribution of total returns. Such objectives are non-linear in the return distribution and generally break Bellman optimality, so direct optimization by scenario-tree enumeration is intractable. We propose ERQDP, an enumeration-free and sampling-free method that solves a rank--quantile surrogate via exact DP (Dynamic Programming), evaluates candidate policies exactly by DP over return Probability Mass Functions (PMFs) on a discretized return grid (with an explicit rounding bound), and refines the surrogate in an anytime loop that reports an explicit upper--lower gap (certificate) for the target objective up to discretization budgets. Across tested benchmarks, ERQDP returns certified solutions or explicit residual gaps, enables fast risk-parameter sweeps with substantial runtime gains, and supports both risk-averse and risk-seeking behaviors.

This paper addresses multi-objective kinodynamic planning in environments with stochastic hybrid adversaries that probabilistically transition to adversarial modes based on the ego state. The goal is to construct the Pareto-front of paths that trade off execution cost and the probability of safety constraint violation (risk). Existing chance-constrained planners evaluate risk over open-loop trajectories, yielding overly conservative solutions that fail to account for ego-agent reactivity. To address this limitation, we shift the planning space to sequences of closed-loop policies, and integrate sample-based risk evaluation directly into tree construction via Monte-Carlo particle rollouts. We first introduce Stochastic Multi-Objective RRT (SMO-RRT), for which we prove probabilistic completeness, followed by Stochastic Multi-Objective Stable Sparse RRT (SMO-SST), which leverages selective pruning to improve numerical performance at the cost of completeness. For both algorithms, we derive a finite-sample bound on the probability of chance constraint violation for systems with non-Gaussian, state-dependent uncertainty, enabling probabilistically safe planning in a broad class of environments applicable to multi-agent systems, social navigation, and autonomous driving.

We study general-utility Markov decision processes (GUMDPs) with risk-aware objectives. In this framework, an agent aims to optimize a risk measure of the distribution of objective values, where the objective function depends on the frequency of visitation of states induced by the agent's policy. First, we motivate, propose, and formalize risk-aware GUMDPs, which enable agents and decision makers to trade off expected performance by risk aversion while benefiting from the rich set of objectives that can be cast under the framework of GUMDPs. We focus our attention on the entropic risk measure (ERM). Second, we show how we can solve risk-aware GUMDPs with ERM objectives by resorting to online planning techniques. In particular, we propose an approach based on Monte Carlo Tree Search (MCTS) to provably solve risk-aware GUMDPs up to any desired accuracy. Third, we provide a set of experimental results showcasing that our approach is successful when optimizing for a spectrum of risk-aware behaviors in the context of GUMDPs under diverse tasks (standard MDPs, maximum state entropy exploration, imitation learning, and multi-objective MDPs).

Offline reinforcement learning enables policy learning from fixed datasets without additional environment interaction, making it appealing for safety-critical applications where online exploration is costly or unsafe. Diffusion-based decision-making methods have recently achieved strong performance in offline RL by modeling rich, multimodal trajectory distributions. However, existing diffusion planners are typically risk-neutral and therefore may overlook rare but catastrophic outcomes that are crucial in real-world deployment. In this work, we propose RS-Diffuser, a risk-sensitive offline diffusion planning framework that combines diffusion-based trajectory generation with distributional value critics. RS-Diffuser learns a diffusion planner over future state trajectories, a separate inverse dynamics model for action decoding, and a Monte Carlo distributional critic that estimates the full return distribution of candidate plans through quantile regression. At sampling time, we incorporate a risk-sensitive guidance signal into the denoising process, using gradients computed from tail-aware objectives such as Conditional Value at Risk to steer generation toward desired risk profiles. As a result, a single trained model can flexibly produce risk-averse, risk-neutral, or risk-seeking behaviors by changing only the inference-time risk parameter. Extensive experiments on risk-sensitive D4RL and risky robot navigation benchmarks demonstrate that RS-Diffuser achieves state-of-the-art performance, improving both overall return and worst-case robustness while reducing safety violations.

Complex, dynamic, and interactive driving environments pose significant challenges for autonomous driving, primarily due to the pervasive uncertainty of surrounding traffic. A fundamental bottleneck in current systems is the disconnect between highly expressive uncertainty modeling and interpretable, safe motion planning. In this paper, we propose a novel sample-conditioned differentiable planning framework that bridges this gap by explicitly incorporating diffusion-generated future trajectories into the optimization process. Rather than compressing predictions into a single deterministic future or relying on black-box end-to-end architectures, our approach leverages a conditional diffusion model to generate a diverse set of plausible future scenarios. Crucially, these samples are directly fed into a differentiable planner, which explicitly mitigates predictive uncertainty via an empirical Conditional Value-at-Risk (CVaR) tail-risk constraint. This allows the planner to optimize a physically interpretable trajectory that is robust to rare yet safety-critical interactions. Furthermore, we introduce a directed graph representation for scene context that yields substantial improvements in both predictive effectiveness and computational efficiency. Validated through extensive open-loop and closed-loop evaluations on the Waymo Open Motion and Argoverse 2 datasets, our framework significantly outperforms state-of-the-art baselines in safety, efficiency, and ride comfort.

Mobile robots can fail before they collide: a velocity that is safe now may commit the robot to a passage that moving obstacles will soon close. We study this predictive near-miss commitment problem and propose Risk-Sensitive Conjectural Scenario Planning (RCSP), a planning layer that evaluates candidate commands against plausible short-horizon obstacle futures. RCSP maintains a lightweight belief over local motion conjectures, samples future interactions, penalizes high-risk tails, and executes through a local safety check. In controlled MuJoCo bottleneck tasks, the RCSP planner reaches the goal without collisions and yields higher secondary safety and path-quality point estimates than a non-adaptive predictor, with additional latency. In ROS2/Gazebo, adding the local safety layer to a standard Nav2 stack reduces dynamic near-miss failures. On official DynaBARN/Jackal transfer, tuned DWA and TEB remain stronger on strict benchmark success, revealing the boundary of the approach. These simulation results position RCSP as a predictive-risk module that complements existing navigation stacks in dynamic bottleneck regimes.

We present MC-Risk, a planner-aligned, multi-component risk field on a bird's-eye-view grid that yields early, calibrated, and class-aware risk localization. MC-Risk linearly composes three interpretable modules: (i) a motorized-agent field that fuses a black-box multimodal trajectory predictor with an analytic Gaussian-torus construction whose lateral width grows with speed/curvature and whose height attenuates with look-ahead; (ii) a VRU risk field that replaces isotropic pedestrian blobs with a forward-biased anisotropic kernel aligned to heading and speed; and (iii) a road penalty field that exploits full HD-map topology, imposing an off-road penalty and lane-aware risk exposure for same/opposite directions. We conduct, to our knowledge, the first standardized quantitative evaluation of a risk-field formulation on RiskBench's collision subset. MC-Risk attains the best overall risk localization and the earliest hazard indication. Finally, we demonstrate a plug-and-play planning interface by using the field as an MPC cost density, enabling risk-aware trajectory generation without additional training.

Many safety-critical control problems are modeled as risk-sensitive partially observable Markov decision processes, where the controller must make decisions from incomplete observations while balancing task performance against safety risk. Although belief-space planning provides a principled solution, maintaining and planning over beliefs can be computationally costly and sensitive to model specification in practical domains. We propose a lightweight risk-gated reinforcement learning approximation for risk-sensitive control under partial observability. The method constructs a compact finite-history proxy state and learns an action-conditioned predictor of near-term safety violation. This predicted candidate-action risk is used in two complementary ways: as a risk penalty during value learning, and as a decision-time gate that interpolates between optimistic and conservative ensemble value estimates. As a result, low-risk actions are evaluated closer to reward-seeking estimates, while high-risk actions are evaluated more conservatively. We evaluate the approach in two safety-critical partially observable domains: automated glucose regulation and safety-constrained navigation. Across adult and adolescent glucose-control cohorts, the method improves overall glycemic tradeoffs and substantially reduces runtime relative to a belief-space planning baseline. On Safety-Gym navigation benchmarks, it achieves a more favorable reward-cost balance than unconstrained RL and several standard safe-RL baselines. These results suggest that action-conditioned near-term risk can provide an effective local signal for approximate risk-sensitive POMDP control when full belief-space planning is impractical.

In production Wide-Area Networks (WANs), correlated failures dominate availability losses, forcing operators to reserve large safety margins that leave substantial capacity underutilized. Achieving high utilization under strict availability targets therefore requires risk-aware Traffic Engineering (TE) over dozens to hundreds of probabilistic failure scenarios-yet solving this problem at operational timescales remains elusive. We demonstrate that existing risk-aware formulations can be unified under an embedded Sort-and-Select structure, exposing a fundamental trade-off between expressiveness and tractability: classical optimizers either restrict scenario selection for efficiency or incur prohibitive decomposition costs. While deep learning appears promising, prior Deep TE methods mainly target maximum link utilization and rely on scaling-based feasibility, which fundamentally breaks under explicit capacity constraints and scenario-dependent risk. We present NeuroRisk, a physics-informed deep unrolled optimizer that exploits the structure of Sort-and-Select. NeuroRisk enforces feasibility via gated edge-local reservations and represents scenario sets through permutation-invariant, gradient-aligned cues. Evaluations on production-style WANs show that NeuroRisk achieves small optimality gaps relative to the solver with orders of magnitude speedup $(10^2- 10^5 \times)$ on risk objectives, while outperforming neural baselines on nominal throughput.

Temporally contrastive representation learning induces a latent structure capable of reducing long-horizon planning to inference in a low-dimensional linear system. However, existing contrastive planning work learns a single latent geometry which cannot distinguish multiple valid behaviors trading task efficiency against risk exposure for the same start-goal query. We introduce MoMo, a preference-conditioned contrastive planner allowing a scalar user preference to continuously modulate plan conservativeness at inference time, without retraining. MoMo learns a joint conditioning of the representation geometry and latent prediction operator via Feature-Wise Linear Modulation and low-rank neural modulation, respectively. We show that our formulation preserves the probability density ratio encoded in the representation space that is required for inference-driven contrastive planning, further retaining its inference-time efficiency. Across six environments, MoMo smoothly adapts plan safety according to user preferences, yielding improved temporal and preferential consistency over state augmentation baselines.

Contact variability, sensing uncertainty, and external disturbances make grasp execution stochastic. Expected-quality objectives ignore tail outcomes and often select grasps that fail under adverse contact realizations. Risk-sensitive POMDPs address this failure mode, but many use particle-filter beliefs that scale poorly, obstruct gradient-based optimization, and estimate Conditional Value-at-Risk (CVaR) with high-variance approximations. We instead formulate grasp acquisition as variational inference over latent contact parameters and object pose, representing the belief with a differentiable Gaussian mixture. We use Gumbel-Softmax component selection and location-scale reparameterization to express samples as smooth functions of the belief parameters, enabling pathwise gradients through a differentiable CVaR surrogate for direct optimization of tail robustness. In simulation, our variational neural belief improves robust grasp success under contact-parameter uncertainty and exogenous force perturbations while reducing planning time by roughly an order of magnitude relative to particle-filter model-predictive control. On a serial-chain robot arm with a multifingered hand, we validate grasp-and-lift success under object-pose uncertainty against a Gaussian baseline. Both methods succeed on the tested perturbations, but our controller terminates in fewer steps and less wall-clock time while achieving a higher tactile grasp-quality proxy. Our learned belief also calibrates risk more accurately, keeping mean absolute calibration error below 0.14 across tested simulation regimes, compared with 0.58 for a Cross-Entropy Method planner.

Multi-robot systems can be extremely efficient for accomplishing team-wise tasks by acting concurrently and collaboratively. However, most existing methods either assume static task features or simply replan when environmental changes occur. This paper addresses the challenging problem of coordinating multi-robot systems for collaborative tasks involving dynamic and moving targets. We explicitly model the uncertainty in target motion prediction via Conformal Prediction(CP), while respecting the spatial-temporal constraints specified by Linear Temporal Logic (LTL). The proposed framework (UMBRELLA) combines the Monte Carlo Tree Search (MCTS) over partial plans with uncertainty-aware rollouts, and introduces a CP-based metric to guide and accelerate the search. The objective is to minimize the Conditional Value at Risk (CVaR) of the average makespan. For tasks released online, a receding-horizon planning scheme dynamically adjusts the assignments based on updated task specifications and motion predictions. Spatial and temporal constraints among the tasks are always ensured, and only partial synchronization is required for the collaborative tasks during online execution. Extensive large-scale simulations and hardware experiments demonstrate substantial reductions in both the average makespan and its variance by 23% and 71%, compared with static baselines.

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.