arXiv subjects

Vadim Indelman

Publications and source records attributed to Vadim Indelman.

At least 19 recordsLinked to original sources

arXiv2026

Graph Sparse Sampling: Breaking the Curse of the Horizon in Continuous MDP Planning

Planning under uncertainty in continuous domains is essential for autonomous systems, yet computationally demanding. Tree-based search methods such as Monte Carlo Tree Search (MCTS) remain popular, but their branching structure can require sampling budgets that grow exponentially with lookahead depth in the worst case. From a tree perspective, continuous state or action spaces become especially challenging, since the planner must decide where to search in an infinite branching hierarchy. We propose Graph Sparse Sampling (GSS), an online planning algorithm that shares sampled futures across many candidate decisions, rather than sampling separate successors for each candidate action. This branch-free graph exposes large GPU-friendly batches, while using heuristics to focus computation. We prove finite-sample performance guarantees for GSS covering full-rank or low-rank generative simulators via smoothed backups, and discrete or sampled continuous action spaces. Under suitable overlap, regularity, and action-coverage conditions, these bounds have polynomial dependence on the planning horizon, formalizing when shared futures can avoid the exponential horizon dependence of tree-shaped sparse sampling. We demonstrate continuous-control simulations where GSS substantially outperforms tree-based planners on long horizons or achieves near-optimal performance, supporting no-branching graph planning as a complementary design principle for online control.

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arXiv2026

Finite-Time Analysis of MCTS in Continuous POMDP Planning

This paper presents a finite-time analysis for Monte Carlo Tree Search (MCTS) in Partially Observable Markov Decision Processes (POMDPs), with probabilistic concentration bounds in both discrete and continuous observation spaces. While MCTS-style solvers such as POMCP achieve empirical success in many applications, rigorous finite-time guarantees remain an open problem due to the nonstationarity and the interdependencies induced by heuristic action selection (e.g., UCB). In the discrete setting, we address these challenges by extending the polynomial exploration bonus to UCB in POMDP setting, yielding polynomial concentration bounds for the empirical value estimation at the root node. For continuous observation spaces, we introduce an abstract partitioning framework and propose a finite-time bound on partitioning loss. Under mild conditions, we prove highprobability bound on value estimates in POMDPs with continuous observation space. Specifically, we propose Voro-POMCPOW, a variant of POMCPOW with f inite-time guarantees that adaptively partitions the continuous observation space using Voronoi cells. This approach maintains a finite branching factor while preserving the original observation generator. Empirical validation demonstrates that the proposed Voro-POMCPOW shows competitive performance while providing theoretical guarantees. Although our analysis focuses on continuous POMDPs, the techniques developed herein are also applicable to continuous MDPs, closing another gap on the MDP side.

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arXiv2026

Open-loop POMDP Simplification and Safe Skipping of Replanning with Formal Performance Guarantees

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.

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arXiv2026

Accelerated Online Risk-Averse Policy Evaluation in POMDPs with Theoretical Guarantees and Novel CVaR Bounds

Risk-averse decision-making under uncertainty in partially observable domains is a central challenge in artificial intelligence and is essential for developing reliable autonomous agents. The formal framework for such problems is the partially observable Markov decision process (POMDP), where risk sensitivity is introduced through a risk measure applied to the value function, with Conditional Value-at-Risk (CVaR) being a particularly significant criterion. However, solving POMDPs is computationally intractable in general, and approximate methods rely on computationally expensive simulations of future agent trajectories. This work introduces a theoretical framework for accelerating CVaR value function evaluation in POMDPs with formal performance guarantees. We derive new bounds on the CVaR of a random variable X using an auxiliary random variable Y, under assumptions relating their cumulative distribution and density functions; these bounds yield interpretable concentration inequalities and converge as the distributional discrepancy vanishes. Building on this, we establish upper and lower bounds on the CVaR value function computable from a simplified belief-MDP, accommodating general simplifications of the transition dynamics. We develop estimators for these bounds within a particle-belief MDP framework with probabilistic guarantees, and employ them for acceleration via action elimination: actions whose bounds indicate suboptimality under the simplified model are safely discarded while ensuring consistency with the original POMDP. Empirical evaluation across multiple POMDP domains confirms that the bounds reliably separate safe from dangerous policies while achieving substantial computational speedups under the simplified model.

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arXiv2026

POMDPPlanners: Open-Source Package for POMDP Planning

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.

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arXiv2026

Online Risk-Averse Planning in POMDPs Using Iterated CVaR Value Function

We study risk-sensitive planning under partial observability using the dynamic risk measure Iterated Conditional Value-at-Risk (ICVaR). A policy evaluation algorithm for ICVaR is developed with finite-time performance guarantees that do not depend on the cardinality of the action space. Building on this foundation, three widely used online planning algorithms--Sparse Sampling, Particle Filter Trees with Double Progressive Widening (PFT-DPW), and Partially Observable Monte Carlo Planning with Observation Widening (POMCPOW)--are extended to optimize the ICVaR value function rather than the expectation of the return. Our formulations introduce a risk parameter $α$, where $α= 1$ recovers standard expectation-based planning and $α< 1$ induces increasing risk aversion. For ICVaR Sparse Sampling, we establish finite-time performance guarantees under the risk-sensitive objective, which further enable a novel exploration strategy tailored to ICVaR. Experiments on benchmark POMDP domains demonstrate that the proposed ICVaR planners achieve lower tail risk compared to their risk-neutral counterparts.

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arXiv2025

Towards Optimal Performance and Action Consistency Guarantees in Dec-POMDPs with Inconsistent Beliefs and Limited Communication

Multi-agent decision-making under uncertainty is fundamental for effective and safe autonomous operation. In many real-world scenarios, each agent maintains its own belief over the environment and must plan actions accordingly. However, most existing approaches assume that all agents have identical beliefs at planning time, implying these beliefs are conditioned on the same data. Such an assumption is often impractical due to limited communication. In reality, agents frequently operate with inconsistent beliefs, which can lead to poor coordination and suboptimal, potentially unsafe, performance. In this paper, we address this critical challenge by introducing a novel decentralized framework for optimal joint action selection that explicitly accounts for belief inconsistencies. Our approach provides probabilistic guarantees for both action consistency and performance with respect to open-loop multi-agent POMDP (which assumes all data is always communicated), and selectively triggers communication only when needed. Furthermore, we address another key aspect of whether, given a chosen joint action, the agents should share data to improve expected performance in inference. Simulation results show our approach outperforms state-of-the-art algorithms.

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arXiv2025

Online POMDP Planning with Anytime Deterministic Optimality Guarantees

Decision-making under uncertainty is a critical aspect of many practical autonomous systems due to incomplete information. Partially Observable Markov Decision Processes (POMDPs) offer a mathematically principled framework for formulating decision-making problems under such conditions. However, finding an optimal solution for a POMDP is generally intractable. In recent years, there has been a significant progress of scaling approximate solvers from small to moderately sized problems, using online tree search solvers. Often, such approximate solvers are limited to probabilistic or asymptotic guarantees towards the optimal solution. In this paper, we derive a deterministic relationship for discrete POMDPs between an approximated and the optimal solution. We show that at any time, we can derive bounds that relate between the existing solution and the optimal one. We show that our derivations provide an avenue for a new set of algorithms and can be attached to existing algorithms that have a certain structure to provide them with deterministic guarantees with marginal computational overhead. In return, not only do we certify the solution quality, but we demonstrate that making a decision based on the deterministic guarantee may result in superior performance compared to the original algorithm without the deterministic certification.

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arXiv2025

Online Hybrid-Belief POMDP with Coupled Semantic-Geometric Models

Robots operating in complex and unknown environments frequently require geometric-semantic representations of the environment to safely perform their tasks. While inferring the environment, they must account for many possible scenarios when planning future actions. Since objects' class types are discrete and the robot's self-pose and the objects' poses are continuous, the environment can be represented by a hybrid discrete-continuous belief which is updated according to models and incoming data. Prior probabilities and observation models representing the environment can be learned from data using deep learning algorithms. Such models often couple environmental semantic and geometric properties. As a result, semantic variables are interconnected, causing semantic state space dimensionality to increase exponentially. In this paper, we consider planning under uncertainty using partially observable Markov decision processes (POMDPs) with hybrid semantic-geometric beliefs. The models and priors consider the coupling between semantic and geometric variables. Within POMDP, we introduce the concept of semantically aware safety. Obtaining representative samples of the theoretical hybrid belief, required for estimating the value function, is very challenging. As a key contribution, we develop a novel form of the hybrid belief and leverage it to sample representative samples. We show that under certain conditions, the value function and probability of safety can be calculated efficiently with an explicit expectation over all possible semantic mappings. Our simulations show that our estimates of the objective function and probability of safety achieve similar levels of accuracy compared to estimators that run exhaustively on the entire semantic state-space using samples from the theoretical hybrid belief. Nevertheless, the complexity of our estimators is polynomial rather than exponential.

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arXiv2025

Online Robust Planning under Model Uncertainty: A Sample-Based Approach

Online planning in Markov Decision Processes (MDPs) enables agents to make sequential decisions by simulating future trajectories from the current state, making it well-suited for large-scale or dynamic environments. Sample-based methods such as Sparse Sampling and Monte Carlo Tree Search (MCTS) are widely adopted for their ability to approximate optimal actions using a generative model. However, in practical settings, the generative model is often learned from limited data, introducing approximation errors that can degrade performance or lead to unsafe behaviors. To address these challenges, Robust MDPs (RMDPs) offer a principled framework for planning under model uncertainty, yet existing approaches are typically computationally intensive and not suited for real-time use. In this work, we introduce Robust Sparse Sampling (RSS), the first online planning algorithm for RMDPs with finite-sample theoretical performance guarantees. Unlike Sparse Sampling, which estimates the nominal value function, RSS computes a robust value function by leveraging the efficiency and theoretical properties of Sample Average Approximation (SAA), enabling tractable robust policy computation in online settings. RSS is applicable to infinite or continuous state spaces, and its sample and computational complexities are independent of the state space size. We provide theoretical performance guarantees and empirically show that RSS outperforms standard Sparse Sampling in environments with uncertain dynamics.

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arXiv2025

Bounding Conditional Value-at-Risk via Auxiliary Distributions with Bounded Discrepancies

In this paper, we develop a theoretical framework for bounding the CVaR of a random variable $X$ using another related random variable $Y$, under assumptions on their cumulative and density functions. Our results yield practical tools for approximating $\operatorname{CVaR}_α(X)$ when direct information about $X$ is limited or sampling is computationally expensive, by exploiting a more tractable or observable random variable $Y$. Moreover, the derived bounds provide interpretable concentration inequalities that quantify how the tail risk of $X$ can be controlled via $Y$.

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arXiv2025

Simplifying Complex Observation Models in Continuous POMDP Planning with Probabilistic Guarantees and Practice

Solving partially observable Markov decision processes (POMDPs) with high dimensional and continuous observations, such as camera images, is required for many real life robotics and planning problems. Recent researches suggested machine learned probabilistic models as observation models, but their use is currently too computationally expensive for online deployment. We deal with the question of what would be the implication of using simplified observation models for planning, while retaining formal guarantees on the quality of the solution. Our main contribution is a novel probabilistic bound based on a statistical total variation distance of the simplified model. We show that it bounds the theoretical POMDP value w.r.t. original model, from the empirical planned value with the simplified model, by generalizing recent results of particle-belief MDP concentration bounds. Our calculations can be separated into offline and online parts, and we arrive at formal guarantees without having to access the costly model at all during planning, which is also a novel result. Finally, we demonstrate in simulation how to integrate the bound into the routine of an existing continuous online POMDP solver.

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arXiv2025

Action-Gradient Monte Carlo Tree Search for Non-Parametric Continuous (PO)MDPs

Online planning in continuous state, action, and observation spaces remains challenging for autonomous systems. While Monte Carlo Tree Search (MCTS) scales effectively via sampling, most continuous (PO)MDP solvers do not exploit gradient-based action optimization. We propose Action-Gradient MCTS (AGMCTS), a framework that combines global tree search with local gradient-based action refinement, while maintaining consistent value estimates. We provide three key theoretical contributions: (1) an action score gradient theorem for particle belief states; (2) the Multiple Importance Sampling (MIS) Tree that supports frequent action-branch updates by reusing prior samples without introducing estimator drift; and (3) tractable action score gradients for smooth generative models using the Area Formula. Empirical results demonstrate that AGMCTS outperforms state-of-the-art sample-based solvers in multiple challenging continuous MDP and POMDP benchmarks.

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arXiv2025

Action-Consistent Decentralized Belief Space Planning with Inconsistent Beliefs and Limited Data Sharing: Framework and Simplification Algorithms with Formal Guarantees

In multi-robot systems, ensuring safe and reliable decision making under uncertain conditions demands robust multi-robot belief space planning (MR-BSP) algorithms. While planning with multiple robots, each robot maintains a belief over the state of the environment and reasons how the belief would evolve in the future for different possible actions. However, existing MR-BSP works have a common assumption that the beliefs of different robots are same at planning time. Such an assumption is often unrealistic as it requires prohibitively extensive and frequent data sharing capabilities. In practice, robots may have limited communication capabilities, and consequently beliefs of the robots can be different. Crucially, when the robots have inconsistent beliefs, the existing approaches could result in lack of coordination between the robots and may lead to unsafe decisions. In this paper, we present decentralized MR-BSP algorithms, with performance guarantees, for tackling this crucial gap. Our algorithms leverage the notion of action preferences. The base algorithm VerifyAC guarantees a consistent joint action selection by the cooperative robots via a three-step verification. When the verification succeeds, VerifyAC finds a consistent joint action without triggering a communication; otherwise it triggers a communication. We design an extended algorithm R-VerifyAC for further reducing the number of communications, by relaxing the criteria of action consistency. Another extension R-VerifyAC-simp builds on verifying a partial set of observations and improves the computation time significantly. The theoretical performance guarantees are corroborated with simulation results in discrete setting. Furthermore, we formulate our approaches for continuous and high-dimensional state and observation spaces, and provide experimental results for active multi-robot visual SLAM with real robots.

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arXiv2025

Anytime Incremental $ρ$POMDP Planning in Continuous Spaces

Partially Observable Markov Decision Processes (POMDPs) provide a robust framework for decision-making under uncertainty in applications such as autonomous driving and robotic exploration. Their extension, $ρ$POMDPs, introduces belief-dependent rewards, enabling explicit reasoning about uncertainty. Existing online $ρ$POMDP solvers for continuous spaces rely on fixed belief representations, limiting adaptability and refinement - critical for tasks such as information-gathering. We present $ρ$POMCPOW, an anytime solver that dynamically refines belief representations, with formal guarantees of improvement over time. To mitigate the high computational cost of updating belief-dependent rewards, we propose a novel incremental computation approach. We demonstrate its effectiveness for common entropy estimators, reducing computational cost by orders of magnitude. Experimental results show that $ρ$POMCPOW outperforms state-of-the-art solvers in both efficiency and solution quality.

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arXiv2024

Previous Knowledge Utilization In Online Anytime Belief Space Planning

Online planning under uncertainty remains a critical challenge in robotics and autonomous systems. While tree search techniques are commonly employed to construct partial future trajectories within computational constraints, most existing methods discard information from previous planning sessions considering continuous spaces. This study presents a novel, computationally efficient approach that leverages historical planning data in current decision-making processes. We provide theoretical foundations for our information reuse strategy and introduce an algorithm based on Monte Carlo Tree Search (MCTS) that implements this approach. Experimental results demonstrate that our method significantly reduces computation time while maintaining high performance levels. Our findings suggest that integrating historical planning information can substantially improve the efficiency of online decision-making in uncertain environments, paving the way for more responsive and adaptive autonomous systems.

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arXiv2024

Anytime Probabilistically Constrained Provably Convergent Online Belief Space Planning

Taking into account future risk is essential for an autonomously operating robot to find online not only the best but also a safe action to execute. In this paper, we build upon the recently introduced formulation of probabilistic belief-dependent constraints. We present an anytime approach employing the Monte Carlo Tree Search (MCTS) method in continuous domains. Unlike previous approaches, our method assures safety anytime with respect to the currently expanded search tree without relying on the convergence of the search. We prove convergence in probability with an exponential rate of a version of our algorithms and study proposed techniques via extensive simulations. Even with a tiny number of tree queries, the best action found by our approach is much safer than the baseline. Moreover, our approach constantly finds better than the baseline action in terms of objective. This is because we revise the values and statistics maintained in the search tree and remove from them the contribution of the pruned actions.

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arXiv2024

Simplified POMDP Planning with an Alternative Observation Space and Formal Performance Guarantees

Online planning under uncertainty in partially observable domains is an essential capability in robotics and AI. The partially observable Markov decision process (POMDP) is a mathematically principled framework for addressing decision-making problems in this challenging setting. However, finding an optimal solution for POMDPs is computationally expensive and is feasible only for small problems. In this work, we contribute a novel method to simplify POMDPs by switching to an alternative, more compact, observation space and simplified model to speedup planning with formal performance guarantees. We introduce the notion of belief tree topology, which encodes the levels and branches in the tree that use the original and alternative observation space and models. Each belief tree topology comes with its own policy space and planning performance. Our key contribution is to derive bounds between the optimal Q-function of the original POMDP and the simplified tree defined by a given topology with a corresponding simplified policy space. These bounds are then used as an adaptation mechanism between different tree topologies until the optimal action of the original POMDP can be determined. Further, we consider a specific instantiation of our framework, where the alternative observation space and model correspond to a setting where the state is fully observable. We evaluate our approach in simulation, considering exact and approximate POMDP solvers and demonstrating a significant speedup while preserving solution quality. We believe this work opens new exciting avenues for online POMDP planning with formal performance guarantees.

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