Title: ESCORT: Efficient Stein-variational and Sliced Consistency-Optimized Temporal Belief Representation for POMDPs
Venue: NeurIPS 2025
Accepted: yes
Keywords: POMDPs

Particle-based Variational Inference

Reinforcement Learning
Abstract: In Partially Observable Markov Decision Processes (POMDPs), maintaining and updating belief distributions over possible underlying states provides a principled way to summarize action-observation history for effective decision-making under uncertainty. As environments grow more realistic, belief distributions develop complexity that standard mathematical models cannot accurately capture, creating a fundamental challenge in maintaining representational accuracy. Despite advances in deep learning and probabilistic modeling, existing POMDP belief approximation methods fail to accurately represent complex uncertainty structures such as high-dimensional, multi-modal belief distributions, resulting in estimation errors that lead to suboptimal agent behaviors. To address this challenge, we present ESCORT (Efficient Stein-variational and sliced Consistency-Optimized Representation for Temporal beliefs), a particle-based framework for capturing complex, multi-modal distributions in high-dimensional belief spaces. ESCORT extends SVGD with two key innovations: correlation-aware projections that model dependencies between state dimensions, and temporal consistency constraints that stabilize updates while preserving correlation structures. This approach retains SVGD's attractive-repulsive particle dynamics while enabling accurate modeling of intricate correlation patterns. Unlike particle filters prone to degeneracy or parametric methods with fixed representational capacity, ESCORT dynamically adapts to belief landscape complexity without resampling or restrictive distributional assumptions. We demonstrate ESCORT's effectiveness through extensive evaluations on both POMDP domains and synthetic multi-modal distributions of varying dimensionality, where it consistently outperforms state-of-the-art methods in terms of belief approximation accuracy and downstream decision quality.


Peer reviews:
{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper proposes ESCORT, a novel framework that applies Stein Variational Gradient Descent (SVGD) to belief representation in Partially Observable Markov Decision Processes (POMDPs). The main contribution lies in adapting SVGD to the POMDP setting by addressing its known limitations in high-dimensional and multi-modal distributions. The method is evaluated across a suite of synthetic and real POMDP tasks, showing improved belief approximation and downstream policy performance over baselines.\n\nSTRENGTHS AND WEAKNESSES:\n## Strengths\n\nApplying SVGD to belief approximation in POMDPs is a meaningful and underexplored direction, and the paper is generally well-written and logically structured.\n\n\n## Weaknesses\n\n1. The motivation for applying SVGD to POMDPs is not sufficiently convincing. The authors are encouraged to provide a more detailed analysis, for example: why does SVGD avoid the curse of dimensionality that affects traditional particle-based methods? And how does it offer better adaptation to varying uncertainty complexity compared to parametric methods? These comparisons require deeper technical justification. \n\n2.  The contributions listed in the introduction would benefit from being clearly itemized as bullet points for improved readability and clarity. \n\n3.  The limitations of standard SVGD are only briefly mentioned with citations, without adequate explanation. In particular, what exactly is meant by “correlation structure” in a mathematical sense? As it stands, readers may not understand why SVGD fails to capture these structures, nor how this failure degrades downstream performance in POMDPs. A more thorough explanation is needed. \n\n4.  The proposed method addresses SVGD’s limitations via a regularization term, but its specific impact is not independently evaluated. Studying its effects only indirectly through overall POMDP performance is insufficient. An ablation study isolating the contribution of the regularization term is necessary. \n\n5.  The purpose of the Model-Based Belief Update component is unclear. What exactly is the form of the displacement term \\delta x_i​ in the update equation? How does this belief update differ from a standard Bayes filter? These questions should be clarified. \n\n6.  In Section 3.4, the mathematical definition of \"consistency\" is vague. Moreover, its effect is not empirically validated—an ablation study is needed, along with a dedicated metric to evaluate whether consistency has actually improved in the experiments. \n\n7.  For distribution approximation, the paper should include RMSE as an evaluation metric. Since SIR is essentially a Bayesian filtering method, a standard benchmark in this setting is comparing the RMSE between the posterior mean and the ground-truth state.\n\nQUESTIONS:\nSee weaknesses\n\nLIMITATIONS:\nPlease discuss the limitations in the last section.", "TITLE": "Official Review", "RECOMMENDATION": 3, "REVIEWER_CONFIDENCE": 5, "CLARITY": 2, "IMPACT": 2, "ORIGINALITY": 3, "DATE": "2025-06-24"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe paper proposes a new belief update approach for POMDPs. It addresses the problem that belief update in POMDPs suffers from the curse of dimensionality in high-dimensional state spaces. The paper tries to address this by leveraging the fact that some dimensions may be correlated. Thus, a regularizer that respects this fact can help do better. The paper combines SVGD update with additional regularizer terms that capture correlation across dimensions and also try to minimize the earth-mover distance across time. Their experiments show benefits over other baselines, especially when the dimensionality is increased.\n\nSTRENGTHS AND WEAKNESSES:\n## Pros\n\n1. Belief update for high-dimensional state-spaces is an important problem, and doing it well by incorporating the world structure is the focus of this paper.\n2. Combining SVGD with structure/correlation-aware and temporality-aware regularizers appears novel in my knowledge in the context of POMDPs.\n3. Experiments show benefits over other baselines, esp. when the dimensionality is increased.\n\n## Cons\nMy main concerns are around: (1) the unclear details about the temporality regularizer, (2) attribution of the gains to two possible sources i.e., the correlation regularizer vs. the temporality regularizer or both; (3) the question of whether evaluating on 20-dimensions is high enough and the fact that a plot might be a better way than a table for showing the scaling trend, and lastly, (4) are the environments too simplistic and whether this approach can work with raw visual observations like those tackled by the DVRL framework (and even those might be considered too simplistic by modern day standards of visual complexity).\n\nSee also the \"Questions\" below.\n\n### Suggestions for Improvement\n\n1. There is a typo (I think) in Equation 5 around the summation.\n2. I wonder if a plot with X-axis as the dimensionality and Y-axis as the performance would be more illustrative in place of Table 2. In tabular form, it is difficult to see the “trend” wrt. the dimensionality.\n\nQUESTIONS:\n1. In Section 3.2, what is the target $p$ in the context of the actual POMDP? Is it the unnormalized product of previous belief $\\times$ transition distribution $\\times$ observation distributions for that time-step?\n2. Are transition and observation distributions (and approximate inference) learned, i.e., via neural networks, like in DVRL? Or was this not necessary because of access to privileged information or special aspects of the environment structure? If yes, then I wonder if the method would scale to state-spaces with much larger dimensionalities, which is typical of neural representations.\n3. Have authors tried DVRL with smaller latent sizes? I wonder if DVRL alone would be capable of “compressing” redundant dimensions in the input to a smaller number of latent dimensions to fight the curse of dimensionality?\n4. Is policy the only learned part of the model?\n5. How do you specify $\\lambda(\\theta)$ in Section 3.4? Is $A\\theta$ more like $A_\\theta$, or is this $A$ related to the correlation structure from 3.2?\n6. Is it possible to ablate the various regularizers used during belief update, e.g., the role of the correlation-regularizer versus the role of the temporal regularizer?\n\nLIMITATIONS:\nyes", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 3, "CLARITY": 2, "IMPACT": 2, "ORIGINALITY": 2, "DATE": "2025-07-02"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe paper studies a novel belief representation for POMDPs, which is based on Stein Variational Gradient Descent. The contributions focus on developing a regularization that is context-aware and maintains temporal consistency.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths\n1. POMDPs are an important framework for decision-making under uncertainty, and new particle-based belief representation are valuable as they can potentially be combined with an array of approximate POMDP solvers (as demonstrated in the experiments).\n2. For a subset of POMDPs, the paper provides encouraging results, particularly in high-dimensional domains. Ablation studies are also provided.\n\nWeaknesses\n1. A key issue is that the results presented on temporal consistency regularization only apply to POMDPs with certain assumptions, which are only detailed in the Appendix. In particular, Assumption 5 on bounded transition dynamics is important, because that implies that there’s a metric defined over the state space that allows the agent to judge whether a belief update is unrealistic or not. This might be reasonable in the navigation-like domains the authors consider, but it is a quite strong limiting assumption.\n2. In the model-based belief update, there is an inconsistency regarding how the particles are updated (see Questions).\n\nQUESTIONS:\n1. Have the authors considered domains that would violate Assumption 5? In kidnapped robot problems, unrealistic belief updates might actually be necessary, for instance.\n2. On line 230, an equation is presented to describe how a particle is propagated through the transition model. The transition function T returns a probability distribution for a particular state and action, and not a single state (as the equation seems to imply). Furthermore, Gaussian transition noise is added, which raises the question whether it is limited to such noise models. Can the authors clarify both issues?\n3. In the experiments, the position error is reported as an evaluation metric. Why not the value, as that is what the POMDP algorithms are optimizing for?\n\nLIMITATIONS:\nThe checklist states that limitations are addressed in the Conclusions section, but there the specific assumptions on the POMDP dynamics are not mentioned, nor any other limitations.", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 3, "CLARITY": 3, "IMPACT": 2, "ORIGINALITY": 3, "DATE": "2025-07-03"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe paper introduces ESCORT, a new particle-based method for faithfully approximating complex multi- modal belief distributions in high-dimensional POMDPs. The key idea is to extend Stein Variational Gradient Descent (SVGD) with (i) correlation-aware projections and (ii) temporal consistency constraints that enables accurate modeling. Experimental results demonstrate that ESCORT outperforms prior approaches in both belief approximation accuracy and decision-making.\n\nSTRENGTHS AND WEAKNESSES:\n### Strengths\n\n- The paper tackles an important problem. The key ideas are well presented and seem to be novel and interesting, though I am not the expert in this field.\n- Experimental results show strong performance of the proposed method. Lastly, the paper is well-organized and the writing is clear.\n\n### Weaknesses\n\n- Experiments are mostly limited to low-dimensional environments, which is somewhat inconsistent to the authors claim on high-dimeonsional POMDPs. Experimental results on more high-dimensional environments would further strengthen the paper.\n- I would like to see how the computational cost compares to prior approaches, which could be the computational complexity or the actual computation time. In particular, I am curious whether the proposed approach could scale to more high-dimensional environments in terms of practical computations.\n- As it often requires different choice of hyperparameters across environments, it could be better to include hyperparameter sensitivity analysis. Also, it is unclear how the hyperparameters are chose.\n\nQUESTIONS:\n- (Line 313) “received equivalent computational budgets” → Could the authors elaborate what this means?\n- How the hyperparameters are chosen?\n- It feels like many important practical implementation details are deferred to the appendix, and part of them could be moved to the main text.\n- Could the authors discuss the theoretical guarantee of the proposed method?\n- (Line 273) missing parenthesis\n\nLIMITATIONS:\nyes", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 1, "CLARITY": 3, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-07-10"}