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Scaling Observation-aware Planning in Uncertain Domains

Adrian Zvizdenco, Arthur Conrado Veiga Bosquetti, Alberto Lluch Lafuente, Christoph Matheja

May 21, 2026arXiv:2605.22364v1
cs.AI
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Scorecard· 5/16
5.0/10 impact

Abstract

Deciding which sensing capabilities to deploy on an agent in uncertain domains is a fundamental engineering challenge, in which one balances task achievability against the high costs of hardware and processing. This problem has previously been formalized as the Optimal Observability Problem (OOP), based on the well-known Partially Observable Markov Decision Process (POMDP) model for decision-making. This work studies (sub-)symbolic techniques to scale solving of decidable fragments of the OOP, namely the Sensor Selection Problem (SSP) and the Positional Observability Problem (POP). Besides improving the original approach based on parameter synthesis, we develop a new solving method that identifies sensible observation functions via decomposition of POMDPs, improving performance by 3 and 5 orders of magnitude for instance size and runtime, respectively.

AI Impact Assessments

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Scientific Impact Assessment

Core Contribution

This paper tackles the computational scalability of the Optimal Observability Problem (OOP) for POMDPs—the question of how to optimally assign sensing capabilities (observation functions) to an agent operating under uncertainty, subject to budget constraints. Building on the formalization by Konsta et al. (2024), which reduced decidable OOP fragments to parameter synthesis for typed parametric Markov chains (tpMCs) solved via SMT, this work offers two main contributions:

1. Improved SMT encodings: Native Boolean variable encoding, Bellman inequality relaxations, and pseudo-Boolean cardinality constraints that collectively yield ~10³× faster solving and ~75× larger solvable instances compared to the original approach.

2. A decomposition-based algorithm (A_G): A heuristic enumeration method that decomposes the OOP into individual POMDP evaluations by partitioning states into "atomic distinguishability groups" based on optimal action equivalence. This achieves an additional ~10³× speedup and ~10²× instance size increase beyond the SMT improvements.

Methodological Rigor

The paper is methodologically structured but has notable limitations in rigor:

Strengths in methodology:

  • The atomic distinguishability group concept (Definition 12-13) is well-defined and provides a principled basis for reducing the search space. The strong and weak action equivalence relations are clean abstractions.
  • Soundness of the A_G algorithm is established: it only returns valid solutions since each candidate is verified by an oracle.
  • The authors honestly acknowledge incompleteness of A_G in the general case and provide a concrete counterexample (M_trap in Appendix D.1).
  • Benchmark reproducibility is addressed through containerization and coefficient-of-variation analysis.
  • Weaknesses:

  • The experimental evaluation is limited to three synthetic topologies (Line, Grid, Maze), all of which have highly regular structure that inherently limits the number of atomic distinguishability groups. For Line: S(2,k)=1; for Grid: at most 8 groups; for Maze: S(4,k)≤7. This means the dramatic speedups partly reflect favorable structural properties rather than general algorithmic superiority.
  • Completeness remains an open conjecture for the studied topologies. The paper does not provide theoretical guarantees on solution quality when A_G returns "unknown."
  • The Z3 version sensitivity (version 4.13.0 specifically chosen because later versions degrade performance) raises concerns about fragility and long-term reproducibility.
  • The SMT instability discussion (Section 3.1) is informative but somewhat inconclusive—the original ordering happened to be best, which is fortunate but not methodologically satisfying.
  • The gradient-based PMC oracle approach (Section 4.2) is described but essentially abandoned due to poor performance, adding length without substantive contribution.
  • Potential Impact

    The problem addressed—optimal sensor placement under budget constraints—has clear practical relevance in robotics, autonomous systems, security, and cyber-physical systems. Cost-effective sensor deployment is a genuine engineering concern.

    However, the practical impact is tempered by several factors:

  • The models studied (grid worlds, mazes, lines) are toy benchmarks far from real-world complexity.
  • The restriction to positional strategies (both deterministic and randomized) limits applicability, as real agents often benefit from memory.
  • The paper operates within a specific formalism (POMDPs with discrete states) that may not capture continuous or high-dimensional sensing problems.
  • The largest solved instances (~200K states for deterministic strategies on Line) are impressive relative to prior work but still modest for many real applications.
  • The decomposition paradigm—separating observation function search from POMDP evaluation—is a conceptually valuable architectural insight that could inspire follow-up work beyond the specific algorithms proposed.

    Timeliness & Relevance

    The paper addresses a timely topic at the intersection of AI planning, formal verification, and system design. As autonomous systems proliferate, principled methods for sensor budget optimization become increasingly relevant. The work builds directly on a 2024 CAV paper, making it a timely follow-up. The connection to ETR-complete problems and SMT solving places it within active research communities.

    However, the field of POMDP solving has been advancing rapidly with deep learning and Monte Carlo methods, which this paper does not engage with substantially. The formal verification perspective is valuable but represents a niche within the broader POMDP community.

    Strengths & Limitations

    Key Strengths:

  • Clear, substantial performance improvements (orders of magnitude) over prior work, well-documented with tables.
  • The atomic distinguishability group abstraction is elegant and effective for structured domains.
  • The two-pronged approach (SMT improvements + decomposition) provides complementary improvements.
  • Open-source implementation enhances reproducibility.
  • The paper is generally well-written with running examples that aid understanding.
  • Key Limitations:

  • The A_G algorithm's effectiveness is tightly coupled to domain structure; performance on irregular or adversarial topologies is unknown.
  • Incompleteness of A_G means it may miss valid solutions, with no bound on how often this occurs in practice.
  • Limited benchmark diversity—only three synthetic topologies tested.
  • The paper is quite long (30 pages with appendices) relative to its core insights, with several exploratory dead ends (gradient descent, budget repairing) that dilute the narrative.
  • No comparison with other POMDP planning approaches beyond the direct predecessor [19].
  • The paper appears to be a master's thesis extension (reference [28]), which sometimes shows in the exploratory nature of some sections.
  • Additional Observations

    The paper's contribution is primarily engineering-oriented rather than foundational. The theoretical insight (atomic distinguishability groups) is relatively straightforward given the observation that states with identical optimal action sets can be grouped. The main value lies in demonstrating that this simple idea, combined with careful SMT encoding, yields dramatic practical improvements. The work would benefit from evaluation on more diverse and realistic problem instances to establish broader applicability.

    Rating:5/ 10
    Significance 5Rigor 5.5Novelty 5Clarity 6

    Generated May 22, 2026

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