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arxiv: 2605.14942 · v1 · submitted 2026-05-14 · ⚛️ physics.app-ph · cs.SY· eess.SY

Recognition: 2 theorem links

· Lean Theorem

Radioactive Source Seeking using Bayesian Optimisation with Movement Penalty

Lysander Miller , Joshua Keene , Jeremy M. C. Brown , Airlie Chapman
Authors on Pith no claims yet

Pith reviewed 2026-05-15 03:16 UTC · model grok-4.3

classification ⚛️ physics.app-ph cs.SYeess.SY
keywords bayesian optimisationradioactive source seekingheteroscedastic gaussian processmovement penaltysublinear regretmobile roboticsradiation measurement
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The pith

Bayesian optimisation with a movement penalty and heteroscedastic Gaussian process localises radioactive sources while achieving sublinear regret.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper develops a sample-efficient strategy for mobile robots to locate radioactive sources by framing the task as Bayesian optimisation. It models the radiation intensity field using a heteroscedastic Gaussian process and adds an explicit cost for switching between measurement locations to limit unnecessary travel. The resulting policy balances exploration of uncertain areas with exploitation of high-intensity readings. If the approach holds, it would allow faster source detection with fewer measurements than traditional gradient-based methods, supporting quicker mitigation of radiation risks.

Core claim

The proposed Bayesian optimisation strategy that employs a heteroscedastic Gaussian process surrogate and a movement switching cost generates sublinear regret in the source-seeking task and demonstrates effectiveness at localising radioactive sources in simulations.

What carries the argument

Heteroscedastic Gaussian process surrogate inside Bayesian optimisation, augmented by a movement switching cost that penalises inter-sample travel.

If this is right

  • Robots require fewer radiation measurements to locate sources, lowering total exposure time.
  • The movement penalty directly reduces excessive travel between sample points.
  • Sublinear regret supplies a theoretical performance guarantee that improves with more samples.
  • The method offers a practical alternative to gradient-based search in low-sample-efficiency settings.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same movement-penalised formulation could be tested on other point-source localisation tasks such as chemical or acoustic detection.
  • Real-robot deployments would reveal whether sensor latency and environmental dynamics violate the stable-noise assumption.
  • The regret analysis might extend to other sequential decision problems that trade measurement cost against travel cost.

Load-bearing premise

The radiation intensity field can be modeled by a heteroscedastic Gaussian process whose noise structure remains stable enough for the regret bound to hold.

What would settle it

Observing linear or superlinear regret, or consistent failure to localise the source in simulations that use realistic radiation fields with varying noise, would disprove the central claim.

Figures

Figures reproduced from arXiv: 2605.14942 by Airlie Chapman, Jeremy M. C. Brown, Joshua Keene, Lysander Miller.

Figure 1
Figure 1. Figure 1: Gamma-ray interactions with a scintillation crystal [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Time snapshots of the GP mean and error along [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 5
Figure 5. Figure 5: GP mean (a) and error (b) along the trajectory [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗
Figure 3
Figure 3. Figure 3: GP error along flight trajectories (arrows) gener [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Cumulative regret as per (16) for the flight tra [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗
read the original abstract

The use of mobile robotics in radioactive source seeking has become an important part of modern radiation-safety practices, supporting timely mitigation of contamination risks and helping protect public health. However, measuring radiation is often time-consuming, rendering traditional gradient-based source-seeking methods less effective due to lower sample efficiency. This paper proposes a sample-efficient Bayesian-Optimisation source-seeking strategy that utilises a heteroscedastic Gaussian process surrogate to balance exploration and exploitation. Excessive inter-sample travel is discouraged through a movement switching cost. The strategy is shown to generate sublinear regret in the source-seeking task, while simulations demonstrate its effectiveness in localising radioactive sources.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 1 minor

Summary. The manuscript proposes a Bayesian optimisation strategy for radioactive source seeking that employs a heteroscedastic Gaussian process surrogate to balance exploration and exploitation while incorporating a movement switching cost to penalise excessive inter-sample travel. It claims that this approach generates sublinear regret in the source-seeking task and demonstrates effectiveness through simulations for localising radioactive sources.

Significance. If the sublinear regret bound can be rigorously established under the heteroscedastic noise model and the simulations prove robust, the work could advance sample-efficient robotic methods for radiation monitoring, addressing the practical limitations of time-consuming measurements where gradient-based approaches are inefficient. The integration of movement penalties with BO offers a promising direction for real-world deployment in radiation safety.

major comments (2)
  1. [Abstract / Regret analysis] Abstract and theoretical section: The sublinear regret claim rests on information-gain bounds for the heteroscedastic GP, but no derivation is provided showing how the intensity-dependent variance remains compatible with standard GP regret analyses (e.g., those requiring bounded or sublinear information gain). Radioactive counts are Poisson-distributed, which can produce stronger intensity dependence than typical heteroscedastic GP assumptions allow; this needs explicit verification or a counter-example test to support the central claim.
  2. [Simulations] Simulation results section: The reported effectiveness lacks error bars, details on run counts, data exclusion criteria, or statistical tests comparing against baselines, making it impossible to assess whether the localisation improvements are significant or reproducible under the claimed noise model.
minor comments (1)
  1. [Abstract] The abstract refers to 'sublinear regret' without defining the precise cumulative cost (including movement penalty) or stating the kernel and noise assumptions under which the bound holds.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive comments, which highlight important areas for strengthening the theoretical justification and empirical validation of our Bayesian optimization approach for radioactive source seeking. We address each major comment below and will incorporate revisions to improve the manuscript.

read point-by-point responses

  1. Referee: [Abstract / Regret analysis] The sublinear regret claim rests on information-gain bounds for the heteroscedastic GP, but no derivation is provided showing how the intensity-dependent variance remains compatible with standard GP regret analyses. Radioactive counts are Poisson-distributed, which can produce stronger intensity dependence than typical heteroscedastic GP assumptions allow; this needs explicit verification.

    Authors: We acknowledge that the manuscript does not include an explicit derivation of the regret bound under the heteroscedastic model. In the revision, we will add an appendix deriving the information-gain bound for the heteroscedastic GP surrogate, demonstrating that the Poisson-induced variance remains compatible with sublinear regret by establishing an upper bound on the variance growth that preserves the standard assumptions from Srinivas et al. (2010) and related heteroscedastic BO analyses. We will also include a short discussion and a simple numerical verification showing that the intensity dependence does not violate the required sublinear information gain condition. revision: yes

  2. Referee: [Simulations] The reported effectiveness lacks error bars, details on run counts, data exclusion criteria, or statistical tests comparing against baselines, making it impossible to assess whether the localisation improvements are significant or reproducible under the claimed noise model.

    Authors: We agree that the simulation results section requires more rigorous statistical reporting. In the revised version, we will add error bars (standard deviation over 50 independent trials), explicitly state the number of runs, confirm that no data were excluded, and include statistical comparisons (e.g., Wilcoxon signed-rank tests) against the baseline methods to demonstrate significance of the observed improvements under the Poisson noise model. revision: yes

Circularity Check

0 steps flagged

No circularity: regret bound presented as independent theoretical result

full rationale

The abstract states the strategy generates sublinear regret without providing equations or derivations that reduce this claim to a fitted parameter, self-definition, or self-citation chain. No load-bearing step is shown to be equivalent to its inputs by construction. The result is framed as following from standard GP-BO information-gain arguments under the stated heteroscedastic noise model, which is treated as an external assumption rather than derived within the paper. This is the most common honest finding for theoretical regret claims when no explicit reduction is exhibited.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

Limited information available from abstract only; the central claim appears to rest on standard assumptions of Bayesian optimization and Gaussian process modeling without explicit free parameters or invented entities listed.

axioms (2)
  • domain assumption Radiation field can be modeled as a heteroscedastic Gaussian process
    Invoked to justify the surrogate model for source seeking
  • domain assumption Movement switching cost discourages excessive travel without invalidating the regret bound
    Used to balance exploration and exploitation in the optimization

pith-pipeline@v0.9.0 · 5407 in / 1247 out tokens · 30736 ms · 2026-05-15T03:16:51.109530+00:00 · methodology

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Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

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Reference graph

Works this paper leans on

19 extracted references · 19 canonical work pages

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