arxiv: 2605.14085 · v1 · pith:FRJ5SPOMnew · submitted 2026-05-13 · 📡 eess.SY · cs.SY

Receding Horizon Multi-Agent Deceptive Path Planner

Xubin Fang , Brian M. Sadler , Rick S. Blum This is my paper

Pith reviewed 2026-05-15 05:20 UTC · model grok-4.3

classification 📡 eess.SY cs.SY

keywords deceptive path planningreceding horizon controlmulti-agent systemsBoltzmann distributionstochastic policiesonline adaptationpath planning

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The pith

Receding-horizon optimization with Boltzmann policies generates tunable stochastic deceptive paths for single and multiple agents.

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

The paper shows how deceptive path planning, where agents hide true goals by deviating from expected optimal routes, can be performed online for one or more agents. Instead of solving one expensive full-horizon optimization, the method repeatedly solves short-horizon problems inside a receding loop and draws actions from a Boltzmann distribution whose energy is a user-specified cost. That cost combines a deception term with penalties on resource use, path roughness, and, when needed, interactions among agents. The resulting policies are stochastic, locally recomputed at each step, and adjustable by changing cost weights or temperature so that the same planner can shift its deception level or react to new obstacles and goal changes without restarting from scratch.

Core claim

Deceptive path planning for autonomous agents is achieved by evaluating a user-defined composite cost over short-horizon candidate trajectories, forming a Boltzmann distribution over those trajectories, and executing only the first action before repeating the process in a receding-horizon loop; optional coupling terms in the cost allow coordinated deception among multiple agents, and the entire procedure updates locally without retraining or global replanning.

What carries the argument

Boltzmann distribution over short-horizon candidate trajectories whose energy is a user-defined cost that includes deception, resource, smoothness, and optional inter-agent coupling terms.

If this is right

Stochastic policies are obtained without offline training or repeated full-horizon solves.
Deception intensity can be adjusted continuously by changing cost weights or the Boltzmann temperature.
Multiple agents can coordinate deceptive behavior by adding coupling terms to the shared cost.
Agents adapt paths immediately when goals shift or obstacles appear because only local replanning is required.
The same planner supports both single-agent and multi-agent deception with only parameter changes.

Where Pith is reading between the lines

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

The approach may remain deceptive against observers whose own prediction horizon matches the planner's short horizon.
Real-time sensor data could be folded directly into the cost evaluation at each receding step.
Coordinated deception might emerge automatically if the coupling terms are chosen to reward mutual unpredictability.
The framework could be tested on physical robots by measuring observer error rates under live environmental updates.

Load-bearing premise

Short-horizon optimizations repeated inside a receding loop can maintain effective deception without needing the global view of a full-horizon plan.

What would settle it

Run an observer that knows the cost function and the receding-horizon structure; measure whether the observer's prediction of the true goal remains worse than chance after observing several executed steps.

Figures

Figures reproduced from arXiv: 2605.14085 by Brian M. Sadler, Rick S. Blum, Xubin Fang.

**Figure 1.** Figure 1: Exaggeration: single agent trajectory heatmaps over 500 trials. Three exaggeration deception scheduling cases are shown [PITH_FULL_IMAGE:figures/full_fig_p007_1.png] view at source ↗

**Figure 2.** Figure 2: Ambiguity: single agent trajectory heatmaps over 500 trials. Three ambiguity deception scheduling cases are shown (L [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗

**Figure 3.** Figure 3: Examples of exaggeration paths. The stochastic policy [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗

**Figure 4.** Figure 4: Forty exaggeration sample trajectories, with blue and [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗

**Figure 5.** Figure 5: Example empirical distribution of the Continuous [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗

**Figure 6.** Figure 6: Deception with a moving false goal. Each panel shows 500 trials. Ambiguity, panels (a–b), and exaggeration, panels [PITH_FULL_IMAGE:figures/full_fig_p009_6.png] view at source ↗

**Figure 7.** Figure 7: Two-agent deception example, with total move budget constraints. (a) Different relative agent budgets (1,4), same start [PITH_FULL_IMAGE:figures/full_fig_p010_7.png] view at source ↗

**Figure 8.** Figure 8: Volleyball coach schematic of the role-free [PITH_FULL_IMAGE:figures/full_fig_p010_8.png] view at source ↗

**Figure 9.** Figure 9: Volleyball example of the deceptive split over 300 roll [PITH_FULL_IMAGE:figures/full_fig_p011_9.png] view at source ↗

read the original abstract

Deceptive path planning enables autonomous agents to obscure their true goals from observers by deviating from an expected optimal path. Prior work largely solves full-horizon, end-to-end optimization for single agents, which is expensive to recompute online and difficult to scale or adapt en route. We propose a unified framework for deceptive path planning using a Boltzmann distribution, computing over short-horizon candidate trajectories within a receding-horizon loop. By param- By iterating a user-defined cost that captures deception, resources, and smoothness, and optionally includes coupling terms between agents, the framework yields stochastic policies that balance the tradeoff between optimal paths and deceptive deviation. Policies are updated locally and do not require training. The level of deception and adherence to constraints can be dynamically tuned, enabling online adaptation to changes in goals and constraints such as obstacles. This step-by-step tuning opens the door to new forms of dynamic deception. Simulation studies demonstrate the flexibility of our approach, maintaining deception while adapting to environmental and constraint updates, avoiding the recomputation required by full-horizon methods, and supporting intuitive tuning via a small set of parameters

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.

Desk Editor's Note private letter to a colleague

The receding-horizon Boltzmann method gives a workable online way to handle multi-agent deceptive paths with tunable parameters, but the simulations do not yet show whether short horizons can keep deception consistent over time.

read the letter

The paper's core move is to replace full-horizon optimization with a receding loop that draws short candidate trajectories from a Boltzmann distribution over a cost that mixes deception, resource use, smoothness, and optional inter-agent coupling. Policies update locally at each step, need no training, and let the user change the deception level or constraints on the fly when obstacles or goals shift. That setup is the concrete addition over the single-agent full-horizon work it cites, and it directly targets the recomputation problem that makes earlier methods hard to run online or scale to multiple agents. The simulations are reported to show the system keeps some deception while reacting to updates, which matches the practical goal stated in the abstract. The approach stays within standard tools—Boltzmann sampling and user-defined costs—so the implementation looks reproducible from the description. The main gap is in the evidence. The abstract claims flexibility and adaptation but supplies no quantitative metrics, no error bars, no direct comparison to full-horizon baselines, and no analysis of how well local choices accumulate into sustained global deception. The stress-test point about short horizons struggling to maintain a misleading prefix is reasonable on its face; an observer who sees the trajectory roll out or remembers past segments could spot the true goal once the local bias is no longer enforced. The paper would need to address that explicitly, either with longer-horizon tests or with observer models that include memory. This is aimed at robotics researchers who need real-time multi-agent planners that can incorporate deception without heavy offline computation. A reader already working on receding-horizon methods or cost-based planning would find the tuning knobs and coupling terms useful to try. It is worth sending to peer review so the authors can supply the missing numbers and test the long-term consistency claim under realistic observation.

Referee Report

2 major / 2 minor

Summary. The paper presents a receding-horizon framework for multi-agent deceptive path planning. It samples short-horizon candidate trajectories from a Boltzmann distribution whose energy is a user-defined cost combining deception, resource usage, smoothness, and optional inter-agent coupling terms. The resulting stochastic policies are updated locally in a receding loop, claimed to balance optimal and deceptive behavior while adapting online to goal or constraint changes without full-horizon recomputation or training.

Significance. If the central claim holds, the method supplies a computationally lighter alternative to full-horizon deceptive planners and extends naturally to multi-agent settings with dynamic environments. The absence of training and the explicit tunability of deception level via a small parameter set would be practically useful for online robotics and security applications.

major comments (2)

[Simulation Studies] Simulation Studies section: the claims that the approach 'maintains deception while adapting' and 'avoids the recomputation required by full-horizon methods' are supported only by qualitative descriptions; no quantitative metrics (deception success rate, path-length deviation, success under observer models, or statistical comparisons to baselines with error bars) are reported, leaving the empirical support for the central tradeoff claim weak.
[§3] §3 (Receding-horizon formulation and Boltzmann policy): the argument that iterated short-horizon minimization accumulates into sustained long-term deception rests on the assumption that local cost bias persists across replans, but no analysis, bound, or counter-example is provided for cases where an observer with memory sees the true goal once the deceptive deviation falls outside the current horizon; this directly affects the weakest assumption identified in the stress-test note.

minor comments (2)

[Abstract] Abstract contains an obvious typographical artifact ('By param- By iterating') that should be removed.
[§2] The precise functional form of the deception term inside the cost (e.g., how false-goal bias is encoded) is referenced but never written explicitly; adding the equation would improve reproducibility.

Simulated Author's Rebuttal

2 responses · 1 unresolved

We thank the referee for the constructive and detailed feedback. We have revised the manuscript to strengthen the empirical evaluation with quantitative metrics and to add analysis addressing the persistence of deception across replans. Our point-by-point responses follow.

read point-by-point responses

Referee: [Simulation Studies] Simulation Studies section: the claims that the approach 'maintains deception while adapting' and 'avoids the recomputation required by full-horizon methods' are supported only by qualitative descriptions; no quantitative metrics (deception success rate, path-length deviation, success under observer models, or statistical comparisons to baselines with error bars) are reported, leaving the empirical support for the central tradeoff claim weak.

Authors: We agree that quantitative support was insufficient in the original submission. The revised manuscript now includes deception success rates against multiple observer models, average path-length deviations from the optimal trajectory, success rates under dynamic constraints, and statistical comparisons (means and standard deviations over 50 Monte Carlo runs) to both full-horizon deceptive planners and non-deceptive receding-horizon baselines. These results, presented with error bars in new figures and tables in the Simulation Studies section, confirm that the method maintains tunable deception levels while adapting online with substantially lower recomputation cost. revision: yes
Referee: [§3] §3 (Receding-horizon formulation and Boltzmann policy): the argument that iterated short-horizon minimization accumulates into sustained long-term deception rests on the assumption that local cost bias persists across replans, but no analysis, bound, or counter-example is provided for cases where an observer with memory sees the true goal once the deceptive deviation falls outside the current horizon; this directly affects the weakest assumption identified in the stress-test note.

Authors: The referee correctly identifies a gap in the original analysis. We have added a new paragraph and illustrative counter-example in §3 that shows how an observer with memory can infer the goal when the deceptive deviation exits the current horizon and the local bias is insufficient. The revision also includes a brief sensitivity discussion on how increasing the horizon length or adjusting the Boltzmann temperature can reduce this exposure. A general theoretical bound on long-term deception under arbitrary observer memory, however, is not derived here. revision: partial

standing simulated objections not resolved

A rigorous mathematical bound guaranteeing sustained deception against observers with unbounded memory is not provided and would require a separate theoretical development beyond the scope of this work.

Circularity Check

0 steps flagged

No significant circularity; standard Boltzmann sampling on user-defined costs

full rationale

The paper defines a user-specified cost function that includes terms for deception, resources, smoothness, and optional multi-agent coupling. It then samples short-horizon trajectories from a Boltzmann distribution (standard softmax) inside a receding-horizon loop and updates policies locally. No equation reduces a claimed prediction to a fitted input by construction, no uniqueness theorem is imported from self-citation, and no ansatz is smuggled via prior work. The central result is a direct, tunable application of existing probabilistic planning techniques without self-referential reduction.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The framework depends on user-defined cost weights and the assumption that local short-horizon updates suffice for deception.

free parameters (1)

cost weights for deception, resources, and smoothness
User-defined parameters that control the balance in the iterated cost function.

axioms (1)

domain assumption Short-horizon trajectories suffice to maintain deception under environmental changes
Invoked to justify the receding-horizon loop over full-horizon optimization.

pith-pipeline@v0.9.0 · 5492 in / 1144 out tokens · 54891 ms · 2026-05-15T05:20:56.105703+00:00 · methodology

discussion (0)

Reference graph

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