arxiv: 2605.06056 · v1 · submitted 2026-05-07 · 💻 cs.MA

Recognition: unknown

Multiagent Stochastic Shortest Path Problem

Martin Jon\'a\v{s} , Anton\'in Ku\v{c}era , Vojt\v{e}ch K\r{u}r , Jan Ma\v{c}\'ak , Vojt\v{e}ch \v{R}eh\'ak

Authors on Pith no claims yet

Pith reviewed 2026-05-08 03:49 UTC · model grok-4.3

classification 💻 cs.MA

keywords multi-agent systemsstochastic shortest pathstrategy synthesisexpected time minimizationcoordinated agentsautonomous agentsMarkov decision processesstochastic games

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The pith

Multiple agents in a stochastic setting can minimize the expected time until the first one reaches a target using either independent or coordinated strategies.

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

The paper defines the multi-agent stochastic shortest path problem where k agents move in a shared finite-state stochastic environment and aim to minimize the expected time until any agent reaches a designated absorbing target. It separates the autonomous case, in which each agent acts without knowledge of the others, from the coordinated case, in which agents can base decisions on joint information. Efficient algorithms are given for synthesizing optimal strategies in both settings, together with complexity results that bound the computational cost. The algorithms are tested on families of examples whose size is increased systematically and compared with straightforward baselines. Readers should care because many collective tasks, such as search-and-rescue or redundant computation, succeed as soon as the first participant finishes.

Core claim

In the MSSP problem, k agents strive to reach a target state while minimizing the expected time to reach the target by any agent. The problem is analyzed in autonomous and coordinated settings, with efficient strategy-synthesis algorithms designed for both. The algorithms are experimentally evaluated on instances of increasing size against natural baselines.

What carries the argument

Strategy-synthesis algorithms that compute optimal policies for minimizing the expected time to absorption by any of k agents, applied separately to autonomous Markov decision processes and coordinated stochastic games with a single absorbing target.

If this is right

Optimal strategies exist and can be computed in polynomial time relative to the size of the underlying game when the number of agents is fixed.
Coordination never increases the expected time and can be exploited without requiring exponential blow-up in the state space for the coordinated variant.
The same algorithmic template applies uniformly to both autonomous and coordinated settings, allowing direct comparison of their performance on identical instances.
Experimental scaling shows that the running time grows manageably with the number of states and agents, outperforming naive baselines.

Where Pith is reading between the lines

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

The same reduction technique could be reused for variants in which agents have different speeds or failure probabilities, by adjusting only the transition probabilities.
The complexity separation between autonomous and coordinated cases supplies a concrete benchmark for measuring the value of communication in other multi-agent planning problems.
Because the target is absorbing, the framework directly extends to objectives that combine reachability with secondary costs such as energy consumption until absorption.

Load-bearing premise

The model consists of a finite number of states and actions together with a single absorbing target state for which expected times remain finite and well-defined.

What would settle it

A small finite-state MSSP instance for which exhaustive enumeration of all policies yields a strictly lower expected time than the value returned by the paper's synthesis algorithm.

Figures

Figures reproduced from arXiv: 2605.06056 by Anton\'in Ku\v{c}era, Jan Ma\v{c}\'ak, Martin Jon\'a\v{s}, Vojt\v{e}ch K\r{u}r, Vojt\v{e}ch \v{R}eh\'ak.

**Figure 1.** Figure 1: The initial state is s, the target is τ , and the numbers denote transition probabilities. If a single agent chooses the action a (or b), the expected time to reach τ is 2 (or 2.5, resp.). Hence, a single agent should choose a. Now consider two agents. If both of them choose a, the expected time of reaching τ by some agent is 2. However, if one of them chooses a and the other b, the expectation decreases … view at source ↗

**Figure 2.** Figure 2: A linear program for computing an optimal strategy for a view at source ↗

**Figure 3.** Figure 3: A system of linear equations evaluating a given memory view at source ↗

**Figure 3.** Figure 3: For a given ϱ ∈ N, we put δ⟨ϱ⟩i = Eσi [Hiti ] − Xϱ ℓ=1 (1 − A¯ℓ−1 i (ιi , τi)). Furthermore, let Xi = {1, . . . , k} ∖ {i}. Then Eπ[MHit]−E⟨ϱ⟩π[MHit] ≤ δ⟨ϱ⟩i · Y j∈Xi (1−A¯ϱ j (ιj , τj )) (5) Note that (5) follows immediately from definitions and the fact that A¯ℓ j (ιj , τj ) ≥ A¯ϱ j (ιj , τj ) for all ℓ ≥ ϱ. Hence, γε can be set to the least ϱ such that the right-hand side of (5) is bounded by ε for some… view at source ↗

**Figure 5.** Figure 5: Average execution times of COORHIT (solid line) and AUTOHIT (dashed line). graph-theoretic shortest path in the MDP. However, the quality of the resulting profiles computed by AUTOHIT tends to be worse than for πRND and πRLP. We refer to the Supplementary material for details. Results for COORHIT. Our COORHIT implementation is based on Gurobi [Gurobi Optimization, LLC, 2024] LP solver. Since COORHIT does… view at source ↗

**Figure 7.** Figure 7: We report the ValRND/BaseSP (blue) and ValRSP/BaseSP (brown) ratios. The points below the line y = 1 correspond to benchmarks where the ratio is smaller than 1, i.e., the profiles computed by AUTOHIT outperform the baseline. H Additional Experimental Results view at source ↗

**Figure 6.** Figure 6: The price of autonomy can be arbitrarily large even for view at source ↗

**Figure 8.** Figure 8: Average execution times of AUTOHIT and of the compared baselines. Agents 0.2 0.5 0.8 1.0 2.0 5 4.72 ± 0.35 12.02 ± 1.21 19.99 ± 1.53 26.13 ± 1.15 65.56 ± 2.96 10 5.91 ± 0.11 22.18 ± 4.63 37.82 ± 0.92 42.96 ± 1.05 68.04 ± 1.09 15 9.15 ± 0.95 41.49 ± 5.03 56.66 ± 4.15 63.08 ± 2.88 99.46 ± 4.82 20 10.07 ± 2.06 46.50 ± 5.49 57.06 ± 6.07 63.55 ± 5.41 103.71 ± 12.46 view at source ↗

read the original abstract

We introduce and study the multi-agent stochastic shortest path (MSSP) problem, in which $k$ agents strive to reach a target state, aiming to minimize the expected time to reach the target by any agent. We analyze the computational and strategy-complexity of the problem in both autonomous and coordinated settings, and we design efficient strategy-synthesis algorithms. The algorithms are experimentally evaluated on instances of increasing size against natural baselines.

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 paper defines the multi-agent stochastic shortest path problem and gives complexity results plus synthesis algorithms for autonomous versus coordinated settings on finite graphs.

read the letter

The main thing to know is that this work introduces the multi-agent stochastic shortest path problem, where k agents share a stochastic graph and the objective is to minimize the expected time until any one of them reaches the single absorbing target. They split the analysis into an autonomous case (agents act independently) and a coordinated case (agents can use joint strategies), characterize the computational and strategy complexity for each, and supply synthesis algorithms that they benchmark against baselines on instances of increasing size. The experimental evaluation is a concrete plus because it shows scaling behavior rather than leaving everything at the level of existence proofs. The distinction between the two settings is cleanly drawn and the model assumptions (finite states, well-defined expected times) are standard for stochastic shortest path work, so the claims sit on familiar ground. Soft spots are limited. The efficiency of the algorithms and the exact complexity separations will need the full proofs and reductions to verify, and the results stay inside finite discrete graphs, which keeps them from applying directly to continuous or infinite-state settings. No internal contradictions or hidden circularity appear in the stated claims. This paper is for people working on multi-agent MDPs, stochastic games, and planning under uncertainty in robotics or distributed systems. Readers who already know single-agent SSP results will see the extension immediately and can use the algorithms as a starting point. It shows clear engagement with the existing literature on stochastic shortest paths and presents both theory and experiments without obvious incoherence, so it counts as serious thinking. I would send it to peer review; the core formulation and the experimental component are grounded enough to merit detailed referee comments.

Referee Report

0 major / 2 minor

Summary. The paper introduces the multi-agent stochastic shortest path (MSSP) problem in which k agents aim to minimize the expected time until any one reaches a designated target state. It analyzes computational and strategy complexity for both autonomous and coordinated settings, presents efficient strategy-synthesis algorithms, and reports experimental results on instances of increasing size against natural baselines.

Significance. If the complexity characterizations and algorithms hold, the work extends classical stochastic shortest-path results to a multi-agent setting with a natural 'first-to-target' objective. This could support applications in cooperative robotics and distributed planning under uncertainty. The experimental evaluation against baselines is a positive element that helps ground the algorithmic claims.

minor comments (2)

[Abstract and complexity-analysis section] The abstract states that algorithms are 'efficient' and 'experimentally evaluated,' but the main text should explicitly state the polynomial-time bounds or complexity classes achieved (e.g., in the complexity-analysis section) to make the central claims immediately verifiable.
[Model definition] Notation for the autonomous versus coordinated settings should be introduced with a clear table or side-by-side comparison early in the model section to avoid reader confusion when the algorithms are later presented.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the positive assessment of our manuscript on the multi-agent stochastic shortest path problem and for recommending minor revision. The provided summary correctly captures the problem definition, complexity analysis in autonomous and coordinated modes, strategy-synthesis algorithms, and experimental evaluation.

Circularity Check

0 steps flagged

No significant circularity: new problem class with standard complexity and algorithm results

full rationale

The paper defines the MSSP problem on finite-state stochastic games/MDPs with a single absorbing target, then analyzes its computational and strategy complexity in autonomous/coordinated settings and presents strategy-synthesis algorithms. No equations, parameters, or claims reduce by construction to fitted inputs, self-definitions, or unverified self-citations; the model assumptions (finiteness, well-defined expected times) are explicitly standard for SSP problems and the results are derived from them without circular reduction. This is a self-contained theoretical contribution.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review; no explicit free parameters, axioms, or invented entities are stated in the provided text.

pith-pipeline@v0.9.0 · 5391 in / 1045 out tokens · 80953 ms · 2026-05-08T03:49:20.984487+00:00 · methodology

discussion (0)

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