GymPN: A Library for Decision-Making in Process Management Systems

Remco Dijkman; Riccardo Lo Bianco; Willem van Jaarsveld

REVIEW 4 major objections 4 minor 18 references

GymPN: A Library for Decision-Making in Process Management Systems

T0 review · 4 major / 4 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read GymPN models business-process decisions as partially observable Action-Evolution Petri nets, and its DRL agent learns the optimal assignment policy on all eight benchmark patterns.

desk verdict Useful library paper with one well-tested feature and one untested feature; the multi-token expansion needs a preservation argument. read the letter →

arxiv 2506.20404 v1 pith:7YLMOP2Q submitted 2025-06-25 cs.AI

Riccardo Lo Bianco , Willem van Jaarsveld , Remco Dijkman This is my paper · ORCID

classification cs.AI

keywords ProcessModelsDecisionMakingReinforcementLearningManagementSystemsPetriNetsGraphNeuralNetworksPartialObservabilityAction-Evolution

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

GymPN is a software library that turns business-process decision problems—which task to do next, when, and who should do it—into a Petri-net model that a deep reinforcement learning agent can solve. The paper's central claim is that the library's two new features, partial observability and multiple action transitions, let a single framework represent realistic process decisions that earlier Action-Evolution Petri net implementations could not. On eight benchmark problems covering the standard workflow patterns (sequence, parallelism, arbitrary cycle, and exclusive choice, each in joint and disjoint variants), a PPO agent learned policies that match the known optimum in every case. If correct, this gives process managers a practical, open tool for finding optimal allocation policies rather than relying on hand-tuned heuristics.

What carries the argument

The central object is the assignment graph, a graph-structured observation that the simulator extracts from the current marking of an Action-Evolution Petri net (A-E PN)—a timed, colored Petri net whose 'action' transitions are the decisions an agent makes and whose 'evolution' transitions are the nondeterministic events of the process. The mapping of Definition 4 and Algorithm 1 builds this graph only from observable places and attributes: each non-empty observable place becomes a node carrying the token's observable attributes, each transition becomes a node with a one-hot encoded type so multiple action transitions are distinguishable, and arcs between observable elements become edges. The two new observability functions, $O_P$ and $O_A$, decide which places and which token attributes are visible, and the unobservable elements are simply omitted. The graph is fed to a graph neural network that selects an action node, so the agent's policy operates on a partial view of the true process state.

What would settle it

Take a small A-E Petri net in which a single place holds two tokens and one action transition consumes both tokens at once (or has a guard depending on both), expand the net as Algorithm 1 does, and check whether the expanded net enables the same transitions with the same timing and rewards. If the enabled bindings, clock updates, or reward sequence differ from the original net, the assignment graph misrepresents the true process state and a policy trained on it cannot be trusted as optimal.

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Extended reading notes

Core claim

The paper presents GymPN, an extension of the Action-Evolution Petri net (A-E PN) framework for business-process decision making, and claims two novelties: it introduces observability functions that can hide entire places or individual token attributes from the agent's assignment-graph observations, and it extends the mapping from Petri net to assignment graph so that multiple action transitions—whether they share resources (joint actions) or use separate pools (disjoint actions)—are represented and distinguished by one-hot encoded transition types. To do this, the net is first expanded so that every place holds at most one token, then mapped to a graph whose nodes and edges carry only the observable places, attributes, and transitions. The paper evaluates the library on eight problem patterns and reports that a trained PPO agent achieves the optimal cumulative reward in all of them, with zero variance on the deterministic problems.

Load-bearing premise

The load-bearing premise is that expanding a net in which a place may hold several tokens into a net in which each place holds at most one token preserves exactly which actions are possible, with the same timings and bindings; the paper assumes this preservation rather than stating or proving it.

Editorial extensions

If this is right

Process analysts can model partially observable decision problems—for instance hiding the arrival process from the agent—without switching to a different formalism, because observability is expressed as two functions on places and attributes.
A single trained agent can handle processes with several independent decision points, including cases where two actions draw on the same resource pool, because action transitions are one-hot encoded in the observation.
The same library API covers all four basic workflow patterns, so the reported result suggests that optimal assignment policies can be learned across a wide range of process structures rather than for one bespoke formulation.
Because the deterministic policy attains the computed optimum in every benchmark, the method is a candidate replacement for hand-coded heuristics in settings where the optimal policy is known to exist in the modeled class.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

The paper's evaluation hides the arrival process from the agent in the partial-observability example, but all eight benchmarks are effectively fully observable; a stronger test of the novelty would hide a token attribute that changes the optimal choice and check whether the agent learns a policy that compensates for the missing information.
The correctness of the learned policies ultimately rests on the unproved assumption that expanding multi-token places into single-token places preserves the original net's enabled transitions, bindings, and timing; a directed test of that preservation on a net with a transition that consumes two tokens from one place would either validate or break the library's core mapping.
The one-hot encoding of action transitions means the observation graph grows with the number of decision points; scaling to processes with dozens of action transitions may require a compact action representation, a question the paper does not address.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Quick take on 2506.20404.

This is a real systems contribution, but it's narrower than the abstract makes it sound. The library extends the authors' A-E PN framework with two features: partial observability and multiple action transitions. The multiple-action part is tested on eight workflow patterns and works: the PPO policies match the hand-derived optima exactly. That's genuine evidence that the mapping from A-E PN to assignment graph, and the one-hot encoding of action types, is sound for those toy problems.

The partial-observability feature, though, is only defined, never evaluated. There's not a single experiment where you hide a place or attribute and check that the agent still learns something sensible. So the second headline claim is unsupported.

The bigger concern is Algorithm 1. It maps an 'expanded' A-E PN in which every place holds at most one token. The expansion that produces this form is described in one paragraph and never formally defined, and there's no argument that it preserves the enabled transitions, bindings, or rewards of the original multi-token net. The eight benchmarks never have more than one token in any place at the moment an action is chosen – arrivals are immediately assigned and resources sit as static tokens – so they can't detect a failure of that expansion. For a framework whose definition allows multisets, this is a real gap. I don't think it's fatal; it's an addressable omission. But as written, the general claim that GymPN can model realistic processes isn't supported.

You also get no training hyperparameters or network architecture, which is a reproducibility problem for a library paper. And the text has copy-paste errors: figures 6 and 9 get mixed up, and the intro lists section 6 twice. Minor, but sloppy.

What the paper does well: it lowers the barrier for process-management researchers to use DRL. You define the A-E PN in terms of places, transitions, guards, rewards; the library builds the Gym environment and handles observations and actions. That's genuinely useful, and the evaluation, though narrow, is honest: they report the known optima and the learned policies match.

Bottom line: this deserves serious review. Send it, but expect a major revision. The authors need to (1) run at least one partial-observability experiment, (2) either prove the expansion preserves dynamics or define it formally and test it on a multi-token case, and (3) report training details. Then it would be a solid contribution for the BPM community.

Referee Report

4 major / 4 minor

Summary. The paper presents GymPN, a Python library that extends the Action-Evolution Petri Net (A-E PN) framework with two features: partial observability of process state, realized through place- and attribute-level observability masks, and support for multiple action transitions, realized via a one-hot encoding of transition types and a mapping from an expanded Petri net to an assignment graph. The library is evaluated on eight task-assignment instances covering sequence, parallelism, arbitrary cycle, and exclusive-choice workflow patterns with joint or disjoint resource pools; the paper reports that a PPO agent reaches the hand-computed optimum reward in all eight instances. The library is released as open source, and the paper includes a comparison with related decision-making frameworks.

Significance. If the claims hold, GymPN addresses a real gap: previous A-E PN implementations assume full observability and a single decision type, while real business processes often require decisions at multiple stages and may hide part of the state. The open-source release, the clearly specified eight benchmark patterns, and the exact match of the reported PPO rewards to the stated optima in Table 2 are strengths that give some confidence in the multi-action encoding for the tested cases. However, the significance is currently conditional: the partial-observability novelty is only defined and never evaluated, and the multi-action mapping relies on an unformalized and unproven expansion step that the experiments do not stress. These gaps need to be closed before the paper's central claims are fully supported.

major comments (4)

[§4.2, Definition 4, Algorithm 1] Algorithm 1 and Definition 4 are stated for an 'expanded' A-E PN in which every place holds at most one token, but the expansion procedure itself is never formally defined and no proof is given that it preserves the set of enabled transitions, their bindings, firing times, or rewards. The paper only shows two example expansions (Figs. 6 and 9) and a short informal paragraph. Without a preservation argument, the assignment graph may misrepresent the true process state, and a policy learned on the expanded net may be suboptimal or invalid for the original multi-token net. This is load-bearing because the multiple-action claim rests on the faithfulness of this mapping.
[§6, Table 2] The eight benchmark patterns do not, as described, exercise a genuine multi-token decision point: under the optimal deterministic policy, arrivals are assigned before queues build, and the resource pools are static token sets. Thus the empirical results validate Algorithm 1 only in the trivial single-token-per-place case and cannot detect a failure of the unproven expansion on a multi-token marking. The authors should either provide a formal proof of expansion correctness or add a benchmark with a congested queue where multiple waiting tokens are simultaneously visible at a decision point, and verify the learned policy against an independently derived optimum.
[§4.1, §6] Partial observability, one of the two headline novelties, is never evaluated. Section 4.1 defines the observability functions O_P and O_A, but Section 6 evaluates only fully observable task-assignment problems. There is no experiment that masks a place or attribute, no comparison between a partially observable agent and a fully observable baseline, and no discussion of how the action space or the optimal policy changes under hidden information. The claim that GymPN 'supports partial process observability' is therefore only a modeling claim, not a demonstrated capability.
[§5, Table 2] No training hyperparameters or network architecture are reported. The paper states only that PPO is used and that graph neural networks approximate the policy and value functions; it gives no learning rate, batch size, number of training steps, GNN architecture, or number of random seeds. With only 10 evaluation episodes per problem and no variance across independent training runs, the exact equality of PPO and optimum rewards in Table 2 is not sufficient to establish that GymPN reliably learns optimal policies. A reproducibility appendix with these details would substantially strengthen the paper.

minor comments (4)

[§4.2, Figs. 6–10] In the joint-action example, the text says the expansion produces Fig. 6 and the mapping produces Fig. 7, but the joint expansion and its assignment graph are shown in Figs. 9 and 10; both references should be corrected.
[Definition 1] The tuple in Definition 1 has a trailing comma and a stray 'A' after the closing parenthesis ('..., ρ0), A'); this formatting error should be fixed.
[§2, Table 1] The package is referred to as 'POMDPs.jl' in the running text and 'POMDP.jl' in Table 1; the name should be used consistently.
[§1] The outline in Section 1 lists 'section 6' twice and repeats the evaluation description; the section numbering and outline should be tightened.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the derivation is self-contained and the optimality claims are checked against externally derived optima, not against the model's own outputs.

full rationale

GymPN extends the authors' own A-E PN framework [10,11], but this is normal prior-work reuse, not a circular argument: the paper does not use the framework to prove its own novel claims. The two novelties (partial observability masks OP/OA and one-hot-encoded multiple action transitions) are defined independently of the evaluation outcomes. The claimed optimal policies are validated against hand-computed optima in Table 2, such as 'always assign resource1 to activities of type1 and resource2 to activities of type2', which are derived from the problem parameters (completion times and arrival rates), not from the trained policy or from the assignment-graph mapping. No fitted parameter is hidden inside the evaluation and then renamed a prediction. The main weakness is a correctness gap, not circularity: the expansion from multi-token to one-token-per-place A-E PNs is never defined or proven to preserve enabled transitions, bindings, rewards, and timing, and the eight benchmarks may not exercise genuine multi-token decision points. That gap is a threat to validity, but it does not make any derived claim equivalent to its inputs by construction. Self-citations to [10,11] for the assignment-graph/GNN mechanism are not load-bearing in a circular sense because the empirical benchmark provides independent evidence for the central claim.

Assumptions & free parameters 1 free parameters · 4 assumptions · 0 invented entities

The central claim rests on the prior A-E PN framework (domain assumption), an unproven expansion-equivalence step, and informal optimality arguments. No invented entities are introduced; the only hand-chosen parameters are the unreported PPO training hyperparameters.

free parameters (1)

PPO training hyperparameters = not reported
Learning rate, batch size, number of training episodes, GNN layer sizes, and entropy coefficients are not stated in the paper, yet the Table 2 results depend on these choices.

assumptions (4)

domain assumption The A-E PN framework, including the assignment graph representation and the GNN policy architecture from Lo Bianco et al. [10,11], is correct and complete.
GymPN builds directly on this framework; any error or limitation in [10,11] carries over.
ad hoc to paper The expansion of a marked A-E PN into a single-token-per-place net preserves the set of enabled transitions and bindings.
Algorithm 1 operates on the expanded net; the paper states the expansion occurs but provides no proof or reference for semantic equivalence. Section 4.2.
domain assumption The hand-derived Optimum values in Table 2 are indeed the maximum cumulative rewards for the eight patterns.
Optimality of the 'always assign R1 to task 1 and R2 to task 2' policy is argued informally, not proven. Section 6.
domain assumption The eight workflow patterns from Van Der Aalst et al. [18] are representative of business process decision-making problems.
Used as the evaluation benchmark set; representativeness is assumed.

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Cite this review

Pith. "Pith review of GymPN: A Library for Decision-Making in Process Management Systems." pith.science (2026). https://pith.science/paper/7YLMOP2Q

@misc{pith2026250620404,
  author       = {Pith},
  title        = {Pith review of: GymPN: A Library for Decision-Making in Process Management Systems},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/7YLMOP2Q}},
  note         = {Machine review of arXiv:2506.20404}
}

read the original abstract

Process management systems support key decisions about the way work is allocated in organizations. This includes decisions on which task to perform next, when to execute the task, and who to assign the task to. Suitable software tools are required to support these decisions in a way that is optimal for the organization. This paper presents a software library, called GymPN, that supports optimal decision-making in business processes using Deep Reinforcement Learning. GymPN builds on previous work that supports task assignment in business processes, introducing two key novelties: support for partial process observability and the ability to model multiple decisions in a business process. These novel elements address fundamental limitations of previous work and thus enable the representation of more realistic process decisions. We evaluate the library on eight typical business process decision-making problem patterns, showing that GymPN allows for easy modeling of the desired problems, as well as learning optimal decision policies.

Figures

Figures reproduced from arXiv: 2506.20404 by the authors.

**Figure 1.** A task assignment problem expressed in A-E PN notation. A reward of 1 is provided every time a case is completed. Thus, the objective is to minimize the cycle time of cases (to maximize the reward). The A-E PN relies on the periodic iteration between non-deterministic events, represented by E transitions and triggered when the network tag is E, and sequential decision making, represented by the choice of which toke… view at source ↗

**Figure 2.** The classic reinforcement learning cycle integrated with A-E PN [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗

**Figure 3.** An example of A-E PN with disjoint actions. X A (X,Y)@+tf Waiting1 E X X@+1 Arrival Arrive {task_type=0}@0 {task_type=1}@0 Start1 (X,Y) Busy1 Y E Y Y X A (X,Y)@+tf Resources Waiting2 X if X.task_type=1 Start2 (X,Y) {resource_id=2}@0 {resource_id=1}@0 {resource_id=0}@0 Busy2 Y E Complete1 Complete2 X if X.task_type=0 Guard Function: None Reward Function: r = 0 Guard Function: None Reward Function: r = 0 Guard Functio… view at source ↗

Figures from the paper (9 more)

**Figure 4.** Figure 4: An example of A-E PN with joint actions. Definition 4 (Mapping from Petri Net to GymPN Assignment Graph). A mapping from (expanded) A-E PN to assignment graph is a function from a marked A-E PN T to an assignment graph G having one node for each place or transition in …

**Figure 5.** Figure 5: A-E PN with disjoint actions. The expansion procedure would produce the A-E PN reported in fig. 6, where every place contains a single token. A Resources1.1 Waiting1 E Arrive {task_type=0}@3 {task_type=1}@3 Start1.1 {resource_id=2}@2 {resource_id=1}@2 {resource_id=0}@2…

**Figure 6.** Figure 6: Expanded A-E PN with disjoint actions. The GymPN mapping algorithm applied to the A-E PN in fig. 6, produces the assignment graph in fig. 7. TYPE: Waiting1 FEATURES: [1] TYPE: E_Transition FEATURES: [1, 0, 0] TYPE: Arrival FEATURES: [1] TYPE: Arrival FEATURES: [0] TYPE…

**Figure 7.** Figure 7: Assignment graph observation for A-E PN with disjoint actions. In the same way, we can derive the assignment graph for an A-E PN with joint actions ( fig. 4). To this end, let us consider the marking reported in fig. 8. In this case, the expansion procedure would produ…

**Figure 8.** Figure 8: A-E PN with joint actions. E Arrival.1 Arrive {task_type=0}@1 Arrival.2 {task_type=1}@1 {task_type=1}@0 Waiting2 {task_type=0}@0 Resources.1 {resource_id=0}@0 {resource_id=1}@0 {resource_id=2}@0 Resources.2 Resources.3 A A A A A A Start1.1 Start2.1 Start1.2 Start2.2 St…

**Figure 9.** Figure 9: Expanded A-E PN with joint actions. The assignment graphs in the two considered cases clearly discriminate different action types, allowing the policy network to distinguish different action nodes. It can be noticed that, in fig. 7, two disconnected graphs are produce…

**Figure 10.** Figure 10: Assignment graph observation for A-E PN with joint actions. problem, as well as training and testing DRL and heuristic policies. It consists of three main modules, as illustrated in fig. 11: the Simulator that can be used to model and simulate a business process decis…

**Figure 11.** Figure 11: The GymPN component model. The Simulator facilitates modeling and simulating a business process decisionmaking problem. To this end, the simulator contains four specialized modules: A-E PN, Observation Mapping, Reward Mapping, and Action Mapping. The A-E PN module im…

**Figure 12.** Figure 12: BPMN diagrams of the eight example problems used for evaluation. In problems (a), (b), (e), (f ), (g), and h cases are composed of a single activity which needs to be executed multiple times, while in problems (c) and (d) cases are composed of two activities, one of e…

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

18 extracted references · 15 canonical work pages

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Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.

[1] [1]

URL https://github

Akkerman, F., Begnardi, L., Lo Bianco, R., Temizoz, T., Dijkman, R., Iacob, M., Mes, M., Zhang, Y., Van Jaarsveld, W.: DynaPlex. URL https://github. com/WillemvJ/Dynaplex (2022)

work page 2022

[2] [2]

Annals of Operations Research240(1), 351– 380 (May 2016)

Amaran, S., Sahinidis, N.V., Sharda, B., Bury, S.J.: Simulation optimization: a review of algorithms and applications. Annals of Operations Research240(1), 351– 380 (May 2016)

work page 2016

[3] [3]

Bynum, M.L., Hackebeil, G.A., Hart, W.E., Laird, C.D., Nicholson, B.L., Siirola, J.D., Watson, J., Woodruff, D.L.: Pyomo–optimization modeling in python, vol. 67. Springer Science & Business Media, third edn. (2021)

work page 2021

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Dijkman, R.M.: SimPN: A Python Library for Modeling and Simulating Timed, Colored Petri Nets

work page

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Journal of Machine Learning Research18(26), 1–5 (2017)

Egorov, M., Sunberg, Z.N., Balaban, E., Wheeler, T.A., Gupta, J.K., Kochender- fer, M.J.: POMDPs.jl: A Framework for Sequential Decision Making under Uncer- tainty. Journal of Machine Learning Research18(26), 1–5 (2017)

work page 2017

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Journal of Telecommunications and the Digital Economy10(2), 44–61 (Jun 2022), place: [South Melbourne, Vic.] Publisher: Telecommunications Association

Ghlala, R., Kodia, Z., Ben Said, L.: Enhancing decision-making consistency in business process using a rule-based approach: case of business intelligence process. Journal of Telecommunications and the Digital Economy10(2), 44–61 (Jun 2022), place: [South Melbourne, Vic.] Publisher: Telecommunications Association

work page 2022

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Hubbs, C.D., Perez, H.D., Sarwar, O., Sahinidis, N.V., Grossmann, I.E., Wassick, J.M.: OR-Gym: A Reinforcement Learning Library for Operations Research Prob- lems (Oct 2020), arXiv:2008.06319 [cs]

arXiv 2020

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Kumar, A., Aalst, W., Verbeek, H.: Dynamic work Distribution in Workflow Man- agement Systems: How to Balance Quality and Performance. J. of Management Information Systems18, 157–194 (Jan 2002)

work page 2002