Interpretable Policy Distillation for Power Grid Topology Control

Aleksandra Dmitruka; Karlis Freivalds

arxiv: 2606.00561 · v1 · pith:NLNQ27NGnew · submitted 2026-05-30 · 💻 cs.LG · cs.AI

Interpretable Policy Distillation for Power Grid Topology Control

Aleksandra Dmitruka , Karlis Freivalds This is my paper

Pith reviewed 2026-06-28 19:22 UTC · model grok-4.3

classification 💻 cs.LG cs.AI

keywords policy distillationreinforcement learningpower grid controldecision treesrandom forestsinterpretabilitytopology controlGrid2Op

0 comments

The pith

A PPO policy for power grid topology control can be distilled into decision trees and random forests that exceed the teacher in reward and survival at much lower inference cost.

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

The paper trains a Proximal Policy Optimization agent on the Grid2Op 14-bus environment using stress-focused data collection to handle critical states. It then distills this teacher policy into a decision tree and a random forest surrogate. On held-out validation episodes, both surrogates deliver higher mean rewards and longer survival lengths than the original neural policy. The decision tree shows strong agreement with the teacher's action choices and can be inspected directly by operators. Analysis of feature importance indicates that the tree relies more on bus topology signals while the PPO focuses on line loadings.

Core claim

Across held-out validation episodes, both the decision tree and random forest surrogates exceed the PPO teacher in mean reward and survival length at a fraction of the inference cost. The decision tree exhibits high exact-action agreement with the PPO argmax and near-complete agreement within its top-ranked actions, while feature-importance analysis reveals a shift from line-loading signals in the PPO to bus-topology variables in the distilled tree.

What carries the argument

Stress-focused policy distillation into compact tree-based models that approximate the PPO policy for grid topology actions.

Load-bearing premise

That gains observed on held-out episodes from the same 14-bus Grid2Op environment with stress-focused collection will hold for safe real-world use or other grid setups without extra safeguards.

What would settle it

Evaluating the surrogates on a modified grid configuration or with live operational traces and checking if mean reward, survival length, and safety metrics remain superior to the teacher or baseline controllers.

Figures

Figures reproduced from arXiv: 2606.00561 by Aleksandra Dmitruka, Karlis Freivalds.

**Figure 1.** Figure 1: summarizes the training diagnostics. The explained variance of the value function grows from near zero to about 0.15 over training. Policy entropy falls from roughly 5.35 to 1.40, indicating partial but not complete determinization. Approximate KL divergence drops sharply after about 50,000 steps, suggesting early stabilization or convergence to a local optimum. The teacher is therefore useful but not nece… view at source ↗

**Figure 2.** Figure 2: Twenty most frequent PPO actions in critical grid states. 5 Results 5.1 Compression Ratio and Imitation Fidelity [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗

**Figure 3.** Figure 3: shows the upper levels of the learned decision tree. The visible splits are primarily topology conditions, such as whether a given element is connected to a specific bus. This is operationally meaningful: the model’s reasoning can be described as a sequence of busbar configuration checks, not as an opaque activation pattern [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗

**Figure 4.** Figure 4: Maximum line loading max(ρ) in three representative validation scenarios. 5.3 Feature Importance and Policy Explanation The top-level decision-tree visualization already suggests that topology variables dominate the distilled decision logic. The same pattern emerges from internal tree Gini importance (reported in the appendix): 14 of the top 20 features are topology variables, while only two are direct lin… view at source ↗

**Figure 5.** Figure 5: Permutation feature importance by individual features (left) and by Grid2Op observation groups (right). 6 Discussion 6.1 Why Can the Students Outperform the Teacher? Several mechanisms make this plausible. First, the teacher is only partially converged: final entropy remains around 1.40 and value-function explained variance well below one, so its stochastic policy can pick suboptimal actions in states whe… view at source ↗

read the original abstract

Deep reinforcement learning (RL) offers a promising route to real-time power grid operation, yet large neural policies are costly to evaluate, hard to deploy on constrained hardware, and opaque to operators. We ask whether a Proximal Policy Optimization (PPO) agent for grid topology control can be compressed into compact tree-based surrogates without losing operational performance. A PPO teacher is trained on Grid2Op's standard 14-bus environment with a stability-oriented reward, using stress-focused data collection on critical, high-loading states. The policy is then distilled into a decision tree and a random forest. Across held-out validation episodes, both surrogates exceed the teacher in mean reward and survival length at a fraction of the inference cost. The decision tree shows high exact-action agreement with the PPO argmax and near-complete agreement within its top-ranked actions, while remaining small enough to be inspected directly. Feature-importance analysis reveals a representational shift: the PPO policy relies mainly on line-loading signals, while the distilled tree is driven primarily by bus-topology variables. These results suggest that stress-focused distillation can convert a black-box neural controller into a lightweight, auditable rule-like surrogate suited for real-time deployment, while also surfacing risks tied to deterministic actions and topology-specific generalization.

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

Distillation to trees beats the PPO teacher on held-out 14-bus episodes but stays inside one narrow environment.

read the letter

The core result is that the authors trained a PPO teacher on Grid2Op's 14-bus case with stress-focused collection, then distilled it into a decision tree and random forest. On held-out episodes both surrogates posted higher mean reward and longer survival than the teacher, at much lower inference cost, with the tree showing strong action agreement and a clear shift in feature importance toward bus-topology signals.

They executed the pipeline cleanly: the data collection choice, the distillation step, the held-out evaluation, and the post-hoc analysis all line up. The feature-importance comparison is a useful observation that the tree learns a different representation than the neural policy. The paper also flags the practical risks around deterministic actions and topology-specific behavior.

The soft spot is scope. Every number comes from the identical 14-bus environment and the same stress-focused sampling distribution. No results appear for the 118-bus case, different load patterns, or out-of-distribution states, so the reported gains could be tied to that particular data bias rather than a general property of the tree approximation. The abstract itself notes this limitation, but it remains the main open question.

The work is aimed at people who already work on RL for power-system control and want compact, auditable policies. A reader who needs a concrete Grid2Op example of distillation will get value from the metrics and the feature analysis. The paper is coherent on its own terms and shows honest engagement with the domain constraints, so it deserves a serious referee even if the generalization experiments are still missing.

Referee Report

2 major / 2 minor

Summary. The manuscript trains a PPO teacher policy on Grid2Op's 14-bus environment for topology control using stability-oriented rewards and stress-focused data collection on high-loading states, then distills the policy into a decision tree and random forest. It reports that both surrogates exceed the teacher in mean reward and survival length on held-out validation episodes, at lower inference cost; the decision tree exhibits high exact-action agreement with the PPO argmax (and near-complete agreement within top-ranked actions), remains small enough for direct inspection, and shows a representational shift where feature importance moves from line-loading signals (dominant in PPO) to bus-topology variables.

Significance. If the empirical results hold under broader testing, the work would demonstrate a practical route to compact, auditable rule-like surrogates for RL-based grid control, addressing deployment constraints on hardware and operator interpretability. The stress-focused distillation procedure and the observed feature-importance shift constitute concrete, falsifiable contributions that could inform similar compression efforts in other safety-critical control domains.

major comments (2)

[Results / Evaluation sections] Results / Evaluation sections: the central claim that surrogates exceed the teacher in mean reward and survival length rests on held-out episodes drawn exclusively from the same 14-bus Grid2Op environment and stress-focused collection distribution; no experiments on alternate topologies (e.g., 118-bus), non-stress loading regimes, or out-of-distribution states are reported, rendering the generalization required for real-world deployment claims untested.
[Abstract and §3 (distillation procedure)] Abstract and §3 (distillation procedure): the assertion of superior surrogate performance and high action agreement supplies no quantitative metrics, confidence intervals, statistical tests, or exact agreement percentages; without these numbers the empirical superiority cannot be verified or compared to baselines.

minor comments (2)

[Abstract] The phrase 'a fraction of the inference cost' is used without reporting wall-clock times, FLOPs, or speedup ratios relative to the neural policy.
[§2] Notation for the stability-oriented reward and the precise definition of 'stress-focused' state sampling should be formalized in §2 to allow exact reproduction.

Simulated Author's Rebuttal

2 responses · 1 unresolved

We thank the referee for the constructive feedback on generalization and quantitative reporting. We address each major comment below and note one standing limitation.

read point-by-point responses

Referee: [Results / Evaluation sections] Results / Evaluation sections: the central claim that surrogates exceed the teacher in mean reward and survival length rests on held-out episodes drawn exclusively from the same 14-bus Grid2Op environment and stress-focused collection distribution; no experiments on alternate topologies (e.g., 118-bus), non-stress loading regimes, or out-of-distribution states are reported, rendering the generalization required for real-world deployment claims untested.

Authors: We agree the evaluation is restricted to the 14-bus benchmark. This is the standard setting in Grid2Op topology-control studies, and our contribution centers on showing that stress-focused distillation can produce compact, interpretable surrogates that match or exceed the teacher within this environment. We will add an explicit limitations paragraph stating that broader generalization to 118-bus systems or non-stress regimes remains untested and is left for future work. No additional experiments will be performed. revision: partial
Referee: [Abstract and §3 (distillation procedure)] Abstract and §3 (distillation procedure): the assertion of superior surrogate performance and high action agreement supplies no quantitative metrics, confidence intervals, statistical tests, or exact agreement percentages; without these numbers the empirical superiority cannot be verified or compared to baselines.

Authors: The referee is correct that the abstract and §3 currently give only qualitative statements. The detailed numerical results (mean rewards, survival times, exact-match percentages, and top-k agreement) appear only in the evaluation section. We will move the key quantitative figures, including standard deviations and agreement rates, into the abstract and §3 so that the superiority claims are directly verifiable. revision: yes

standing simulated objections not resolved

Experiments on the 118-bus topology, non-stress regimes, or out-of-distribution states are not present and cannot be added without substantial new computation.

Circularity Check

0 steps flagged

No circularity detected; empirical evaluation on held-out episodes is independent of inputs

full rationale

The paper trains a PPO policy on the 14-bus Grid2Op environment, distills it into a decision tree and random forest via standard supervised learning on collected trajectories, and reports performance metrics (mean reward, survival length, action agreement) on separate held-out validation episodes. These comparisons are direct empirical measurements and do not reduce by construction to the training data, fitted parameters, or any self-citation chain. No equations, uniqueness theorems, or ansatzes are invoked that would make the reported superiority tautological. The reader's assessment of score 2.0 aligns with the absence of any load-bearing circular step.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim depends on the fidelity of the Grid2Op simulator and standard RL training assumptions; no explicit free parameters or invented entities are introduced beyond conventional training choices.

axioms (2)

domain assumption The Grid2Op 14-bus environment accurately models real power grid dynamics for the purpose of policy evaluation.
All training and validation rest on this simulation environment.
domain assumption The stability-oriented reward function aligns with operational safety objectives.
Used to train the PPO teacher and evaluate surrogates.

pith-pipeline@v0.9.1-grok · 5750 in / 1408 out tokens · 27752 ms · 2026-06-28T19:22:44.678425+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

18 extracted references · 11 canonical work pages · 2 internal anchors

[1]

arXiv preprint arXiv:2503.20688 (2025)

Anguiano Batanero, E., Fernández, Á., Barbero, Á.: Graph-enhanced model-free reinforcement learning agents for efficient power grid topological control. arXiv preprint arXiv:2503.20688 (2025)

work page arXiv 2025
[2]

In: Advances in Neural Information Processing Systems 31

Bastani, O., Pu, Y., Solar-Lezama, A.: Verifiable reinforcement learning via policy extraction. In: Advances in Neural Information Processing Systems 31. pp. 2499– 2509 (2018)

2018
[3]

Random forests,

Breiman, L.: Random forests. Machine Learning45(1), 5–32 (2001). https://doi.org/10.1023/A:1010933404324

work page doi:10.1023/a:1010933404324 2001
[4]

In: Proceedings of the IJCAI 2019 Workshop on Explainable Artificial Intelligence

Coppens, Y., Efthymiadis, K., Lenaerts, T., Nowé, A.: Distilling deep reinforcement learning policies in soft decision trees. In: Proceedings of the IJCAI 2019 Workshop on Explainable Artificial Intelligence. pp. 1–6 (2019)

2019
[5]

io/(2026), version 1.12.4; accessed 22 May 2026

Grid2Op Contributors: Grid2Op documentation.https://grid2op.readthedocs. io/(2026), version 1.12.4; accessed 22 May 2026

2026
[6]

Energy and AI23, 100671 (2026)

Hassouna, M., Holzhüter, C., Lytaev, P., Thomas, J., Sick, B., Scholz, C.: Graph reinforcement learning for power grids: A comprehensive survey. Energy and AI23, 100671 (2026). https://doi.org/10.1016/j.egyai.2025.100671

work page doi:10.1016/j.egyai.2025.100671 2026
[7]

Distilling the Knowledge in a Neural Network

Hinton, G., Vinyals, O., Dean, J.: Distilling the knowledge in a neural network. arXiv preprint arXiv:1503.02531 (2015)

work page internal anchor Pith review Pith/arXiv arXiv 2015
[8]

arXiv preprint arXiv:2003.07339 (2020)

Kelly, A., O’Sullivan, A., de Mars, P., Marot, A.: Reinforcement learning for electricity network operation. arXiv preprint arXiv:2003.07339 (2020)

work page arXiv 2003
[9]

Sustainable Energy, Grids and Networks39, 101510 (2024)

Lehna, M., Holzhüter, C., Tomforde, S., Scholz, C.: HUGO: Highlighting un- seen grid options: Combining deep reinforcement learning with a heuristic target topology approach. Sustainable Energy, Grids and Networks39, 101510 (2024). https://doi.org/10.1016/j.segan.2024.101510

work page doi:10.1016/j.segan.2024.101510 2024
[10]

arXiv preprint arXiv:2503.23101 (2025)

Marchesini, E., Donnot, B., Crozier, C., Dytham, I., Merz, C., Schewe, L., Wester- beck, N., Wu, C., Marot, A., Donti, P.L.: RL2Grid: Benchmarking reinforcement learning in power grid operations. arXiv preprint arXiv:2503.23101 (2025)

work page arXiv 2025
[11]

Lulu.com (2020)

Molnar, C.: Interpretable Machine Learning. Lulu.com (2020)

2020
[12]

In: Proceedings of the Sixteenth International Conference on Machine Learning

Ng, A.Y., Harada, D., Russell, S.: Policy invariance under reward transforma- tions: Theory and application to reward shaping. In: Proceedings of the Sixteenth International Conference on Machine Learning. pp. 278–287 (1999)

1999
[13]

Stopexplainingblackboxmachinelearningmodelsforhighstakesdecisions and use interpretable models instead.Nature Machine Intelligence, 1(5):206–215, 2019

Rudin, C.: Stop explaining black box machine learning models for high stakes decisions and use interpretable models instead. Nature Machine Intelligence1(5), 206–215 (2019). https://doi.org/10.1038/s42256-019-0048-x

work page doi:10.1038/s42256-019-0048-x 2019
[14]

MIT Press, 2 edn

Sutton, R.S., Barto, A.G.: Reinforcement Learning: An Introduction. MIT Press, 2 edn. (2018)

2018
[15]

Gymnasium: A Standard Interface for Reinforcement Learning Environments

Towers, M., Kwiatkowski, A., Terry, J., Balis, J.U., De Cola, G., Deleu, T., Goulão, M., Kallinteris, A., Krimmel, M., KG, A., Perez-Vicente, R., Pierré, A., Schulhoff, S., Tai, J.J., Tan, H., Younis, O.G.: Gymnasium: A standard interface for reinforcement learning environments. arXiv preprint arXiv:2407.17032 (2024)

work page internal anchor Pith review Pith/arXiv arXiv 2024
[16]

arXiv preprint arXiv:2408.11632 (2024)

Vos, D., Verwer, S.: Optimizing interpretable decision tree policies for reinforcement learning. arXiv preprint arXiv:2408.11632 (2024)

work page arXiv 2024
[17]

In: International Conference on Learning Representations (2021)

Yoon, D., Hong, S., Lee, B.J., Kim, K.E.: Winning the L2RPN challenge: Power grid management via semi-markov afterstate actor-critic. In: International Conference on Learning Representations (2021)

2021
[18]

arXiv preprint arXiv:2106.15200 (2021)

Zhou, B., Zeng, H., Liu, Y., Li, K., Wang, F., Tian, H.: Action set based policy optimization for safe power grid management. arXiv preprint arXiv:2106.15200 (2021)

work page arXiv 2021

[1] [1]

arXiv preprint arXiv:2503.20688 (2025)

Anguiano Batanero, E., Fernández, Á., Barbero, Á.: Graph-enhanced model-free reinforcement learning agents for efficient power grid topological control. arXiv preprint arXiv:2503.20688 (2025)

work page arXiv 2025

[2] [2]

In: Advances in Neural Information Processing Systems 31

Bastani, O., Pu, Y., Solar-Lezama, A.: Verifiable reinforcement learning via policy extraction. In: Advances in Neural Information Processing Systems 31. pp. 2499– 2509 (2018)

2018

[3] [3]

Random forests,

Breiman, L.: Random forests. Machine Learning45(1), 5–32 (2001). https://doi.org/10.1023/A:1010933404324

work page doi:10.1023/a:1010933404324 2001

[4] [4]

In: Proceedings of the IJCAI 2019 Workshop on Explainable Artificial Intelligence

Coppens, Y., Efthymiadis, K., Lenaerts, T., Nowé, A.: Distilling deep reinforcement learning policies in soft decision trees. In: Proceedings of the IJCAI 2019 Workshop on Explainable Artificial Intelligence. pp. 1–6 (2019)

2019

[5] [5]

io/(2026), version 1.12.4; accessed 22 May 2026

Grid2Op Contributors: Grid2Op documentation.https://grid2op.readthedocs. io/(2026), version 1.12.4; accessed 22 May 2026

2026

[6] [6]

Energy and AI23, 100671 (2026)

Hassouna, M., Holzhüter, C., Lytaev, P., Thomas, J., Sick, B., Scholz, C.: Graph reinforcement learning for power grids: A comprehensive survey. Energy and AI23, 100671 (2026). https://doi.org/10.1016/j.egyai.2025.100671

work page doi:10.1016/j.egyai.2025.100671 2026

[7] [7]

Distilling the Knowledge in a Neural Network

Hinton, G., Vinyals, O., Dean, J.: Distilling the knowledge in a neural network. arXiv preprint arXiv:1503.02531 (2015)

work page internal anchor Pith review Pith/arXiv arXiv 2015

[8] [8]

arXiv preprint arXiv:2003.07339 (2020)

Kelly, A., O’Sullivan, A., de Mars, P., Marot, A.: Reinforcement learning for electricity network operation. arXiv preprint arXiv:2003.07339 (2020)

work page arXiv 2003

[9] [9]

Sustainable Energy, Grids and Networks39, 101510 (2024)

Lehna, M., Holzhüter, C., Tomforde, S., Scholz, C.: HUGO: Highlighting un- seen grid options: Combining deep reinforcement learning with a heuristic target topology approach. Sustainable Energy, Grids and Networks39, 101510 (2024). https://doi.org/10.1016/j.segan.2024.101510

work page doi:10.1016/j.segan.2024.101510 2024

[10] [10]

arXiv preprint arXiv:2503.23101 (2025)

Marchesini, E., Donnot, B., Crozier, C., Dytham, I., Merz, C., Schewe, L., Wester- beck, N., Wu, C., Marot, A., Donti, P.L.: RL2Grid: Benchmarking reinforcement learning in power grid operations. arXiv preprint arXiv:2503.23101 (2025)

work page arXiv 2025

[11] [11]

Lulu.com (2020)

Molnar, C.: Interpretable Machine Learning. Lulu.com (2020)

2020

[12] [12]

In: Proceedings of the Sixteenth International Conference on Machine Learning

Ng, A.Y., Harada, D., Russell, S.: Policy invariance under reward transforma- tions: Theory and application to reward shaping. In: Proceedings of the Sixteenth International Conference on Machine Learning. pp. 278–287 (1999)

1999

[13] [13]

Stopexplainingblackboxmachinelearningmodelsforhighstakesdecisions and use interpretable models instead.Nature Machine Intelligence, 1(5):206–215, 2019

Rudin, C.: Stop explaining black box machine learning models for high stakes decisions and use interpretable models instead. Nature Machine Intelligence1(5), 206–215 (2019). https://doi.org/10.1038/s42256-019-0048-x

work page doi:10.1038/s42256-019-0048-x 2019

[14] [14]

MIT Press, 2 edn

Sutton, R.S., Barto, A.G.: Reinforcement Learning: An Introduction. MIT Press, 2 edn. (2018)

2018

[15] [15]

Gymnasium: A Standard Interface for Reinforcement Learning Environments

Towers, M., Kwiatkowski, A., Terry, J., Balis, J.U., De Cola, G., Deleu, T., Goulão, M., Kallinteris, A., Krimmel, M., KG, A., Perez-Vicente, R., Pierré, A., Schulhoff, S., Tai, J.J., Tan, H., Younis, O.G.: Gymnasium: A standard interface for reinforcement learning environments. arXiv preprint arXiv:2407.17032 (2024)

work page internal anchor Pith review Pith/arXiv arXiv 2024

[16] [16]

arXiv preprint arXiv:2408.11632 (2024)

Vos, D., Verwer, S.: Optimizing interpretable decision tree policies for reinforcement learning. arXiv preprint arXiv:2408.11632 (2024)

work page arXiv 2024

[17] [17]

In: International Conference on Learning Representations (2021)

Yoon, D., Hong, S., Lee, B.J., Kim, K.E.: Winning the L2RPN challenge: Power grid management via semi-markov afterstate actor-critic. In: International Conference on Learning Representations (2021)

2021

[18] [18]

arXiv preprint arXiv:2106.15200 (2021)

Zhou, B., Zeng, H., Liu, Y., Li, K., Wang, F., Tian, H.: Action set based policy optimization for safe power grid management. arXiv preprint arXiv:2106.15200 (2021)

work page arXiv 2021