The representation problem
A regional policy acts on part of a network, but its actions can change conditions elsewhere. Its input must therefore describe both the local components and their relationships. Simple feature averages give a fixed-size input, yet distinct connection patterns can produce the same averages.
I investigate this problem through typed component encoders for network topology control. The encoder maps variable collections of generators, loads and line terminals into fixed-width representations while retaining their connection states. It processes the network jointly; each policy reads the representations assigned to its region, together with selected raw local features.
Component identity and connection-aware pooling
Different component types provide different measurements. Type-specific maps project them into a shared latent space, and a learned connection-state embedding identifies the current attachment. Pooling then distinguishes components already connected to a busbar from those that could be moved to it by an action.
The resulting substation and line embeddings retain information about both current and possible connections. The maps are shared across components of each type. This supports variable component counts inside the encoder, while the evaluated policy readouts and action catalogues remain specific to the benchmark.
xc: measurements · τ(c): component type · bc: connection state
φ shares parameters within a component type. The state bc distinguishes the two busbars and a disconnected component; every zc has dimension 128 in this comparison.
During pooling, separate learned maps weight currently attached and potentially attachable components. Line embeddings then combine measurements with representations of the busbars at both endpoints. This structural information is present even with zero message-passing rounds.
Three choices of information exchange
The comparison keeps the embedding width at 128 and uses the same training budget, reward, action catalogue and regional selector. It varies how information moves between substation and line representations. Fixed width controls the size of the representation; it does not make the architectures identical in parameter count or computation.
- Typed encoding · K = 0
- The common component and connection-aware encoder, including line-endpoint information. No additional neighborhood updates.
- Message passing · K = 2
- Two rounds of updates along substation–line incidence relations. Current connection states remain in the features, including for disconnected lines.
- Reference PTDF/LODF
- The typed K = 0 encoder with messages weighted by physical sensitivities to injections and line outages. These sensitivities are computed once for a reference topology and remain fixed.
Evaluation: duration and constraint violations
The three trained policies are evaluated on the same 42 Bus118 validation scenarios after 250 million interactions. Episode duration measures how much of a scenario is completed. Mean overload excess measures the positive amount by which the most heavily loaded line exceeds its limit, averaged over observed steps and then across scenarios.
Encoder comparison
Message passing has the lowest mean overload excess: 1.004 × 10⁻³, compared with 1.573 × 10⁻³ for the typed baseline, a reduction of about 36%. Mean duration changes more modestly, from 70.85% to 73.09% of the horizon. It completes 20 scenarios, compared with 21 for the baseline.
Reference physics gives the longest mean duration, 75.32%, and completes 23 scenarios. However, it has higher mean excess than message passing and spends more observed time overloaded than either alternative. The encoder that best sustains operation is therefore different from the one that best limits overload in this comparison.
Experimental protocol and numerical results
The benchmark is Bus118 network topology control. The three configurations share the Reduced + lines action catalogue, Convex reward, reduced_pq_por observations, asynchronous PPO and a single-region selector. The fixed intervention gate is disabled. Training uses seed 0, 20 parallel actors, 1,000-step rollouts, four update epochs and a constant learning rate of 10⁻⁴.
Typed component mappings and bus-state embeddings distinguish current and potential attachments. Fixed substation–line incidence defines local message passing, including disconnected lines; current connection states enter through the features. K = 0 still contains structural and endpoint information. K = 2 changes the number of update rounds, not the 128-dimensional embedding width.
PTDF and LODF are sensitivity matrices from a reference DC network: they describe how injections and line outages affect flows. The matrices are fixed and are not recomputed after topology actions. This comparison tests a reference-physics prior, not an adaptive physics model.
The final 250M checkpoints are compared on 42 identical development-validation scenarios. Metrics are recomputed from retained per-scenario records. The graph experiment uses a different coordination setup from the separate Two-Lane study, so those results are not combined into a single architecture ranking.
| Policy / encoder | Duration (%) | Completed | Overloaded time (%) | Mean excess (× 10⁻³) |
|---|---|---|---|---|
| Typed encoding · K = 0 | 70.85 | 21/42 | 1.73 | 1.573 |
| Message passing · K = 2 | 73.09 | 20/42 | 1.53 | 1.004 |
| Physics-guided · PTDF/LODF | 75.32 | 23/42 | 1.92 | 1.288 |
Reading the metrics. Duration is the mean fraction of the scenario horizon reached; completion counts scenarios that reach the full horizon. Overloaded time is the mean per-scenario fraction of observed operation with at least one line at or above its thermal limit. Mean excess averages the positive part of maximum line loading minus one, first over observed operation within each episode, then across scenarios. Early termination changes the duration over which overload is measured.
Variation across scenarios
The policies also succeed on different scenarios. At least one completes 28 of the 42 scenarios; the best individual policy completes 23. Fourteen remain incomplete under all three. This motivates investigating policy selection, but the combined coverage is not the performance of an implemented ensemble.
Paired scenario outcomes
Contribution and scope
The contribution is a connection-aware observation architecture and an empirical comparison of local and physics-weighted information exchange. The study identifies different operating trade-offs at a common embedding width. It does not establish a uniformly superior encoder.
The current evidence uses one training seed per configuration and development-validation scenarios. Repeated training runs and evaluation on unseen networks are still needed to assess robustness and transfer. Shared component maps make reuse a plausible direction; they do not by themselves demonstrate generalization.
