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Uncertainty-aware Predict-Then-Optimize Framework for Equitable Post-Disaster Power Restoration

This paper proposes EPOPR, an uncertainty-aware predict-then-optimize framework that combines Equity-Conformalized Quantile Regression and Spatial-Temporal Attentional Reinforcement Learning to balance restoration efficiency and equity, effectively reducing average outage durations and inter-community disparities in post-disaster power recovery.

Original authors: Lin Jiang, Dahai Yu, Rongchao Xu, Tian Tang, Guang Wang

Published 2026-08-06

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CC BY 4.0

Original authors: Lin Jiang, Dahai Yu, Rongchao Xu, Tian Tang, Guang Wang

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine the world of computer science as a giant, bustling kitchen where chefs (algorithms) are trying to fix a massive mess after a storm. Sometimes, the storm is a hurricane that knocks out the lights for millions of people. The goal of this specific branch of science is to figure out the best order to flip the switches back on. But here's the tricky part: the chefs don't just want to be fast; they want to be fair. They are building tools that use "Uncertainty Quantification" (which is just a fancy way of saying, "How sure are we about our guess?") and "Reinforcement Learning" (where a computer learns by playing a game, trying different moves, and getting points for good choices). Why does anyone care? Because when the power goes out, it's not just an inconvenience; for some families, it's a safety crisis. If the system only listens to the loudest voices or the biggest crowds, the quietest neighborhoods might wait the longest in the dark.

This paper tells the story of a team of researchers who noticed a glitch in how cities usually fix power outages. They found that the current system is a bit like a teacher who only helps students who raise their hands the most. In reality, after a hurricane, wealthier neighborhoods often know how to submit repair requests faster and in higher numbers, while poorer, disadvantaged communities might not know the channels or have the resources to complain as loudly. The result? The power company sends crews to the noisy, crowded areas first, leaving the quiet, struggling neighborhoods in the dark for days longer than they should be. The researchers also realized that predicting how long a repair will take is a nightmare because the data is messy; some areas have tons of repair history, while others have almost none, making it hard to guess the future.

To fix this, the authors built a new system called EPOPR (Equity-aware Predict-Then-Optimize Power Restoration). Think of EPOPR as a super-smart, fair-minded dispatcher with two special superpowers.

First, it has a "Fairness Crystal Ball" (called ECQR). Usually, when computers try to guess how long a repair will take, they get really confident about rich areas (because they have lots of data) but guess wildly for poor areas (because they have little data). This new crystal ball is special because it forces the computer to be equally honest about its uncertainty for everyone. It doesn't just say, "We think this will take 2 hours"; it says, "We are pretty sure it's between 1 and 3 hours for the rich neighborhood, and we are also sure it's between 1 and 3 hours for the poor neighborhood," even if the data is scarce. It adjusts its confidence so that no group gets left behind with a bad guess.

Second, it has a "Fairness Game Player" (called STA-SAC). This is the part that decides which neighborhood to visit next. Imagine a delivery driver who usually just picks the closest house to save gas. But this driver has a new rule: they must make sure no neighborhood waits too much longer than any other. The AI plays a game where it gets points for being fast but loses points if it makes the wait times between rich and poor areas too different. It uses a special "attention" mechanism, like a spotlight, to look at the whole map at once, understanding that fixing one area might help or hurt the timeline of another, all while keeping the "fairness score" high.

The team tested their idea using real data from Tallahassee, Florida, from the time of Hurricane Michael in 2018. They ran simulations to see how their new system would perform compared to the old ways of doing things. The results were promising: in their simulations, EPOPR managed to cut the average time people spent without power by 3.60% and, more importantly, reduced the unfair gap in waiting times between different communities by 14.19%.

The paper suggests that by combining a smarter way to guess repair times with a decision-maker that cares about fairness, we can build a system that doesn't just restore power quickly, but restores it justly. It shows that we don't have to choose between being efficient and being fair; with the right tools, we can do both. However, the authors are careful to note that these results come from computer simulations based on past data, meaning the system is ready to be tested in the real world, but it hasn't been proven to work on a live, active hurricane yet. The goal is to ensure that when the next storm hits, no community is left in the dark simply because they didn't shout loud enough.

Technical Summary: Uncertainty-aware Predict-Then-Optimize Framework for Equitable Post-Disaster Power Restoration

Problem Statement
Following extreme weather events, such as hurricanes, power system restoration is critical for social well-being. However, current restoration strategies often rely on the volume of repair requests submitted by residents to prioritize regions. Data-driven analysis reveals that this approach is inequitable: disadvantaged communities (often lower-income) tend to submit fewer requests due to limited awareness of submission channels or access issues. Consequently, these regions are deprioritized, leading to disproportionately longer power outages.

Addressing this inequity presents two technical challenges:

Heteroscedasticity in Prediction: Historical repair request data exhibits significant variance across regions. Traditional deterministic prediction methods fail to capture this variability, and standard uncertainty quantification techniques often result in unequal coverage across sensitive groups (e.g., income levels), potentially exacerbating disparities.
Equity in Optimization: Standard Reinforcement Learning (RL) agents tend to favor actions with lower uncertainty to minimize error accumulation. This behavior inadvertently prioritizes regions with stable (low-variance) repair durations, conflicting with the goal of ensuring equitable restoration times across all communities.

Methodology: The EPOPR Framework
The authors propose EPOPR (Equity-aware Predict-then-Optimize Power Restoration), a framework designed to balance restoration efficiency with equity. It consists of two primary components:

Equity-Conformalized Quantile Regression (ECQR) for Prediction:
- Goal: To predict repair durations with uncertainty intervals that maintain equitable coverage across sensitive features (e.g., income groups).
- Mechanism: Building on Conformalized Quantile Regression (CQR), ECQR introduces a group-based calibration strategy. Instead of calibrating prediction intervals over the entire dataset, it calculates separate calibration factors for each sensitive group ( $F_k$ ).
- Outcome: This ensures that the theoretical coverage rate (e.g., 90%) is uniform across all groups. It employs dynamic prediction intervals that adapt to the varying levels of dispersion (heteroscedasticity) in different regions, preventing disadvantaged groups from suffering from overly wide or inaccurate intervals.
Spatial-Temporal Attentional Soft Actor-Critic (STA-SAC) for Decision-Making:
- Goal: To determine the optimal repair sequence that minimizes total outage duration while satisfying equity constraints.
- Formulation: The problem is modeled as a Constrained Markov Decision Process (CMDP). The objective is to maximize the negative average outage duration (efficiency) subject to a constraint on the Wasserstein distance between outage duration distributions of different sensitive groups (equity).
- Architecture:
  - Actor: Utilizes a Spatial-Temporal Attention mechanism based on a Transformer architecture. It handles dynamic action sets (regions available for repair) and captures spatiotemporal dependencies among uncertainties. It uses a query-key mechanism to estimate the selection probability of candidate regions.
  - Critic: Employs a Soft Actor-Critic (SAC) backbone with Lagrange multipliers. This integrates cost constraints (equity) directly into the reward-based optimization, allowing the agent to learn a policy that balances efficiency and fairness.

Key Contributions

Data-Driven Insights: The analysis of real-world data from Tallahassee, Florida, confirms that current restoration processes are inequitable, favoring regions with higher request volumes (typically wealthier). It also identifies heteroscedasticity in repair data as a barrier to fair decision-making.
Novel Framework (EPOPR): The integration of ECQR and STA-SAC provides a unified approach to handle uncertainty and equity simultaneously.
- ECQR ensures that uncertainty estimates do not systematically disadvantage specific socioeconomic groups.
- STA-SAC explicitly enforces equity constraints during the optimization of repair sequences, overcoming the bias of standard RL agents toward low-uncertainty actions.
Empirical Validation: The framework was evaluated using real-world outage datasets from Hurricane Michael (2018).

Experimental Results
Using data from Tallahassee (55 regions), EPOPR was compared against several baselines, including Ground Truth (historical data), Greedy Methods, Traveling Salesman Problem (TSP) variants, and other RL-based approaches (RL-DTSP, HRL-DPDP) and uncertainty-aware methods (ROPU).

Efficiency: EPOPR reduced the average power outage duration by 3.60% compared to the best-performing baseline (ROPU).
Equity: EPOPR decreased the inequity between different communities (measured by the maximum Wasserstein distance of outage distributions) by 14.19% compared to ROPU.
Prediction Performance: ECQR significantly improved prediction coverage for low-income regions compared to standard CQR and Conformal Prediction, narrowing the gap in prediction reliability across income groups while maintaining overall statistical efficiency.

Significance and Claims
The paper claims that EPOPR offers a robust solution for post-disaster power restoration by explicitly addressing the intersection of uncertainty quantification and algorithmic fairness. By decoupling the prediction of repair durations from the optimization of repair sequences while ensuring both stages are "equity-aware," the framework mitigates the systemic bias inherent in request-volume-based prioritization. The results suggest that AI-driven strategies can effectively reduce disparities in service delivery for vulnerable populations without sacrificing overall system efficiency. The work is positioned as a step toward "AI and Social Good," demonstrating how technical advancements in uncertainty-aware optimization can directly address social inequities in critical infrastructure recovery.

Technical Summary: Uncertainty-aware Predict-Then-Optimize Framework for Equitable Post-Disaster Power Restoration

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