Research map / Learning theory and algorithms / Combinatorial and search optimization
E2E-AT: A Unified Framework for Tackling Uncertainty in Task-Aware End-to-End Learning
Read the paperCheck your idea against 108,967 papers
AI-extracted summary. Written by AI from the paper's full text. Numbers and claims can be wrong or missing context, so check the paper before you cite or build on it.
Proposes E2E-AT, a robust-optimization adversarial training framework for end-to-end predict-then-optimize learning that treats both input-feature and constrained-optimization parameter uncertainty, with MILP-based certification for affine-parametric QPs, evaluated on a power-system load forecasting and economic dispatch task.
Problem
End-to-end learning combining ML forecasting with downstream constrained optimization ignores uncertainty in the unpredictable parameters of the optimization, not only in the ML input space, causing generalization and robustness gaps.
Approach
Treats input-feature uncertainty and unpredictable CO parameter uncertainty uniformly as a robust optimization problem solved by adversarial training through the optimization layer (implicit differentiation), and certifies worst-case task cost via MILP reformulation of affine-parametric QPs and piecewise-linear networks.
Key results
- NAT's task cost rises from 201.6 clean to 3468.4 under a CO attack with epsilon_phi=0.15, showing CO uncertainty greatly increases cost.
- AT-PARA (epsilon_phi=0.15, alpha=1.0) reduces CO attack cost at epsilon 0.15 from 3468.4 (NAT) to 453.2 and keeps clean cost near 214.0.
- AT-BOTH (epsilon_x=0.03, epsilon_phi=0.15, alpha=0.5) gives integrated-attack cost 1053.7 versus 5214.4 for NAT at (0.03,0.15).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Train with input uncertainty using task loss (AT-INPUT) instead of natural task-loss training | E2E load forecaster · NCED, input attack εx=0.03 | task-aware cost: 1792.1 -> 1022.1 | Helped |
| Train with CO uncertainty (AT-PARA) instead of natural task-loss training | E2E load forecaster · NCED, CO attack εφ=0.15 | task-aware cost: 3468.4 -> 453.2 | Helped |
| Train with integrated input and CO uncertainties (AT-BOTH) instead of natural task-loss training | E2E load forecaster · NCED, integrated attack (0.03, 0.15) | task-aware cost: 5214.4 -> 1274.0 | Helped |
| Use MSE loss adversarial training on input uncertainty instead of natural training | E2E load forecaster · NCED, input attack εx=0.03 | task-aware cost: 1792.1 -> 1125.5 | Helped |
| Use MSE loss adversarial training on input uncertainty instead of natural training | E2E load forecaster · NCED, CO attack εφ=0.15 | task-aware cost: 3468.4 -> 3881.6 | Hurt |
| Use CO-uncertainty training instead of input-only training | E2E load forecaster · NCED, integrated attack (0.03, 0.15) | task-aware cost: 4507.0 -> 1502.0 | Helped |
| Set α=0.5 rather than α=1.0 in AT-INPUT with εx=0.02 (ablation) | AT-INPUT · NCED, integrated attack (0.02, 0.05) | task-aware cost: 934.4 -> 914.8 | Helped |
| Set α=0.5 rather than α=1.0 in AT-INPUT with εx=0.02 (ablation) | AT-INPUT · NCED, clean | task-aware cost: 219.1 -> 203.1 | Helped |
| Set α=0.5 rather than α=1.0 in AT-PARA with εφ=0.05 (ablation) | AT-PARA · NCED, integrated attack (0.02, 0.05) | task-aware cost: 399.1 -> 419.8 | Hurt |
| Set α=0.5 rather than α=1.0 in AT-BOTH with εx=0.02 and εφ=0.05 (ablation) | AT-BOTH · NCED, integrated attack (0.02, 0.05) | task-aware cost: 400.5 -> 516.0 | Hurt |
| Increase the CO attack-training budget from εφ=0.05 to εφ=0.15 (ablation) | AT-PARA, α=1.0 · NCED, CO attack εφ=0.05 | task-aware cost: 214.9 -> 214.0 | Mixed |
| Train on both input and CO uncertainties rather than input uncertainty alone | E2E load forecaster · NCED, integrated attack (0.03, 0.15) | task-aware cost: 4507.0 -> 1274.0 | Helped |
Surprising findings
- Adversarial training on CO parameters also improves robustness to input attacks when the input budget is small, and vice versa.
- Under the larger input budget experiment, input adversarial training also improved CO robustness, contrary to the smaller-budget results.
Limitations
- Exact MILP certification is too expensive for adversarial training and was only run on 15 samples with Gurobi.
- Restricted to QP lower-level problems and linearity in uncertain parameters (DPP setting).
- Gradients of E2E-AT are large and unstable, requiring gradient clipping.
Experimental setup
Datasets: Texas Backbone Power System load forecasting dataset IEEE bus-14 system (PyPower)
Benchmarks: Texas Backbone Power System load forecasting with NCED dispatch/redispatch on modified IEEE bus-14
Metrics: task-aware cost under clean, input, CO, and integrated attac certified worst-case cost via MILP
Baselines: NAT AT-MSE AT-INPUT AT-PARA
Builds on: adversarial training PGD adversarial training for free OptNet CvxpyLayers
Closest papers by meaning
- A Deep Generative Learning Approach for Two-stage Adaptive Robust Optimization (ICLR 2025 · similarity 0.86)
- End-to-End Learning for Stochastic Optimization: A Bayesian Perspective (ICML 2023 · similarity 0.85)
- Towards Robust Learning to Optimize with Theoretical Guarantees (CVPR 2024 · similarity 0.84)
- Learning Scenario Reduction for Two-Stage Robust Optimization with Discrete Uncertainty (NeurIPS 2026 · similarity 0.83)
- BPQP: A Differentiable Convex Optimization Framework for Efficient End-to-End Learning (NeurIPS 2024 · similarity 0.82)
- Energy-Based Transformers are Scalable Learners and Thinkers (ICLR 2026 · similarity 0.81)
Writing a paper in this area? scime draft is a free LaTeX editor with AI included, real-time co-authors and a check of your references and venue rules before you submit. It also imports OpenAI Prism projects.