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A Deep Generative Learning Approach for Two-stage Adaptive Robust Optimization

ICLR 2025 · Learning theory and algorithms › Prediction and decision losses · approach: Distributionally robust optimization · 0 citations (OpenAlex)

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Proposes AGRO, which embeds a VAE-learned uncertainty set (image of a latent ball under the decoder) into column-and-constraint generation and uses projected gradient ascent through the decoder and exact LP recourse to find adversarial yet realistic contingencies for two-stage adaptive robust optimization.

Problem

Two-stage adaptive robust optimization with high-dimensional, irregularly distributed uncertainty, where classical polyhedral/ellipsoidal uncertainty sets are loose and yield over-conservative first-stage decisions, and the exact bilinear KKT adversarial subproblem in CCG is computationally expensiv

Approach

Define a tight uncertainty set as the image of a latent L2-ball under a VAE decoder, calibrated with a conformal-style quantile bound on latent norms, and solve the adversarial subproblem heuristically by projected gradient ascent over the latent variable, differentiating the exact LP recourse cost through the decoder.

Key results

• AGRO outperforms CCG by up to 1.8% in production-distribution planning cost.
• On the New England capacity expansion problem, AGRO with L=4 reduces total cost by about 8% on average over CCG with budget-box uncertainty, with lower total runtime (2299 s vs 29183 s).
• CCG subproblems with ellipsoidal sets could not be solved to optimality within 900 s for larger instances, while AGRO scaled better in runtime.

Measured effects reported in the paper

Surprising findings

• The optimal bottleneck dimension for cost does not coincide with the best generative fidelity/diversity metrics; lower-fidelity VAEs can yield better planning because they avoid over-committing to unrealistic extremes.
• In the low-dimensional production problem, higher-bottleneck VAEs over-produce, while in high-dimensional settings a low L (L=2) underestimates worst-case costs despite lowest VaR approximation error.

Limitations

• PGA is a local heuristic and not guaranteed to find the global worst-case realization; mitigated only by random restarts.
• Coverage of the VAE uncertainty set can fall below the target alpha for low bottleneck dimensions, breaking the probabilistic guarantee.
• Bottleneck dimension L must be tuned by trial and error, and its selection involves a tradeoff between fidelity and diversity.

Experimental setup

Datasets: synthetic Gaussian mixture demand data (production-distribution) New England transmission system historical renewable capacity factor and energy demand data

Benchmarks: synthetic production-distribution problem New England capacity expansion planning problem

Metrics: out-of-sample cost (c^T x + alpha-quantile of recourse cost, runtime VaR approximation error precision density recall coverage

Baselines: column-and-constraint generation with budget uncertainty set column-and-constraint generation with ellipsoidal uncertainty set

Builds on: column-and-constraint generation deep data-driven uncertainty sets variational autoencoder cvxpylayers

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