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Distributionally Robust Performative Optimization

NeurIPS 2025 · Learning theory and algorithms › Prediction and decision losses · approach: Distributionally robust optimization · 1 citations (OpenAlex)

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Proposes distributionally robust performative optimization (DRPO) with Wasserstein ambiguity sets and a repeated robust risk minimization (RRRM) algorithm that alternates DRO solves with ambiguity-set updates, with convergence and suboptimality guarantees.

Problem

Performative stochastic optimization where decisions shift the data distribution, but the true distribution map is unknown and only imperfect reference distributions are available, so solutions can be badly suboptimal under misspecification and data scarcity.

Approach

Builds a Wasserstein ambiguity set around a reference distribution map and decouples the ambiguity-set center (previous decision) from the risk being minimized, so each iteration is a tractable decision-independent DRO problem solved via conic reformulations; exponential smoothing and a 2-Wasserstein convex-concave model handle nonsmoothness and nonconvexity.

Key results

• In strategic classification with 200 training samples, robust models (type-1 and type-2 Wasserstein) significantly outperform the non-robust baseline and the AMKL algorithm, with the type-2 model best across 50 trials.
• In revenue management, the robust price consistently yields higher expected profit than the non-robust surrogate-based price, with smaller optimality gap relative to the optimal price.
• In demand response portfolio optimization, the robust scheme outperforms the non-robust scheme in mean profit, with the non-robust scheme often losing money under high demand.

Measured effects reported in the paper

Surprising findings

• The AMKL KL-divergence baseline performs quite poorly in strategic classification, possibly due to local optima and limited protection against shifts not represented in the reference distribution.
• Theory suggests the distributionally robust model can yield faster convergence than its non-robust counterpart.

Limitations

• Convergence and suboptimality guarantees rely on strong assumptions (strong convexity, smoothness, bounded supports, epsilon-sensitivity of the distribution map).
• Radius rho is hard to select; results depend on the chosen ambiguity radius (0.1 used in experiments).
• Experiments are small-scale simulations on a single laptop, not large real-world deployments.

Experimental setup

Datasets: Kaggle credit scoring dataset (class-balanced subset) simulated revenue management demand simulated demand response beta-noise model

Benchmarks: strategic classification out-of-sample loss (credit scoring) revenue management expected profit demand response mean profit

Metrics: out-of-sample loss expected profit optimality gap

Baselines: AMKL (alternating minimization under KL ambiguity) non-robust performative model non-robust pricing (surrogate model) non-robust DR scheduling

Builds on: performative prediction repeated risk minimization distributionally robust optimization alternating minimization KL ambiguity (AMKL)

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