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Gradient-Based Nonlinear Rehearsal Learning with Multivariate Alterations

AAAI 2025 · Learning theory and algorithms › Prediction and decision losses · approach: Data attribution and recourse · 0 citations (OpenAlex)

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Proposes Grad-Rh, a gradient-based method for multivariate decision-making in nonlinear, non-Gaussian rehearsal learning, using conditional normalizing flows and four surrogate losses tied to the Chebyshev center of the desired region.

Problem

Finding multivariate decisions in sampling-based rehearsal learning is computationally infeasible in polynomial time, and prior work was restricted to linear Gaussian structural rehearsal models.

Approach

Model the data-generating process per bi-directional clique with conditional normalizing flows, then replace the indicator objective of finding decisions that keep outcomes in a convex desired set with differentiable surrogate losses (center MSE/MAE, r-insensitive, Huber) that push samples toward the Chebyshev center or inside the largest inscribed ball, optimized by Adam.

Key results

• On linear datasets Grad-Rh (center MAE) achieves roughly 0.94-0.96 success on Linear1 versus 0.96 for exact QWZ23 while running in about 0.2 s versus 1.1 s.
• On nonlinear MLP1 the exact baseline QWZ23 gets 0.00 success within the 120 s limit, while Grad-Rh's r-insensitive loss achieves 0.26 success in 7.7 s.
• On MLP3 QWZ23 reaches 0.27 success with a 120 s time limit while Grad-Rh center MSE reaches 0.42 in 12.0 s.

Measured effects reported in the paper

Surprising findings

• Expanding the alteration range beyond observed data decreases decision quality, so a larger decision space does not yield better decisions due to distribution shift.
• The exact baseline runs faster than Grad-Rh on the MLP4 dataset but with much lower success probability.

Limitations

• Gradient-based solution is approximate and offers no optimality guarantee.
• Learned SRMs generalize poorly to altered variable values outside the observed range, creating a tradeoff between search space and learnability.
• Evaluated only on single-round decisions and synthetic nonlinear data, since no real datasets with known nonlinear SRMs exist.

Experimental setup

Datasets: Bermuda Ride-hailing Synthetic linear datasets (2) Synthetic nonlinear MLP datasets (4)

Benchmarks: Bermuda Ride-hailing (Traffic) Linear1 Linear2 MLP1 MLP2 MLP3 MLP4

Metrics: success probability of avoiding undesired outcome running time (s)

Baselines: QWZ23 mixed integer linear programming

Builds on: rehearsal learning conditional normalizing flow RealNVP-style affine coupling Chebyshev center linear programming

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