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Spend Wisely: Maximizing Post-Training Gains in Iterative Synthetic Data Bootstrapping

NeurIPS 2025 · Image generation › Fast diffusion sampling · approach: Distributional control of diffusion · 0 citations (OpenAlex)

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Theoretically analyzes how to allocate generation and training budget across iterations of synthetic-data bootstrapping (generate, reward-filter, fine-tune), showing constant policies fail while exponential growth policies are optimal, validated on DPM denoising and Llama-3-8B math reasoning.

Problem

How to allocate a fixed generation and training budget across iterations of iterative synthetic-data bootstrapping (generate, verifier/reward filter, fine-tune) to maximize final performance.

Approach

Frames the per-iteration selected-data size n_t as a budget policy and proves that constant policies cannot converge with high probability, while increasing policies (especially exponential growth) converge, with exponential growth worst-case optimal in total cost.

Key results

• Image denoising at s=10: exponential policy reaches 44.84 PSNR, the best among all schemes, versus 44.64 for the best linear policy and 44.18 for the best constant policy.
• Math reasoning: exponential schedule raises GSM_p1 accuracy from 35% to 47% and GSM_p2 from 16% to 21%, with the best overall final result (65.66 symbolic, 47.26 p1, 20.65 p2).
• Theory: constant policies have reward gap at least c·n_0^{-1/2} with probability at least 1/4, while exponential growth policies achieve O((1+ζ)^{-2T}) convergence.

Measured effects reported in the paper

Surprising findings

• Constant policies match the exponential policy early in training but then plateau and decay due to overfitting.
• For s=20 denoising, the best linear policy (40.26) slightly beats the exponential policy (40.14), so exponential is not uniformly best.

Limitations

• Denoising uses an oracle PSNR-based reward, which may not be available in practice.
• Theoretical guarantees rely on strong assumptions (covering number, local reducibility, loss-reward relation) and results are with high probability bounds.

Experimental setup

Datasets: MNIST GSM-Symbolic GSM8k

Benchmarks: MNIST denoising PSNR (s=10, s=20) GSM-Symbolic GSM_p1 GSM_p2

Metrics: PSNR accuracy FLOPs-based computational cost

Baselines: constant policy linear (polynomial) growth policy pre-trained model

Builds on: STaR self-training with reward filtering

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