# Bidirectional Learning for Offline Infinite-width Model-based Optimization

arXiv: https://arxiv.org/abs/2209.07507 · HTML: https://mlsanity.com/paper/2209.07507/

## Key facts

- Cited by 35 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Sep 2022.

## Built on by (most cited first, 30 of 35)

- [Dataset Distillation: A Comprehensive Review](https://mlsanity.com/paper/2301.07014/) (2023)
- [Dataset Distillation via Factorization](https://mlsanity.com/paper/2210.16774/) (2022)
- [A Comprehensive Survey of Dataset Distillation](https://mlsanity.com/paper/2301.05603/) (2023)
- [Meta-DMoE: Adapting to Domain Shift by Meta-Distillation from Mixture-of-Experts](https://mlsanity.com/paper/2210.03885/) (2022)
- [MetaGCD: Learning to Continually Learn in Generalized Category Discovery](https://mlsanity.com/paper/2308.11063/) (2023)
- [Bridging Model-Based Optimization and Generative Modeling via Conservative Fine-Tuning of Diffusion Models](https://mlsanity.com/paper/2405.19673/) (2024)
- [Bootstrapped Training of Score-Conditioned Generator for Offline Design of Biological Sequences](https://mlsanity.com/paper/2306.03111/) (2023)
- [Adapting to Distribution Shift by Visual Domain Prompt Generation](https://mlsanity.com/paper/2405.02797/) (2024)
- [ExPT: Synthetic Pretraining for Few-Shot Experimental Design](https://mlsanity.com/paper/2310.19961/) (2023)
- [Offline Model-Based Optimization via Policy-Guided Gradient Search](https://mlsanity.com/paper/2405.05349/) (2024)
- [Importance-Aware Adaptive Dataset Distillation](https://mlsanity.com/paper/2401.15863/) (2024)
- [ParetoFlow: Guided Flows in Multi-Objective Optimization](https://mlsanity.com/paper/2412.03718/) (2024)
- [Guided Trajectory Generation with Diffusion Models for Offline Model-based Optimization](https://mlsanity.com/paper/2407.01624/) (2024)
- [Offline Model-Based Optimization: Comprehensive Review](https://mlsanity.com/paper/2503.17286/) (2025)
- [Offline Multi-Objective Optimization](https://mlsanity.com/paper/2406.03722/) (2024)
- [Improved Off-policy Reinforcement Learning in Biological Sequence Design](https://mlsanity.com/paper/2410.04461/) (2024)
- [Offline Model-Based Optimization by Learning to Rank](https://mlsanity.com/paper/2410.11502/) (2024)
- [Generative Adversarial Model-Based Optimization via Source Critic Regularization](https://mlsanity.com/paper/2402.06532/) (2024)
- [Design Editing for Offline Model-based Optimization](https://mlsanity.com/paper/2405.13964/) (2024)
- ["Noisier" Noise Contrastive Eestimation is (Almost) Maximum Likelihood](https://mlsanity.com/paper/2405.16730/) (2024)
- [Robust Guided Diffusion for Offline Black-Box Optimization](https://mlsanity.com/paper/2410.00983/) (2024)
- [Towards Universal Offline Black-Box Optimization via Learning Language Model Embeddings](https://mlsanity.com/paper/2506.07109/) (2025)
- [Improving ProtoNet for Few-Shot Video Object Recognition: Winner of ORBIT Challenge 2022](https://mlsanity.com/paper/2210.00174/) (2022)
- [Neural Genetic Search in Discrete Spaces](https://mlsanity.com/paper/2502.10433/) (2025)
- [ROOT: Rethinking Offline Optimization as Distributional Translation via Probabilistic Bridge](https://mlsanity.com/paper/2509.16300/) (2025)
- [Boosting the Cross-Architecture Generalization of Dataset Distillation through an Empirical Study](https://mlsanity.com/paper/2312.05598/) (2023)
- [Towards Hybrid-grained Feature Interaction Selection for Deep Sparse Network](https://mlsanity.com/paper/2310.15342/) (2023)
- [Sharpness-Aware Black-Box Optimization](https://mlsanity.com/paper/2410.12457/) (2024)
- [Exploring validation metrics for offline model-based optimisation with diffusion models](https://mlsanity.com/paper/2211.10747/) (2022)
- [From Function to Distribution Modeling: A PAC-Generative Approach to Offline Optimization](https://mlsanity.com/paper/2401.02019/) (2024)

## Abstract (arXiv)

In offline model-based optimization, we strive to maximize a black-box objective function by only leveraging a static dataset of designs and their scores. This problem setting arises in numerous fields including the design of materials, robots, DNA sequences, and proteins. Recent approaches train a deep neural network (DNN) on the static dataset to act as a proxy function, and then perform gradient ascent on the existing designs to obtain potentially high-scoring designs. This methodology frequently suffers from the out-of-distribution problem where the proxy function often returns poor designs. To mitigate this problem, we propose BiDirectional learning for offline Infinite-width model-based optimization (BDI). BDI consists of two mappings: the forward mapping leverages the static dataset to predict the scores of the high-scoring designs, and the backward mapping leverages the high-scoring designs to predict the scores of the static dataset. The backward mapping, neglected in previous work, can distill more information from the static dataset into the high-scoring designs, which effectively mitigates the out-of-distribution problem. For a finite-width DNN model, the loss function of the backward mapping is intractable and only has an approximate form, which leads to a significant deterioration of the design quality. We thus adopt an infinite-width DNN model, and propose to employ the corresponding neural tangent kernel to yield a closed-form loss for more accurate design updates. Experiments on various tasks verify the effectiveness of BDI. The code is available at https://github.com/GGchen1997/BDI.