LLM-Inspired Pretrain-Then-Finetune for Small-Data, Large-Scale Optimization

We consider small-data, large-scale decision problems in which a firm must make many operational decisions simultaneously (e.g., across a large product portfolio) while observing only a few, potentially noisy, data points per instance. Inspired by the success of large language models (LLMs), we propose a pretrain-then-finetune approach built on a designed Transformer model to address this challenge. The model is first pretrained on large-scale, domain-informed synthetic data that encode managerial knowledge and structural features of the decision environment, and is then fine-tuned on real observations. This new pipeline offers two complementary advantages: pretraining injects domain knowledge into the learning process and enables the training of high-capacity models using abundant synthetic data, while finetuning adapts the pretrained model to the operational environment and improves alignment with the true data-generating regime. While we have leveraged the Transformer's state-of-the-art representational capacity, particularly its attention mechanism, to efficiently extract cross-task structure, our approach is not an off-the-shelf application. Instead, it relies on problem-specific architectural design and a tailored training procedure to match the decision setting. Theoretically, we develop the first comprehensive error analysis regarding Transformer learning in relevant contexts, establishing nonasymptotic guarantees that validate the method's effectiveness. Critically, our analysis reveals how pretraining and fine-tuning jointly determine performance, with the dominant contribution governed by whichever is more favorable. In particular, finetuning exhibits an economies-of-scale effect, whereby transfer learning becomes increasingly effective as the number of instances grows.

FLOPS: Forward Learning with OPtimal Sampling

Given the limitations of backpropagation, perturbation-based gradient computation methods have recently gained focus for learning with only forward passes, also referred to as queries. Conventional forward learning consumes enormous queries on each data point for accurate gradient estimation through Monte Carlo sampling, which hinders the scalability of those algorithms. However, not all data points deserve equal queries for gradient estimation. In this paper, we study the problem of improving the forward learning efficiency from a novel perspective: how to reduce the gradient estimation variance with minimum cost? For this, we propose to allocate the optimal number of queries over each data in one batch during training to achieve a good balance between estimation accuracy and computational efficiency. Specifically, with a simplified proxy objective and a reparameterization technique, we derive a novel plug-and-play query allocator with minimal parameters. Theoretical results are carried out to verify its optimality. We conduct extensive experiments for fine-tuning Vision Transformers on various datasets and further deploy the allocator to two black-box applications: prompt tuning and multimodal alignment for foundation models. All findings demonstrate that our proposed allocator significantly enhances the scalability of forward-learning algorithms, paving the way for real-world applications.

Sample-Efficient Clustering and Conquer Procedures for Parallel Large-Scale Ranking and Selection

We propose novel "clustering and conquer" procedures for the parallel large-scale ranking and selection (R&S) problem, which leverage correlation information for clustering to break the bottleneck of sample efficiency. In parallel computing environments, correlation-based clustering can achieve an $\mathcal{O}(p)$ sample complexity reduction rate, which is the optimal reduction rate theoretically attainable. Our proposed framework is versatile, allowing for seamless integration of various prevalent R&S methods under both fixed-budget and fixed-precision paradigms. It can achieve improvements without the necessity of highly accurate correlation estimation and precise clustering. In large-scale AI applications such as neural architecture search, a screening-free version of our procedure surprisingly surpasses fully-sequential benchmarks in terms of sample efficiency. This suggests that leveraging valuable structural information, such as correlation, is a viable path to bypassing the traditional need for screening via pairwise comparison--a step previously deemed essential for high sample efficiency but problematic for parallelization. Additionally, we propose a parallel few-shot clustering algorithm tailored for large-scale problems.