The capabilities of large language models (LLMs) significantly depend on training data drawn from various domains. Optimizing domain-specific mixture ratios can be modeled as a bi-level optimization problem, which we simplify into a single-level penalized form and solve with twin networks: a proxy model trained on primary data and a dynamically updated reference model trained with additional data. Our proposed method, Twin Networks for bi-level DatA mixturE optiMization (TANDEM), measures the data efficacy through the difference between the twin models and up-weights domains that benefit more from the additional data. TANDEM provides theoretical guarantees and wider applicability, compared to prior approaches. Furthermore, our bi-level perspective suggests new settings to study domain reweighting such as data-restricted scenarios and supervised fine-tuning, where optimized mixture ratios significantly improve the performance.

The implementation of the following setup is written in JAX [6] and Haiku [35]. We use Residual Networks (ResNets) and Wide ResNets (WRNs) [31, 79]. This is consistent with prior work [30, 49, 60, 72, 82] which use diverse variants of these network families. Furthermore, we adopt the same architecture details as Gowal et al. [30] with Swish/SiLU [33] activation functions. Most of the experiments are conducted on a WRN-28-10 model which has a depth of 28, a width multiplier of 10 and contains 36M parameters. To evaluate the effect of using additional generated data on wider and deeper networks, we also run several experiments using WRN-70-16, which contains 267M parameters.

Contrastive learning approaches have achieved great success in learning visual representations with few labels of the target classes.

In some applications of reinforcement learning, a dataset of pre-collected experience is already availablebut it is also possible to acquire some additional online data to help improve the quality of the policy.However, it may be preferable to gather additional data with a single, non-reactive exploration policyand avoid the engineering costs associated with switching policies. In this paper we propose an algorithm with provable guarantees that can leverage an offline dataset to design a single non-reactive policy for exploration. We theoretically analyze the algorithm and measure the quality of the final policy as a function of the local coverage of the original dataset and the amount of additional data collected.

We sincerely thank the reviewers for their valuable comments. We proofread and fixed the mentioned errors. Related Work: Thank you for the additional references. We will include and discuss them in the revised version. Publishing codes: Upon the acceptance of our paper, we will publicly release the source codes.