Journal of Data Science

The extraordinary capabilities of large language models (LLMs) such as ChatGPT and GPT-4 are in part unleashed by aligning them with reward models that are trained on human preferences represented as rankings of responses to prompts. In this paper, we document the phenomenon of reward collapse, an empirical observation where the prevailing ranking-based approach results in an identical reward distribution for diverse prompts during the terminal phase of training. This outcome is undesirable as open-ended prompts like “write a short story about your best friend” should yield a continuous range of rewards for their completions, while specific prompts like “what is the capital city of New Zealand” should generate either high or low rewards. Our theoretical investigation reveals that reward collapse is primarily due to the insufficiency of the ranking-based objective function to incorporate prompt-related information during optimization. Then we derive closed-form expressions for the reward distribution associated with a set of utility functions in an asymptotic setting. Based on the reward distributions for different utility functions, we introduce a prompt-aware optimization scheme that provably admits a prompt-dependent reward distribution within the interpolating regime. Our experimental results suggest that our proposed prompt-aware utility functions significantly alleviate reward collapse during the training of reward models.

Modern precision medicine aims to utilize real-world data to provide the best treatment for an individual patient. An individualized treatment rule (ITR) maps each patient’s characteristics to a recommended treatment scheme that maximizes the expected outcome of the patient. A challenge precision medicine faces is population heterogeneity, as studies on treatment effects are often conducted on source populations that differ from the populations of interest in terms of the distribution of patient characteristics. Our research goal is to explore a transfer learning algorithm that aims to address the population heterogeneity problem and obtain targeted, optimal, and interpretable ITRs. The algorithm incorporates a calibrated augmented inverse probability weighting estimator for the average treatment effect and employs value function maximization for the target population using Genetic Algorithm to produce our desired ITR. To demonstrate its practical utility, we apply this transfer learning algorithm to two large medical databases, eICU Collaborative Research Database and Medical Information Mart for Intensive Care III. We first identify the important covariates, treatment options, and outcomes of interest based on the two databases, and then estimate the optimal linear ITRs for patients with sepsis. Our research introduces and applies new techniques for data fusion to obtain data-driven ITRs that cater to patients’ individual medical needs in a population of interest. By emphasizing generalizability and personalized decision-making, this methodology extends its potential application beyond medicine to fields such as marketing, technology, social sciences, and education.

Piecewise linear-quadratic (PLQ) functions are a fundamental function class in convex optimization, especially within the Empirical Risk Minimization (ERM) framework, which employs various PLQ loss functions. This paper provides a workflow for decomposing a general convex PLQ loss into its ReLU-ReHU representation, along with a Python implementation designed to enhance the efficiency of presenting and solving ERM problems, particularly when integrated with ReHLine (a powerful solver for PLQ ERMs). Our proposed package, plqcom, accepts three representations of PLQ functions and offers user-friendly APIs for verifying their convexity and continuity. The Python package is available at https://github.com/keepwith/PLQComposite.

Statistical learning methods have been growing in popularity in recent years. Many of these procedures have parameters that must be tuned for models to perform well. Research has been extensive in neural networks, but not for many other learning methods. We looked at the behavior of tuning parameters for support vector machines, gradient boosting machines, and adaboost in both a classification and regression setting. We used grid search to identify ranges of tuning parameters where good models can be found across many different datasets. We then explored different optimization algorithms to select a model across the tuning parameter space. Models selected by the optimization algorithm were compared to the best models obtained through grid search to select well performing algorithms. This information was used to create an R package, EZtune, that automatically tunes support vector machines and boosted trees.