Model Selection

Choosing a Large Language Model (LLM) for a given task requires comparing many strong candidates, yet standard evaluation relies on costly annotations over fixed evaluation sets. To address this challenge, we develop SELECT-LLM, the first framework for active model selection of LLMs. SELECT-LLM aims to find a small set of queries whose annotations are most informative for identifying the best LLM for a given task. To this end, we introduce a query selection rule based on expected information gain, computed from pairwise similarities between candidate model outputs. Because this rule only uses generated model responses, SELECT-LLM can be applied across candidate models without assumptions about their architecture or access to model weights. This makes it suitable for both open-weight and black-box LLMs. We evaluate SELECT-LLM across 23 datasets, 156 evaluated models, diverse task families, and multiple text evaluation metrics. Across all experiments, SELECT-LLM improves over the strongest baseline in every setting, with annotation cost reductions up to 81.8% for best model selection and up to 84.78% for near-best model selection.

We introduce Delphos, a deep reinforcement learning framework for assisting discrete choice model specification process. Delphos aims to support the modeller by providing automated, data-driven suggestions for model specifications, thereby reducing the effort required to develop and refine utility functions. Delphos conceptualises model specification as a sequential decision-making problem, inspired by the way human choice modellers iteratively construct models through a series of reasoned specification decisions. In this setting, an agent learns to specify candidate model specifications by choosing a sequence of modelling actions, such as adding alternative specific constants, accommodating both generic and alternative-specific taste parameters, applying non-linear transformations to attributes, and including interactions with covariates. Each resulting candidate model is estimated and evaluated using a reward function defined by the modeller, which can reflect statistical model fit as well as behavioural expectations. Specifically, Delphos uses a Deep Q-Network to learn how individual specification decisions contribute to the eventual quality of the resulting model and, in turn, which sequences of modelling decisions tend to produce well-performing candidates. We evaluate Delphos on both simulated and empirical datasets using alternative reward functions. In simulated cases, learning curves, Q-value patterns, and performance metrics show that Delphos learns effective specification strategies while exploring only a small fraction of the feasible modelling space. We further apply the framework to two empirical datasets to benchmark and demonstrate its practical use. These experiments illustrate the ability of Delphos to generate competitive, behaviourally plausible models and highlight the potential of this adaptive, learning-based framework to assist the model specification process.

Offline model-based reinforcement learning (MBRL) serves as a competitive framework that can learn well-performing policies solely from pre-collected data with the help of learned dynamics models. To fully unleash the power of offline MBRL, model selection plays a pivotal role in determining the dynamics model utilized for downstream policy learning. However, offline MBRL conventionally relies on validation or off-policy evaluation, which are rather inaccurate due to the inherent distribution shift in offline RL. To tackle this, we propose BOMS, an active model selection framework that enhances model selection in offline MBRL with only a small online interaction budget, through the lens of Bayesian optimization (BO). Specifically, we recast model selection as BO and enable probabilistic inference in BOMS by proposing a novel model-induced kernel, which is theoretically grounded and computationally efficient. Through extensive experiments, we show that BOMS improves over the baseline methods with a small amount of online interaction comparable to only $1\%$-$2.5\%$ of offline training data on various RL tasks.

We study data-driven score construction in conformal selection, which uses conformal p-values and multiple testing to select "interesting" instances with large unobserved labels from a pool of unlabeled data, while controlling the FDR in finite sample. While existing solutions require the score function to be constructed independent of the calibration and test data, it is desirable to select or construct powerful conformity score in a data-driven manner and to leverage all labeled data for score training when presented with many score choices and limited labeled data. We propose Optimized Conformal Selection (OptCS), a general framework that allows valid multiple testing after flexible data-driven score construction. We introduce general conditions under which OptCS constructs valid conformal p-values despite substantial data reuse and handles complex p-value dependencies to maintain finite-sample FDR control. We instantiate this general recipe to propose three FDR-controlling procedures, each optimizing the models differently: (i) selecting a powerful score function among multiple candidates, (ii) training the score with all labeled data without sample splitting, and (iii) combining full-sample training and model selection. We demonstrate the efficacy of our methods via simulation studies and real applications in drug discovery and large language models.

Given a high-dimensional covariate matrix and a response vector, ridge-regularized sparse linear regression selects a subset of features that explains the relationship between covariates and the response in an interpretable manner. To choose hyperparameters that control the sparsity level and amount of regularization, practitioners commonly use k-fold cross-validation. However, cross-validation substantially increases the computational cost of sparse regression as it requires solving many mixed-integer optimization problems (MIOs) for each hyperparameter combination. To address this computational burden, we derive computationally tractable relaxations of the k-fold cross-validation loss, facilitating hyperparameter selection while solving $50$--$80\%$ fewer MIOs in practice. Our computational results demonstrate, across eleven real-world UCI datasets, that exact MIO-based cross-validation can be competitive with mature software packages such as glmnet and L0Learn.

Cross-validation is one of the most widely used tools for risk estimation and model selection in statistics and machine learning, yet its theoretical properties when embedded in a learning procedure remain insufficiently understood. This paper develops a general, distribution-free framework for learning via model selection with cross-validation risk estimation within classical statistical learning theory. We establish VC dimension-based deviation bounds for the entire learning pipeline, providing detailed proofs for both bounded and unbounded loss functions, the latter requiring a novel extension of existing results. A central focus of the analysis is how the structure of the collection of candidate models influences generalization. To this end, we introduce Learning Spaces as collections of candidate models equipped with a partial order whose inclusion structure reflects increasing model complexity. We show how Learning Spaces can be constructed from domain knowledge and analyze how such structural information increases generalization. The framework is illustrated through case studies and a simulation study in high-dimensional linear regression, comparing learning via model selection in two distinct Learning Spaces against ordinary least squares, LASSO, and ridge regression across scenarios of varying alignment between prior knowledge and the true target. The results demonstrate that, when the Learning Space is well-adapted to the target and an efficient search algorithm is employed, learning via model selection can outperform standard methods by orders of magnitude. Through theoretical insights and concrete examples, we provide guidance on selecting the family of candidate models based on domain knowledge to enhance the performance of model selection with cross-validation.