Tobias Wegel

Tobias Wegel, Federico Di Gennaro, Geelon So et al.

When a learner faces a new task with few samples, it must leverage any available side information. In practice, this often comes in the form of model evaluations on related tasks in public benchmarks. A key question then is how to model task relatedness such that it is both realistic and the benchmark evaluations lead to provable gains. Empirically, we observe that weak monotonicity is often approximately satisfied: if a model dominates another on many benchmarks, it also tends to outperform on the new task. We explore the statistical complexity of learning under (approximate) weak monotonicity, leveraging it within two learning paradigms: transfer learning and model selection aggregation. We show that not only can we prune the model class based on monotonicity, but we can also further adapt to the geometry of the available trade-offs by hedging on the frontier.

Zifan Lyu, Chahine Nejma, Tobias Wegel et al.

Large Language Models are typically benchmarked by evaluating every model on every test query. For practitioners seeking the best model to deploy, this is often wasteful: if a model clearly performs worse than others, there is no need to precisely estimate its performance. Best-arm identification algorithms can be naturally applied to drastically reduce costs by adaptively allocating evaluation budget. Further, language models often respond similarly to the same prompt-a property previous work has tried to leverage with mixed success. We propose Synchronized Successive Rejects (SySRs), augmenting the classical Successive Rejects algorithm with paired comparisons. Unlike prior attempts to leverage model similarity in best-model identification, our approach is hyperparameter-free and enjoys performance guarantees that improve with the degree of similarity between evaluated models. Empirically, our method outperforms all baselines in terms of average error rate across 15 standard benchmarks, and in terms of worst-case budget for reliably identifying the best model.

Tobias Wegel, Filip Kovačević, Alexandru Ţifrea et al.

Simultaneously addressing multiple objectives is becoming increasingly important in modern machine learning. At the same time, data is often high-dimensional and costly to label. For a single objective such as prediction risk, conventional regularization techniques are known to improve generalization when the data exhibits low-dimensional structure like sparsity. However, it is largely unexplored how to leverage this structure in the context of multi-objective learning (MOL) with multiple competing objectives. In this work, we discuss how the application of vanilla regularization approaches can fail, and propose a two-stage MOL framework that can successfully leverage low-dimensional structure. We demonstrate its effectiveness experimentally for multi-distribution learning and fairness-risk trade-offs.

Tobias Wegel, Gil Kur, Patrick Rebeschini

Early-stopped iterative optimization methods are widely used as alternatives to explicit regularization, and direct comparisons between early-stopping and explicit regularization have been established for many optimization geometries. However, most analyses depend heavily on the specific properties of the optimization geometry or strong convexity of the empirical objective, and it remains unclear whether early-stopping could ever be less statistically efficient than explicit regularization for some particular shape constraint, especially in the overparameterized regime. To address this question, we study the setting of high-dimensional linear regression under additive Gaussian noise when the ground truth is assumed to lie in a known convex body and the task is to minimize the in-sample mean squared error. Our main result shows that for any convex body and any design matrix, up to an absolute constant factor, the worst-case risk of unconstrained early-stopped mirror descent with an appropriate potential is at most that of the least squares estimator constrained to the convex body. We achieve this by constructing algorithmic regularizers based on the Minkowski functional of the convex body.

Tobias Wegel, Felix Assion, David Mickisch et al.

Machine learning image classifiers are susceptible to adversarial and corruption perturbations. Adding imperceptible noise to images can lead to severe misclassifications of the machine learning model. Using $L_p$-norms for measuring the size of the noise fails to capture human similarity perception, which is why optimal transport based distance measures like the Wasserstein metric are increasingly being used in the field of adversarial robustness. Verifying the robustness of classifiers using the Wasserstein metric can be achieved by proving the absence of adversarial examples (certification) or proving their presence (attack). In this work we present a framework based on the work by Levine and Feizi, which allows us to transfer existing certification methods for convex polytopes or $L_1$-balls to the Wasserstein threat model. The resulting certification can be complete or incomplete, depending on whether convex polytopes or $L_1$-balls were chosen. Additionally, we present a new Wasserstein adversarial attack that is projected gradient descent based and which has a significantly reduced computational burden compared to existing attack approaches.