Hedging on the Frontier: Learning New Tasks with Few Samples

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.

Efficient Logistic Regression with Mixture of Sigmoids

This paper studies the Exponential Weights (EW) algorithm with an isotropic Gaussian prior for online logistic regression. We show that the near-optimal worst-case regret bound $O(d\log(Bn))$ for EW, established by Kakade and Ng (2005) against the best linear predictor of norm at most $B$, can be achieved with total worst-case computational complexity $O(B^3 n^5)$. This substantially improves on the $O(B^{18}n^{37})$ complexity of prior work achieving the same guarantee (Foster et al., 2018). Beyond efficiency, we analyze the large-$B$ regime under linear separability: after rescaling by $B$, the EW posterior converges as $B\to\infty$ to a standard Gaussian truncated to the version cone. Accordingly, the predictor converges to a solid-angle vote over separating directions and, on every fixed-margin slice of this cone, the mode of the corresponding truncated Gaussian is aligned with the hard-margin SVM direction. Using this geometry, we derive non-asymptotic regret bounds showing that once $B$ exceeds a margin-dependent threshold, the regret becomes independent of $B$ and grows only logarithmically with the inverse margin. Overall, our results show that EW can be both computationally tractable and geometrically adaptive in online classification.

Instance-Dependent Regret Bounds for Nonstochastic Linear Partial Monitoring

In contrast to the classic formulation of partial monitoring, linear partial monitoring can model infinite outcome spaces, while imposing a linear structure on both the losses and the observations. This setting can be viewed as a generalization of linear bandits where loss and feedback are decoupled in a flexible manner. In this work, we address a nonstochastic (adversarial), finite-actions version of the problem through a simple instance of the exploration-by-optimization method that is amenable to efficient implementation. We derive regret bounds that depend on the game structure in a more transparent manner than previous theoretical guarantees for this paradigm. Our bounds feature instance-specific quantities that reflect the degree of alignment between observations and losses, and resemble known guarantees in the stochastic setting. Notably, they achieve the standard $\sqrt{T}$ rate in easy (locally observable) games and $T^{2/3}$ in hard (globally observable) games, where $T$ is the time horizon. We instantiate these bounds in a selection of old and new partial information settings subsumed by this model, and illustrate that the achieved dependence on the game structure can be tight in interesting cases.

Controlled Model Debiasing through Minimal and Interpretable Updates

Traditional approaches to learning fair machine learning models often require rebuilding models from scratch, generally without accounting for potentially existing previous models. In a context where models need to be retrained frequently, this can lead to inconsistent model updates, as well as redundant and costly validation testing. To address this limitation, we introduce the notion of controlled model debiasing, a novel supervised learning task relying on two desiderata: that the differences between new fair model and the existing one should be (i) interpretable and (ii) minimal. After providing theoretical guarantees to this new problem, we introduce a novel algorithm for algorithmic fairness, COMMOD, that is both model-agnostic and does not require the sensitive attribute at test time. In addition, our algorithm is explicitly designed to enforce minimal and interpretable changes between biased and debiased predictions -a property that, while highly desirable in high-stakes applications, is rarely prioritized as an explicit objective in fairness literature. Our approach combines a concept-based architecture and adversarial learning and we demonstrate through empirical results that it achieves comparable performance to state-of-the-art debiasing methods while performing minimal and interpretable prediction changes.

Post-processing fairness with minimal changes

In this paper, we introduce a novel post-processing algorithm that is both model-agnostic and does not require the sensitive attribute at test time. In addition, our algorithm is explicitly designed to enforce minimal changes between biased and debiased predictions; a property that, while highly desirable, is rarely prioritized as an explicit objective in fairness literature. Our approach leverages a multiplicative factor applied to the logit value of probability scores produced by a black-box classifier. We demonstrate the efficacy of our method through empirical evaluations, comparing its performance against other four debiasing algorithms on two widely used datasets in fairness research.