The paper investigates regression with bounded responses, comparing two learning frameworks: model selection aggregation, which requires improper algorithms to achieve minimax excess risk, and universal learning, where empirical risk minimization suffices for exponential learning rates. For finite hypothesis classes, the authors show that the $Q$-aggregation estimator simultaneously attains minimax optimal tails and exponential universal rates, while other common estimators fail to do so. For countably infinite classes, they prove an inherent trade‑off between exponential universal and minimax uniform rates, resolved by combining optimal algorithms from each framework via $Q$-aggregation.
arXiv:2609. 07997v1 Announce Type: new Abstract: We characterize the sharp structure-agnostic minimax risk for coefficient estimation in the partial linear model when the outcome and treatment nuisances are learned by two distinct black-box learners, which resolves the open problem in double machine learning posed by Gu (2025).
arXiv:2603. 06957v2 Announce Type: replace-cross Abstract: We study post-training linear autoregressive models with outcome and process rewards.
arXiv:2610. 20903v1 Announce Type: new Abstract: We study bounded regression under model misspecification, evaluating a function $f$ by its $L_1(P_X)$ distance to the conditional mean $\eta(x)=\mathbb{E}[Y\mid X=x]$, rather than the standard $L_2(P_X)$.
Despite a surge of empirical interest in the ``unreasonable effectiveness'' of drastic data pruning for AI systems, a unified theoretical understanding of this phenomenon remains elusive. In this work...
We study the problem of \emph{adversarially robust} PAC learning. In this framework, the learner observes independent samples from an unknown distribution over $\mathcal{X} \times \{0,1\}$, as in clas...
The paper investigates how well practical machine‑learning algorithms approximate Solomonoff’s universal predictor when trained by minimizing log‑loss over diverse datasets. It establishes tight bounds on the worst‑case increase in prediction error caused by approximating the Bayesian mixture predictor, showing that while the excess error can be large in low‑prior environments, it remains bounded on average and under distribution shifts. The authors also extend their analysis to finite‑sample settings relevant to neural networks and Transformers.
The paper presents a high‑dimensional theory of learning with data pruning via weighted empirical risk minimization. It analyzes pruning along a one‑dimensional subspace and derives limiting test‑error curves as input dimension and sample size grow with a fixed ratio. The authors show that, in the high‑sample regime, the optimal strategy is to keep only the 2N hardest examples, achieving a Bayes‑optimal error scaling of order N/P instead of the usual sqrt(N/P).
arXiv:2605. 16103v2 Announce Type: replace Abstract: Q-learning is known to suffer from overestimation bias: because the Bellman update maximizes noisy or imperfect action-value estimates, positive errors can be selected and propagated, causing learned values to exceed the true optimal values.
The paper investigates fundamental limits of algorithmic principles in multiclass learning, specifically proper learning and regularization. It shows that learning cannot always be reduced to proper learning even with an enlarged hypothesis class, that proper learners may need a sublinear number of errors that can be arbitrarily large, and that regularization (SRM or local) is not universally sufficient. The authors also provide a positive theory giving sufficient conditions for SRM learnability and a characterization via integrability of revealed preferences.
arXiv:2510. 22819v3 Announce Type: replace Abstract: The convergence analysis of online learning algorithms is central to machine learning theory, where the last-iterate convergence is particularly important, as it captures the learner's actual decisions and describes the evolution of the learning process over time.
arXiv:2608. 12231v2 Announce Type: replace Abstract: We study adversarial combinatorial bandits with $m$-set actions, where at each round the learner selects $m$ out of $d$ items and observes only the aggregate loss of the selected items.
arXiv:2606. 06043v1 Announce Type: cross Abstract: Follow-the-regularized-leader framework has shown effectiveness and flexibility in online learning problems, where the choice of learning rates are known to be crucial.