Online structured prediction is a task of sequentially predicting outputs with complex structures based on inputs and past observations, encompassing online classification. Recent studies showed that in the full-information setting, we can achieve finite bounds on the surrogate regret, i.e., the extra target loss relative to the best possible surrogate loss. In practice, however, full-information feedback is often unrealistic as it requires immediate access to the whole structure of complex outputs. Motivated by this, we propose algorithms that work with less demanding feedback, bandit and delayed feedback. For bandit feedback, by using a standard inverseweighted gradient estimator, we achieve a surrogate regret bound of O( KT) for the time horizon T and the size of the output set K. However, K can be extremely large when outputs are highly complex, resulting in an undesirable bound. To address this issue, we propose another algorithm that achieves a surrogate regret bound of O(T2/3), which is independent of K. This is achieved with a carefully designed pseudo-inverse matrix estimator. Furthermore, we numerically compare the performance of these algorithms, as well as existing ones. Regarding delayed feedback, we provide algorithms and regret analyses that cover various scenarios, including full-information and bandit feedback, as well as fixed and variable delays.

We introduce MLE-Dojo, a Gym-style framework for systematically reinforcement learning, evaluating, and improving autonomous large language model (LLM) agents in iterative machine learning engineering (MLE) workflows. Unlike existing benchmarks that primarily rely on static datasets or single-attempt evaluations, MLE-Dojoprovides an interactive environment enabling agents to iteratively experiment, debug, and refine solutions through structured feedback loops. Built upon 200+ real-world Kaggle challenges, MLE-Dojocovers diverse, open-ended MLE tasks carefully curated to reflect realistic engineering scenarios such as data processing, architecture search, hyperparameter tuning, and code debugging. Its fully executable environment supports comprehensive agent training via both supervised fine-tuning and reinforcement learning, facilitating iterative experimentation, realistic data sampling, and real-time outcome verification. Extensive evaluations of eight frontier LLMs reveal that while current models achieve meaningful iterative improvements, they still exhibit significant limitations in autonomously generating long-horizon solutions and efficiently resolving complex errors.

We study contextual bandits in the stochastic i.i.d.\ setting, where a learner observes contexts drawn from an unknown distribution, selects actions from a finite set $A$, and aims to identify an approximately optimal policy from a given class based on bandit feedback. Motivated by bandit multiclass classification with zero-one rewards, we focus on the \emph{$s$-sparse} setting in which, for every context, the reward vector has $L_1$-norm at most $s \ll |A|$. Our main result is the design of algorithms that, with high probability, output an $ε$-optimal policy compared to policy class $Π$ using $\tilde{O} ((s/ε^2 + |A|/ε)\log |Π|/δ)$ samples. We extend this bound to general Natarajan classes and complement it with a matching lower bound (up to logarithmic factors), thereby closing a substantial gap left by prior work (Erez et al., 2024, 2025), which incurred an additional $Θ(|A|^9)$ dependence. We obtain these results via two complementary approaches. First, we analyze contextual bandits through the lens of contextual decision making with structured observations, designing an exploration-by-optimization algorithm whose sample complexity is governed by the \emph{decision-estimation coefficient} (DEC; Foster et al., 2021, 2022). We show that, with $s$-sparse rewards, the induced model class admits a sharp DEC bound that scales with $s$ and directly yields the optimal rate. Since this approach is largely information-theoretic and involves solving complex min-max optimization problems, we also develop a second, more specialized algorithmic method based on a low-variance exploration technique. This approach leads to concrete, tractable algorithms and naturally extends to contextual combinatorial semi-bandits, leading to improved sample complexity guarantees for bandit multiclass list classification.

In this paradigm, outcomes must be embedded into the reals with dimension $d \approx n$ in order to design a consistent surrogate loss. Consistent losses are well-motivated theoretically, yet for large $n$, such as in information retrieval and structured prediction tasks, their optimization may be computationally infeasible. In practice, outcomes are typically embedded into some $\mathbb{R}^d$ for $d \ll n$, with little known about their suitability for multiclass classification. We investigate two approaches for trading off consistency and dimensionality in multiclass classification while using a convex surrogate loss. We first formalize partial consistency when the optimized surrogate has dimension $d \ll n$. We then check if partial consistency holds under a given embedding and low-noise assumption, providing insight into when to use a particular embedding into $\mathbb{R}^d$. Finally, we present a new method to construct (fully) consistent losses with $d \ll n$ out of multiple problem instances. Our practical approach leverages parallelism to sidestep lower bounds on $d$.

Implicit bias describes the phenomenon where optimization-based training algorithms, without explicit regularization, show a preference for simple estimators even when more complex estimators have equal objective values. Multiple works have developed the theory of implicit bias for binary classification under the assumption that the loss satisfies an . However, there is a noticeable gap in analysis for multiclass classification, with only a handful of results which themselves are restricted to the cross-entropy loss. In this work, we employ the framework of Permutation Equivariant and Relative Margin-based (PERM) losses [Wang and Scott, 2024] to introduce a multiclass extension of the exponential tail property. This class of losses includes not only cross-entropy but also other losses. Using this framework, we extend the implicit bias result of Soudry et al. [2018] to multiclass classification. Furthermore, our proof techniques closely mirror those of the binary case, thus illustrating the power of the PERM framework for bridging the binary-multiclass gap.

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Online multiclass classification is a ubiquitous problem in machine learning.