We study dynamic regret in online convex optimization, where the objective is to achieve low cumulative loss relative to an arbitrary benchmark sequence. By observing that competing with an arbitrary sequence of comparators u1,...,uT in W Rd can be reframed as competing with a fixed comparator function u: [1,T] W, we cast dynamic regret minimization as a static regret problem in a function space. By carefully constructing a suitable function space in the form of a Reproducing Kernel Hilbert Space (RKHS), our reduction enables us to recover the optimal RT(u1,...,uT) = O( pP t ut ut 1 T) dynamic regret guarantee in the setting of linear losses, and yields new scale-free and directionallyadaptive dynamic regret guarantees. Moreover, unlike prior dynamic-to-static reductions--which are valid only for linear losses--our reduction holds for any sequence of losses, allowing us to recover O u 2H +deff(λ)lnT bounds when the losses have meaningful curvature, where deff(λ)is a measure of complexity of the RKHS. Despite working in an infinite-dimensional space, the resulting reduction leads to algorithms that are computable in practice, due to the reproducing property of RKHSs.

Human-in-the-loop (HIL) imitation learning enables agents to learn complex behaviors safely through real-time human intervention. However, existing methods struggle to efficiently leverage agent-generated data due to dynamically evolving trajectory distributions and imperfections caused by human intervention delays, often failing to faithfully imitate the human expert policy. In this work, we propose Faithful Dynamic Imitation Learning (FaithDaIL) to address these challenges. We formulate learning from human intervention as an online non-convex problem and employ dynamic regret minimization to adapt to the shifting data distribution and track high-quality policy trajectories. To ensure faithful imitation of human expert despite training on mixed agent and human data, we introduce an unbiased imitation objective and achieve it by weighting the behavior distribution relative to the human expert's as a proxy reward. Extensive experiments on MetaDrive and CARLA driving benchmarks demonstrate that FaithDaIL achieves state-ofthe-art performance in safety and task success with significantly reduced human intervention data compared to prior HIL baselines.

In multi-armed bandits with network interference (MABNI), the action taken by one node can influence the rewards of others, creating complex interdependence. While existing research on MABNI largely concentrates on minimizing regret, it often overlooks the crucial concern that an excessive emphasis on the optimal arm can undermine the inference accuracy for sub-optimal arms. Although initial efforts have been made to address this trade-off in single-unit scenarios, these challenges have become more pronounced in the context of MABNI. In this paper, we establish, for the first time, a theoretical Pareto frontier characterizing the trade-off between regret minimization and inference accuracy in adversarial (design-based) MABNI. We further introduce an anytime-valid asymptotic confidence sequence along with a corresponding algorithm, EXP3-N-CS, specifically designed to balance the trade-off between regret minimization and inference accuracy in this setting.

Optimization of parameterized policies for reinforcement learning (RL) is an important and challenging problem in artificial intelligence.

That is, to minimize simple regret. However, this objective remains understudied.

We give a randomized online algorithm that guarantees near-optimal $\widetilde O(\sqrt T)$ expected swap regret against any sequence of $T$ adaptively chosen Lipschitz convex losses on the unit interval. This improves the previous best bound of $\widetilde O(T^{2/3})$ and answers an open question of Fishelson et al. [2025b]. In addition, our algorithm is efficient: it runs in $\mathsf{poly}(T)$ time. A key technical idea we develop to obtain this result is to discretize the unit interval into bins at multiple scales of granularity and simultaneously use all scales to make randomized predictions, which we call multi-scale binning and may be of independent interest. A direct corollary of our result is an efficient online algorithm for minimizing the calibration error for general elicitable properties. This result does not require the Lipschitzness assumption of the identification function needed in prior work, making it applicable to median calibration, for which we achieve the first $\widetilde O(\sqrt T)$ calibration error guarantee.