Knowing how to efficiently balance between exploring unfamiliar parts of an environment and exploiting currently available knowledge is an essential ingredient of anyintelligent organism.

Ournew bound consistently beats state-of-the-art bounds both on a toy example and on UCI datasets (with large enoughn).

Understanding model's sensitivity to its training data is crucial but can also be challenging and costly, especially during training. To simplify such issues, we present the Memory-Perturbation Equation (MPE) which relates model's sensitivity to perturbation in its training data.

Gradient-variation online learning aims to achieve regret guarantees that scale with variations in the gradients of online functions, which is crucial for attaining fast convergence in games and robustness in stochastic o ptimization, hence receiving increased attention. Existing results often req uire the smoothness condition by imposing a fixed bound on gradient Lipschitzness, w hich may be unrealistic in practice. Recent efforts in neural network optim ization suggest a generalized smoothness condition, allowing smoothness to correlate with gradient norms. In this paper, we systematically study gradient-var iation online learning under generalized smoothness. We extend the classic optimi stic mirror descent algorithm to derive gradient-variation regret by analyzin g stability over the optimization trajectory and exploiting smoothness locally. Th en, we explore universal online learning, designing a single algorithm with the optimal gradient-va riation regrets for convex and strongly convex functions simultane ously, without requiring prior knowledge of curvature. This algorithm adopts a tw o-layer structure with a meta-algorithm running over a group of base-learners . To ensure favorable guarantees, we design a new Lipschitz-adaptive meta-a lgorithm, capable of handling potentially unbounded gradients while ensuring a second-order bound to effectively ensemble the base-learners. Finally, we provi de the applications for fast-rate convergence in games and stochastic extended adv ersarial optimization.

The fair-ranking problem, which asks to rank a given set of items to maximize utility subject togroup fairness constraints, has received attention inthe fairness, information retrieval, and machine learning literature.

The fair-ranking problem, which asks to rank a given set of items to maximize utility subject togroup fairness constraints, has received attention inthe fairness, information retrieval, and machine learning literature.

The24], which Q-learning exploration Q-function Q-function asymptotically 39] derived drawbackof example, Zou39] require lowerbounded properties.