In this paper, we study online convex optimization in dynamic environments, and aim to bound the dynamic regret with respect to any sequence of comparators. Existing work have shown that online gradient descent enjoys an $O(\sqrt{T}(1+P_T))$ dynamic regret, where $T$ is the number of iterations and $P_T$ is the path-length of the comparator sequence. However, this result is unsatisfactory, as there exists a large gap from the $\Omega(\sqrt{T(1+P_T)})$ lower bound established in our paper. To address this limitation, we develop a novel online method, namely adaptive learning for dynamic environment (Ader), which achieves an optimal $O(\sqrt{T(1+P_T)})$ dynamic regret. The basic idea is to maintain a set of experts, each attaining an optimal dynamic regret for a specific path-length, and combines them with an expert-tracking algorithm. Furthermore, we propose an improved Ader based on the surrogate loss, and in this way the number of gradient evaluations per round is reduced from $O(\log T)$ to $1$. Finally, we extend Ader to the setting that a sequence of dynamical models is available to characterize the comparators.

Most machine learning algorithm designs aim to enhance label prediction accuracy.

In this research, we examine dynamic environments and choose dynamic regret and adaptive regret to measure the performance.

For environments with large time horizons, we show that the principal's optimal

In this paper, we revisit the problem of smoothed online learning, in which the online learner suffersboth ahitting costandaswitching cost, andtargettwoperformance metrics: competitiveratio anddynamic regretwith switching cost. To bound the competitive ratio, we assume the hitting cost is known to the learner in each round, and investigate the simple idea of balancing the two costs by an optimizationproblem.

Event cameras provide exceptionally high temporal resolution in dynamic vision systems due to their unique event-driven mechanism. However, the sparse and asynchronous nature of event data makes frame-based visual processing methods inappropriate. This study proposes a novel framework, Event-based Graph Spatiotemporal Sensitive Transformer (EGSST), for the exploitation of spatial and temporal properties of event data. Firstly, a well-designed graph structure is employed to model event data, which not only preserves the original temporal data but also captures spatial details. Furthermore, inspired by the phenomenon that human eyes pay more attention to objects that produce significant dynamic changes, we design a Spatiotemporal Sensitivity Module (SSM) and an adaptive Temporal Activation Controller (TAC). Through these two modules, our framework can mimic the response of the human eyes in dynamic environments by selectively activating the temporal attention mechanism based on the relative dynamics of event data, thereby effectively conserving computational resources. In addition, the integration of a lightweight, multi-scale Linear Vision Transformer (LViT) markedly enhances processing efficiency. Our research proposes a fully event-driven approach, effectively exploiting the temporal precision of event data and optimising the allocation of computational resources by intelligently distinguishing the dynamics within the event data. The framework provides a lightweight, fast, accurate, and fully event-based solution for object detection tasks in complex dynamic environments, demonstrating significant practicality and potential for application.