The widespread adoption of edge computing has emerged as a prominent trend for alleviating task processing delays and reducing energy consumption. However, the dynamic nature of network conditions and the varying computation capacities of edge servers (ESs) can introduce disparities between computation loads and available computing resources in edge computing networks, potentially leading to inadequate service quality. To address this challenge, this paper investigates a practical scenario characterized by dynamic task offloading. Initially, we examine traditional Multi-armed Bandit (MAB) algorithms, namely the $\varepsilon$-greedy algorithm and the UCB1-based algorithm. However, both algorithms exhibit certain weaknesses in effectively addressing the tidal data traffic patterns. Consequently, based on MAB, we propose an adaptive task offloading algorithm (ATOA) that overcomes these limitations. By conducting extensive simulations, we demonstrate the superiority of our ATOA solution in reducing task processing latency compared to conventional MAB methods. This substantiates the effectiveness of our approach in enhancing the performance of edge computing networks and improving overall service quality.