Scheduling in cloud computing is an NP-hard problem, where traditional metaheuristic algorithms often fail to deliver approximate solutions within a feasible time frame. As cloud infrastructures become increasingly dynamic, efficient Task Scheduling (TS) remains a major challenge, especially when minimizing makespan, execution time, and resource utilization. To address this, we propose the Ant Colony Asynchronous Advantage Actor-Critic (A4C) algorithm, which synergistically combines the exploratory strengths of Ant Colony Optimization (ACO) with the adaptive learning capabilities of the Asynchronous Advantage Actor-Critic (A3C) model. While ACO efficiently explores task allocation paths, it is prone to getting trapped in local optima. The integration with A3C overcomes this limitation by leveraging deep reinforcement learning for real-time policy and value estimation, enabling adaptive and informed scheduling decisions. Extensive simulations show that the A4C algorithm improves throughput by 18.7%, reduces makespan by 16%, execution time by 14.60%, and response time by 21.4% compared to conventional approaches. These results validate the practical effectiveness of A4C in handling dynamic workloads, reducing computational overhead, and ensuring timely task completion. The proposed model not only enhances scheduling efficiency but also supports quality-driven service delivery in cloud environments, making it well-suited for managing complex and time-sensitive cloud applications.