A many-core processor can execute hundreds of multi-threaded tasks in parallel on its 100s-1000s of processing cores. When deployed in a Quality of Service (QoS)-based system, the many-core must execute a task at a target QoS. The amount of processing required by the task for the QoS varies over the task's lifetime. Accordingly, Dynamic Voltage and Frequency Scaling (DVFS) allows the many-core to deliver precise amount of processing required to meet the task QoS guarantee while conserving power. Still, a global control is necessitated to ensure that the many-core overall does not exceed its power budget. Previously, only non-stochastic controls have been proposed for the problem of QoS-aware power budgeting in many-cores. We propose the first stochastic control for the problem, which has a computational complexity less than the non-stochastic control by a factor of O (lnn) but with equivalent performance. The proposed stochastic control can operate with 6.4x less overhead than the non-stochastic control for a 256-task workload.