As low-power electronics and miniaturization conspire to populate the world with emerging devices, one appealing approach is to power these multi-core/many-core-based devices with energy harvested from various environments. Of the most important issues concerning these devices is how to effectively allocate power budget among the cores competing for power, which is formulated as one specific type of power-performance optimization problem in this paper. We attempt to solve this problem by proposing an Adaptive Power Allocation Technique (APAT) that uses a dynamic programming network. Our goal here is to maximize the overall system performance, taking into account a unique yet challenging fact that, available power budget might have to undergo a significant change when a renewable energy source is scavenging. APAT has a linear time complexity and low hardware overhead. Experiments have confirmed that APAT can reduce 20 similar to 30% of execution time compared to other state-of-the-art power allocation algorithms. In addition, as APAT is quite insensitive to the changing rate of the power, lending itself well for power management in many-core systems powered by energy-harvesting sources.