## 2 Related Work  
It is proven that the use of market-inspired resource allocation heuristics provides promising results in the common situation that HPC systems are overloaded with more jobs than they can handle [27]. These heuristics use some implementation of a value for jobs, both fixed [28] and changing over time [15]. Most of them choose the highest value job first, which might consume too many resources, leaving limited resources for jobs arriving in the future. Therefore, resources required for each job should be optimized. Other heuristics exist such as value density (value divided by resource requirement) which addresses the issue of the highest value job consuming too many resources [29; 30; 31]. This heuristic instead will prefer jobs which are small and have reasonably high value over very large jobs with high value. However, this heuristic, and others like it, do not consider energy consumption. A number of reinforcement learning techniques were compared for scheduling tasks on large-scale distributed systems [32]. In this comparison, energy efficiency was considered by attempting to maximize CPU utilization. This intuitively increases energy efficiency by reducing the wasted energy of having CPUs powered on but in an idle state. Similar reinforcement learning techniques are explored for data centers [33]. However, these researches only considered the fulfillment of the service level agreement (SLA) which provides a fixed value when jobs are completed before a specified deadline. This research instead considers the common case where the value of a job changes gradually as a function of time, known as a value-curve. In addition, the energy efficiency optimization does not focus on the reduction of energy consumption directly. A report identified that the use of profiling results in jointly optimizing the value and energy of a job [17]. Further research also expanded the optimizations to monitoring and adapting the allocations during tasks' execution by migrating to a different set of resources [34]. Both approaches require profiling of jobs at design-time, and the latter also requires the ability for jobs to pause execution and resume on a different set of resources. In contrast, the bandit-based technique in this paper attempts to similarly predict the value and energy of jobs without relying on the assumptions that prior information is obtainable and migration of jobs is possible. In a complementary direction, under-utilization of the servers in a data center has always been observed mainly due to the over-provisioning for the peak demand hours [35]. In [6], various formulations of the cost-aware application placement problem for servers were first introduced without considering network performance. Similarly, in [7], a system was proposed that optimizes power consumption, performance benefits, and transient costs incurred by server consolidation. In [8] an efficient power-aware resource scheduling strategy was proposed that reduces data center power consumption based on live VM migration. A framework for VM migration and placement was proposed in [9] considering both the network topology and network traffic demands to minimize energy consumption while satisfying as many network-demands as possible. In [10], energy-aware VM placement was proposed where application dependencies were considered to reduce network energy consumption. In [11], a network-aware VM consolidation scheme was proposed for solving combined VM consolidation problems to conserve the energy of the data center. In [12], a heuristic to control VM migration based on prioritizing VMs with steady capacity was proposed. In addition to server consolidation, an opportunistic approach to reduce power consumption is proposed in [36]. From all of these studies, it is clear that if an adequate consolidation algorithm can be designed, a significant amount of power reduction can be possible for the HPC data centers.