We study the problem of locating a single facility on a real line based on the reports of self-interested agents, when agents have double-peaked preferences, with the peaks being on opposite sides of their locations. We observe that double-peaked preferences capture real-life scenarios and thus complement the well-studied notion of single-peaked preferences. As a motivating example, assume that the government plans to build a primary school along a street; an agent with single-peaked preferences would prefer having the school built exactly next to her house. However, while that would make it very easy for her children to go to school, it would also introduce several problems, such as noise or parking congestion in the morning. A 5-min walking distance would be sufficiently far for such problems to no longer be much of a factor and at the same time sufficiently close for the school to be easily accessible by the children on foot. There are two positions (symmetrically) in each direction and those would be the agent’s two peaks of her double-peaked preference. Motivated by natural scenarios like the one described above, we mainly focus on the case where peaks are equidistant from the agents’ locations and discuss how our results extend to more general settings. We show that most of the results for single-peaked preferences do not directly apply to this setting, which makes the problem more challenging. As our main contribution, we present a simple truthful-in-expectation mechanism that achieves an approximation ratio of \(1+b/c\) for both the social and the maximum cost, where b is the distance of the agent from the peak and c is the minimum cost of an agent. For the latter case, we provide a 3 / 2 lower bound on the approximation ratio of any truthful-in-expectation mechanism. We also study deterministic mechanisms under some natural conditions, proving lower bounds and approximation guarantees. We prove that among a large class of reasonable strategyproof mechanisms, there is no deterministic mechanism that outperforms our truthful-in-expectation mechanism. In order to obtain this result, we first characterize mechanisms for two agents that satisfy two simple properties; we use the same characterization to prove that no mechanism in this class can be group-strategyproof.

Often because of limitations in generation capacity of power stations, many developing countries frequently resort to disconnecting large parts of the power grid from supply, a process termed load shedding. This leaves households in disconnected parts without electricity, causing them inconvenience and discomfort. Without fairness being taken into due consideration during load shedding, some households may suffer more than others. In this paper, we solve the fair load shedding problem (FLSP) by creating solutions which connect households to supply based on some fairness criteria (i.e., to fairly connect homes to supply in terms of duration, their electricity needs, and their demand), which we model as their utilities. First, we briefly describe some state-of-art household-level load shedding heuristics which meet the first criteria. Second, we model the FLSP as a resource allocation problem, which we formulate into two Mixed Integer Programming (MIP) problems based on the Multiple Knapsack Problem. In so doing, we use the utilitarian, egalitarian and envy-freeness social welfare metrics to develop objectives and constraints that ensure our FLSP solutions results in fair allocations that consider the utilities of agents. Then, we solve the FLSP and show that our MIP models maximize the groupwise and individual utilities of agents, and minimize the differences between their pairwise utilities under a number of experiments. When taken together, our endeavour establishes a set of benchmarks for fair load shedding schemes, and provide insights for designing fair allocation solutions for other scarce resources.

Hypervisor-based virtualization solutions reveal good security and isolation, while container-based solutions make applications and workloads more portable and distributed in an effective, standardized and repeatable way. Therefore, nested virtualization based computing environments (e.g., container over virtual machine), which inherit the capabilities from both solutions, are becoming more and more attractive in clouds (e.g., running Docker over Amazon EC2 VMs). Recent studies have shown that running applications in either VMs or containers still has significant overhead, especially for I/O intensive workloads. This motivates us to investigate whether the nested virtualization based solution can be adopted to build high-performance computing (HPC) clouds for running MPI applications efficiently and where the bottlenecks lie. To eliminate performance bottlenecks, we propose a high-performance two-layer locality and NUMA aware MPI library, which is able to dynamically detect co-resident containers inside one VM as well as detect co-resident VM inside one host at MPI runtime. Thus the MPI processes across different containers and VMs can communicate to each other by shared memory or Cross Memory Attach (CMA) channels instead of network channel if they are co-resident. We further propose an enhanced NUMA aware hybrid design to utilize InfiniBand loopback based channel to optimize large message transfer across containers when they are running on different sockets. Performance evaluations show that compared with the performance of the state-of-art (1Layer) design, our proposed enhance-hybrid design can bring up to 184%, 81% and 12% benefit on point-to-point, collective operations, and end applications. Compared with the default performance, our enhanced-hybrid design delivers up to 184%, 85% and 16% performance improvement.

Multi-task reinforcement learning (MTRL) holds potential for building general-purpose agents, enabling them to generalize across a variety of tasks. However, MTRL may still be susceptible to conflicts between tasks. A primary reason for this problem is that a universal policy struggles to balance short-term and dense learning signals across various tasks, e.g. , distinct reward functions in reinforcement learning. In social cognitive theory, internalized future goals, as a form of cognitive representations, can effectively mitigate potential short-term conflicts in multitask settings. Considering the benefits of future goals, we propose a novel and general framework called Task-Specific Action Correction (TSAC) from the goal perspective as an orthogonal research to previous MTRL methods. Specifically, to avoid myopia, TSAC introduces goal-oriented sparse rewards and decomposes policy learning into two separate policies: a shared policy (SP) and an action correction policy (ACP). The SP outputs a short-term perspective action based on guiding dense rewards. To alleviate conflicts resulting from excessive focus on specific tasks’ details in SP, the ACP incorporates goal-oriented sparse rewards, enabling an agent to adopt a long-term perspective to output a correction action and achieve generalization across tasks. Finally, the actions output by SP and ACP are combined based on the action correction function to form a final action that interact with the environment. Extensive experiments conducted on Meta-World and multi-task StarCraft II multi-agent scenarios demonstrate that TSAC outperforms existing state-of-the-art methods, achieving significant improvements in sample efficiency, generalization and effective action execution across tasks.