Peer grading, allowing students/peers to evaluate others' assignments, offers a promising solution for scaling evaluation and learning to large-scale educational systems. A key challenge in peer grading is motivating peers to grade diligently. While existing spot-checking (SC) mechanisms can prevent peer collusion where peers coordinate to report the uninformative grade, they unrealistically assume that peers have the same grading reliability and cost. This paper studies the general Optimal Spot-Checking (OptSC) problem of determining the probability each assignment needs to be checked to maximize assignments' evaluation accuracy aggregated from peers, and takes into consideration 1) peers' heterogeneous characteristics, and 2) peers' strategic grading behaviors to maximize their own utility. We prove that the bilevel OptSC is NP-hard to solve. By exploiting peers' grading behaviors, we first formulate a single level relaxation to approximate OptSC. By further exploiting structural properties of the relaxed problem, we propose an efficient algorithm to that relaxation, which also gives a good approximation of the original OptSC. Extensive experiments on both synthetic and real datasets show significant advantages of the proposed algorithm over existing approaches.

Animals in social foraging not only present the ordered and aggregated group movement but also the individual movement patterns of Lévy walks that are characterized as the power-law frequency distribution of flight lengths. The environment and the conspecific effects between group members are two fundamental inducements to the collective behavior. However, most previous models emphasize one of the two inducements probably because of the great difficulty to solve the behavior conflict caused by two inducements. Here, we propose an environment-driven social force model to simulate overall foraging process of an agent group. The social force concept is adopted to quantify the conspecific effects and the interactions between individuals and the environment. The cohesion-first rule is implemented to solve the conflict, which means that individuals preferentially guarantee the collective cohesion under the environmental effect. The obtained results efficiently comply with the empirical reports that mean the Lévy walk pattern of individual movement paths and the high consistency and cohesion of the entity group. By extensive simulations, we also validate the impact of two inducements for individual behaviors in comparison with several classic models