Prerequisite relations among concepts play an important role in many educational applications such as intelligent tutoring system and curriculum planning. With the increasing amount of educational data available, automatic discovery of concept prerequisite relations has become both an emerging research opportunity and an open challenge. Here, we investigate how to recover concept prerequisite relations from course dependencies and propose an optimization based framework to address the problem. We create the first real dataset for empirically studying this problem, which consists of the listings of computer science courses from 11 U.S. universities and their concept pairs with prerequisite labels. Experiment results on a synthetic dataset and the real course dataset both show that our method outperforms existing baselines.

Stochastic network design is a general framework for optimizing network connectivity. It has several applications in computational sustainability including spatial conservation planning, pre-disaster network preparation, and river network optimization. A common assumption in previous work has been made that network parameters (e.g., probability of species colonization) are precisely known, which is unrealistic in real- world settings. We therefore address the robust river network design problem where the goal is to optimize river connectivity for fish movement by removing barriers. We assume that fish passability probabilities are known only imprecisely, but are within some interval bounds. We then develop a planning approach that computes the policies with either high robust ratio or low regret. Empirically, our approach scales well to large river networks. We also provide insights into the solutions generated by our robust approach, which has significantly higher robust ratio than the baseline solution with mean parameter estimates.

Classification-based optimization is a recently developed framework for derivative-free optimization, which has shown to be effective for non-convex optimization problems with many local optima. This framework requires to sample a batch of solutions for every update of the search model. However, in reinforcement learning, direct policy search often offers only sequential policy evaluation. Thus, classificationbased optimization is not efficient for direct policy search where solutions have to be sampled sequentially. In this paper, we adapt the classification-based optimization for sequential sampled solutions by forming the batch of reused historical solutions. Experiments on helicopter hovering control task and reinforcement learning benchmark tasks in OpenAI Gym show that the new algorithm is superior to state-of-the-art derivative-free optimization approaches.

We study the problem of computing an Extensive-Form Perfect Equilibrium (EFPE) in 2-player games. This equilibrium concept refines the Nash equilibrium requiring resilience with respect to a specific vanishing perturbation, representing  mistakes of the players at each decision node. The scientific challenge is intrinsic to the EFPE definition: it requires a perturbation over the agent form, but the agent form is computationally inefficient due to the presence of highly nonlinear constraints. We show that the sequence form can be exploited in a non-trivial way and that, for general-sum games, finding an EFPE is equivalent to solving a suitably perturbed linear complementarity problem. We prove that Lemke's algorithm can be applied, showing that computing an EFPE is PPAD-complete. In the notable case of zero-sum games, the problem is in FP and can be solved by linear programming. Our algorithms also allow one to find a Nash equilibrium when players cannot perfectly control their moves, being subject to a given execution uncertainty, as is the case in most realistic physical settings.

Reserve price is an effective tool for revenue maximization in ad auctions. The optimal reserve price depends on bidders' value distributions, which, however, are generally unknown to auctioneers. A common practice for auctioneers is to first collect information about the value distributions by a sampling procedure and then apply the reserve price estimated with the sampled bids to the following auctions. In order to maximize the total revenue over finite auctions, it is important for the auctioneer to find a proper sample size to trade off between the cost of the sampling procedure and the optimality of the estimated reserve price. We investigate the sample size optimization problem for Generalized Second Price auctions, which is the most widely-used mechanism in ad auctions, and make three main contributions along this line. First, we bound the revenue losses in the form of competitive ratio during and after sampling. Second, we formulate the problem of finding the optimal sample size as a non-convex mixed integer optimization problem. Then we characterize the properties of the problem and prove the uniqueness of the optimal sample size. Third, we relax the integer optimization problem to a continuous form and develop an efficient algorithm based on the properties to solve it. Experimental results show that our approach can significantly improve the revenue for the auctioneer in finitely repeated ad auctions.

Online multi-kernel learning is promising in the era of mobile computing, in which a combined classifier with multiple kernels are offline trained, and online adapts to personalized features for serving the end user precisely and smartly. The online adaptation is mainly carried out at the end-devices, which requires the adaptation algorithms to be light, efficient and accurate. Previous results focused mainly on efficiency. This paper proposes an novel online model adaptation framework for not only efficiency but also optimal online adaptation. At first, an online optimal incremental simplex tableau (IST)algorithm is proposed, which approaches the model adaption by linear programming and produces the optimized model update in each step when a personalized training data is collected.But keeping online optimal in each step is expensive and may cause over-fitting especially when the online data is noisy. A Fast-IST approach is therefore proposed, which measures the deviation between the training data and the current model. It schedules updating only when enough deviation is detected. The efficiency of each update is further enhanced by running IST only limited iterations, which bounds the computation complexity. Theoretical analysis and extensive evaluations show that Fast-IST saves computation cost greatly, while achieving speedy and accurate model adaptation.It provides better model adaptation speed and accuracy while using even lower computing cost than the state-of-the art.

A common strategy for improving optimization algorithms is to restart the algorithm when it is believed to be trapped in an inferior part of the search space. However, while specific restart strategies have been developed for specific problems (and specific algorithms), restarts are typically not regarded as a general tool to speed up an optimization algorithm. In fact, many optimization algorithms do not employ restarts at all. Recently, "bet-and-run" was introduced in the context of mixed-integer programming, where first a number of short runs with randomized initial conditions is made, and then the most promising run of these is continued. In this article, we consider two classical NP-complete combinatorial optimization problems, traveling salesperson and minimum vertex cover, and study the effectiveness of different bet-and-run strategies. In particular, our restart strategies do not take any problem knowledge into account, nor are tailored to the optimization algorithm. Therefore, they can be used off-the-shelf. We observe that state-of-the-art solvers for these problems can benefit significantly from restarts on standard benchmark instances.

In this paper, we propose a Spatio-temporal Attributed Parse Graph (ST-APG) to integrate semantic attributes with trajectories for cross-view people tracking. Given videos from multiple cameras with overlapping field of view (FOV), our goal is to parse the videos and organize the trajectories of all targets into a scene-centered representation. We leverage rich semantic attributes of human, e.g., facing directions, postures and actions, to enhance cross-view tracklet associations, besides frequently used appearance and geometry features in the literature.In particular, the facing direction of a human in 3D, once detected, often coincides with his/her moving direction or trajectory. Similarly, the actions of humans, once recognized, provide strong cues for distinguishing one subject from the others. The inference is solved by iteratively grouping tracklets with cluster sampling and estimating people semantic attributes by dynamic programming.In experiments, we validate our method on one public dataset and create another new dataset that records people's daily life in public, e.g., food court, office reception and plaza, each of which includes 3-4 cameras. We evaluate the proposed method on these challenging videos and achieve promising multi-view tracking results.

Most of the existing proactive scheduling approaches assume the durations of activities can be described by independent random variables that have no relation with time. We deal with the more challenging problem where the duration uncertainty is related to the scheduled time period. We propose a sampling based approach by extending the Consensus method from stochastic optimization. Experimental results show the effectiveness of our approach in solution quality and stability.

Submodular function maximization has numerous applications in machine learning and artificial intelligence. Many real applications require multiple submodular objective func-tions to be maximized, and which function is regarded as important by a user is not known in advance. In such cases, it is desirable to have a small family of representative solutions that would satisfy any user’s preference. A traditional approach for solving such a problem is to enumerate the Pareto optimal solutions. However, owing to the massive number of Pareto optimal solutions (possibly exponentially many), it is difficult for a user to select a solution. In this paper, we propose two efficient methods for finding a small family of representative solutions, based on the notion of regret ratio. The first method outputs a family of fixed size with a nontrivial regret ratio. The second method enables us to choose the size of the output family, and in the biobjective case, it has a provable trade-off between the size and the regret ratio. Using real and synthetic data, we empirically demonstrate that our methods achieve a small regret ratio.