Attacker-defender Stackelberg games have become a popular game-theoretic approach for security with deployments for LAX Police, the FAMS and the TSA. Unfortunately, most of the existing solution approaches do not model two key uncertainties of the real-world: there may be noise in the defender’s execution of the suggested mixed strategy and/or the observations made by an attacker can be noisy. In this paper, we analyze a framework to model these uncertainties, and demonstrate that previous strategies perform poorly in such uncertain settings. We also analyze RECON, a novel algorithm that computes strategies for the defender that are robust to such uncertainties, and explore heuristics that further improve RECON’s efficiency.

This paper proposes a new challenging optimization problem, called COOLING-AWARE WORKLOADPLACEMENT PROBLEM, that looks for a workload placement that optimizes the overall data center power consumption given by the sum of the server power consumption and of the computer room air conditioner power consumption. We formulate CWPP as a Mixed Integer Non Linear Problem using a cross-interferencematrix that links the workload placement to the cold airtemperature. Since state-of-the-art Mixed Integer Non Linear solvers can solve to optimality only the smallest instances, we devised two heuristics to obtain good feasible solutions: (i) a heuristic algorithm based on an integer linear relaxation of the problem, and (ii) a VariableNeighborhood Search algorithm. Both heuristic algorithms are evaluated against the best lower bounds obtained with a Mixed Integer Non Linear solver. Preliminary computational results show that both heuristics provide solutions that have a small percentage gap from the optimal solutions.

In this paper, we propose a novel method to select the most informativesubset of features, which has little redundancy andvery strong discriminating power. Our proposed approach automaticallydetermines the optimal number of features and selectsthe best subset accordingly by maximizing the averagepairwise informativeness, thus has obvious advantage overtraditional filter methods. By relaxing the essential combinatorialoptimization problem into the standard quadratic programmingproblem, the most informative feature subset canbe obtained efficiently, and a strategy to dynamically computethe redundancy between feature pairs further greatly acceleratesour method through avoiding unnecessary computationsof mutual information. As shown by the extensive experiments,the proposed method can successfully select the mostinformative subset of features, and the obtained classificationresults significantly outperform the state-of-the-art results onmost test datasets.

We explore in this paper efficient algorithmic solutions to robustsubspace segmentation. We propose the SSQP, namely SubspaceSegmentation via Quadratic Programming, to partition data drawnfrom multiple subspaces into multiple clusters. The basic idea ofSSQP is to express each datum as the linear combination of otherdata regularized by an overall term targeting zero reconstructioncoefficients over vectors from different subspaces. The derivedcoefficient matrix by solving a quadratic programming problem istaken as an affinity matrix, upon which spectral clustering isapplied to obtain the ultimate segmentation result. Similar tosparse subspace clustering (SCC) and low-rank representation (LRR),SSQP is robust to data noises as validated by experiments on toydata. Experiments on Hopkins 155 database show that SSQP can achievecompetitive accuracy as SCC and LRR in segmenting affine subspaces,while experimental results on the Extended Yale Face Database Bdemonstrate SSQP's superiority over SCC and LRR. Beyond segmentationaccuracy, all experiments show that SSQP is much faster than bothSSC and LRR in the practice of subspace segmentation.

Variable selection problems are typically addressed under apenalized optimization framework. Nonconvex penalties such as the minimax concave plus (MCP) and smoothly clipped absolute deviation(SCAD), have been demonstrated to have the properties of sparsity practically and theoretically. In this paper we propose a new nonconvex penalty that we call exponential-type penalty. The exponential-type penalty is characterized by a positive parameter,which establishes a connection with the ell 0 and ell 1 penalties.We apply this new penalty to sparse supervised learning problems. To solve to resulting optimization problem, we resort to a reweighted ell 1 minimization method. Moreover, we devise an efficient method for the adaptive update of the tuning parameter. Our experimental results are encouraging. They show that the exponential-type penalty is competitive with MCP and SCAD.

In this paper, we shed light on how powerful congestion control based on local interactions may be obtained. We show how ants can use repellent pheromones and incorporate the effect of crowding to avoid traffic congestion on the optimal path. Based on these interactions, we propose an ant algorithm, the M-unit EigenAnt algorithm, that leads to the selection of the M shortest paths. The ratio of selection of each of these paths is also optimal and regulated by an optimal amount of pheromone on each of them. To the best of our knowledge, the M -unit EigenAnt algorithm is the first antalgorithm that explicitly ensures the selection of the M shortest paths and regulates the amount of pheromone on them such that it is asymptotically optimal. In fact, it is in contrast with most ant algorithms that aim to discover just a single best path. We provide its convergence analysis and show that the steady state distribution of pheromone aligns with the eigenvectors of the cost matrix, and thus is related to its measure of quality. We also provide analysis to show that this property ensues even when the food is moved or path lengths change during foraging. We show that this behavior is robust in the presence of fluctuations and quickly reflects the change in the M optimal solutions. This makes it suitable for not only distributed applications butalso dynamic ones as well. Finally, we provide simulation results for the convergence to the optimal solution under different initial biases, dynamism in lengths of paths, and discovery of new paths.

The conservation of wildlife corridors between existing habitat preserves is important for combating the effects of habitat loss and fragmentation facing species of concern. We introduce the Steiner Multigraph Problem to model the problem of minimum-cost wildlife corridor design for multiple species with different landscape requirements. This problem can also model other analogous settings in wireless and social networks. As a generalization of Steiner forest, the goal is to find a minimum-cost subgraph that connects multiple sets of terminals. In contrast to Steiner forest, each set of terminals can only be connected via a subset of the nodes. Generalizing Steiner forest in this way makes the problem NP-hard even when restricted to two pairs of terminals. However, we show that if the node subsets have a nested structure, the problem admits a fixed-parameter tractable algorithm in the number of terminals. We successfully test exact and heuristic solution approaches on a wildlife corridor instance for wolverines and lynx in western Montana, showing that though the problem is computationally hard, heuristics perform well, and provably optimal solutions can still be obtained.

Sustainable resource management in many domains presents large continuous stochastic optimization problems, which can often be modeled as Markov decision processes (MDPs). To solve such large MDPs, we identify and leverage linearity in state and action sets that is common in resource management. In particular, we introduce linear dynamic programs (LDPs) that generalize resource management problems and partially observable MDPs (POMDPs). We show that the LDP framework makes it possible to adapt point-based methods--the state of the art in solving POMDPs--to solving LDPs. The experimental results demonstrate the efficiency of this approach in managing the water level of a river reservoir. Finally, we discuss the relationship with dual dynamic programming, a method used to optimize hydroelectric systems.

Automated feature discovery is a fundamental problem in machine learning. Although classical feature discovery methods do not guarantee optimal solutions in general, it has been recently noted that certain subspace learning and sparse coding problems can be solved efficiently, provided the number of features is not restricted a priori. We provide an extended characterization of this optimality result and describe the nature of the solutions under an expanded set of practical contexts. In particular, we apply the framework to a semi-supervised learning problem, and demonstrate that feature discovery can co-occur with input reconstruction and supervised training while still admitting globally optimal solutions. A comparison to existing semi-supervised feature discovery methods shows improved generalization and efficiency.

The rectangle-packing problem consists of finding an enclosing rectangle of smallest area that can contain a given set of rectangles without overlap. Our new benchmark includes rectangles of successively higher precision, challenging the previous state-of-the-art, which enumerates all locations for placing rectangles, as well as all bounding box widths and heights up to the optimal box. We instead limit the rectangles’ coordinates and bounding box dimensions to the set of subset sums of the rectangles’ dimensions. We also dynamically prune values by learning from infeasible subtrees and constrain the problem by replacing rectangles and empty space with larger rectangles. Compared to the previous state-of-the-art, we test 4,500 times fewer bounding boxes on the high-precision benchmark and solve N =9 over two orders of magnitude faster. We also present all optimal solutions up to N =15, which requires 39 bits of precision to solve. Finally, on the open problem of whether or not one can pack a particular infinite series of rectangles into the unit square, we pack the first 50,000 such rectangles witha greedy heuristic and conjecture that the entire infinite series can fit..