Green security — protection of forests, fish and wildlife — is a critical problem in environmental sustainability. We focus on the problem  of  optimizing the defense of forests againstillegal logging, where often we are faced with the challenge of teaming up many different groups,  from national police to forest guards to NGOs, each with differing capabilities and costs. This paper introduces a new, yet fundamental problem: SimultaneousOptimization of Resource Teams and Tactics (SORT).  SORT contrasts with most previous game-theoretic research for green security — in particular based onsecurity games — that has solely focused on optimizing patrolling tactics, without consideration of team formation or coordination.  We develop new models and scalable algorithms to apply SORT towards illegal logging in large forest areas. We evaluate our methods on a variety of synthetic examples, as well as a real-world case study using data from our on-going collaboration in Madagascar .

Graph matching plays an important role in many fields in computer vision. It is a well-known general NP-hard problem and has been investigated for decades. Among the large amount of algorithms for graph matching, the algorithms utilizing the path following strategy exhibited state-of-art performances. However, the main drawback of this category of algorithms lies in their high computational burden. In this paper, we propose a novel path following strategy for graph matching aiming to improve its computation efficiency. We first propose a path estimation method to reduce the computational cost at each iteration, and subsequently a method of adaptive step length to accelerate the convergence. The proposed approach is able to be integrated into all the algorithms that utilize the path following strategy. To validate our approach, we compare our approach with several recently proposed graph matching algorithms on three benchmark image datasets. Experimental results show that, our approach improves significantly the computation efficiency of the original algorithms, and offers similar or better matching results.

We consider the problem of sampling from a discrete probability distribution specified by a graphical model. Exact samples can, in principle, be obtained by computing the mode of the original model perturbed with an exponentially many i.i.d. random variables. We propose a novel algorithm that views this as a combinatorial optimization problem and searches for the extreme state using a standard integer linear programming (ILP) solver, appropriately extended to account for the random perturbation. Our technique, GumbelMIP, leverages linear programming (LP) relaxations to evaluate the qualityof samples and prune large portions of the search space, and can thus scale to large tree-width models beyond the reach of current exact inference methods. Further, when the optimization problem is not solved to optimality, our method yields a novel approximate sampling technique. We empirically demonstrate that our approach parallelizes well, our exact sampler scales better than alternative approaches, and our approximate sampler yields better quality samples than a Gibbs sampler and a low-dimensional perturbation method.

We consider optimal route planning when the objective function is a general nonlinear and non-monotonic function. Such an objective models user behavior more accurately, for example, when a user is risk-averse, or the utility function needs to capture a penalty for early arrival. It is known that as non-linearity arises, the problem can become NP-hard and little is known on computing optimal solutions when in addition there is no monotonicity guarantee. We show that an approximately optimal non-simple path can be efficiently computed under some natural constraints. In particular, we provide a fully polynomial approximation scheme under hop constraints. Our approximation algorithm can extend to run in pseudo-polynomial time under an additional linear constraint that sometimes is useful. As a by-product, we show that our algorithm can be applied to the problem of finding a path that is most likely to be on time for a given deadline.

Uncertainty in activity durations is a key characteristic of many real world scheduling problems in manufacturing, logistics and project management. RCPSP/max with durational uncertainty is a general  model that can be used to represent durational uncertainty in a wide variety of scheduling problems where there exist resource constraints. However, computing schedules or execution strategies for RCPSP/max with durational uncertainty is NP-hard and hence we focus on providing approximation methods in this paper. We provide a principled approximation approach based on Sample Average Approximation (SAA) to compute proactive schedules for RCPSP/max  with durational uncertainty. We further contribute an extension to SAA for improving scalability significantly without sacrificing on solution quality. Not only is our approach able to compute schedules at comparable runtimes as existing approaches, it also provides lower α-quantile makespan (also referred to as α-robust makespan) values than the best known approach on benchmark problems from the literature.

Unsupervised feature selection (UFS) aims to reduce the time complexity and storage burden, as well as improve the generalization performance. Most existing methods convert UFS to supervised learning problem by generating labels with specific techniques (e.g., spectral analysis, matrix factorization and linear predictor). Instead, we proposed a novel coupled analysis-synthesis dictionary learning method, which is free of generating labels. The representation coefficients are used to model the cluster structure and data distribution. Specifically, the synthesis dictionary is used to reconstruct samples, while the analysis dictionary analytically codes the samples and assigns probabilities to the samples. Afterwards, the analysis dictionary is used to select features that can well preserve the data distribution. The effective L2p-norm (0 < p <1) regularization is imposed on the analysis dictionary to get much sparse solution and is more effective in feature selection.We proposed an iterative reweighted least squares algorithm to solve the L2p-norm optimization problem and proved it can converge to a fixed point. Experiments on benchmark datasets validated the effectiveness of the proposed method

In regularized risk minimization, the associated optimization problem becomes particularly difficult when both the loss and regularizer are nonsmooth. Existing approaches either have slow or unclear convergence properties, are restricted to limited problem subclasses, or require careful setting of a smoothing parameter. In this paper, we propose a continuation algorithm that is applicable to a large class of nonsmooth regularized risk minimization problems, can be flexibly used with a number of existing solvers for the underlying smoothed subproblem, and with convergence results on the whole algorithm rather than just one of its subproblems. In particular, when accelerated solvers are used, the proposed algorithm achieves the fastest known rates of $O(1/T^2)$ on strongly convex problems, and $O(1/T)$ on general convex problems. Experiments on nonsmooth classification and regression tasks demonstrate that the proposed algorithm outperforms the state-of-the-art.

In many learning tasks with structural properties, structured sparse modeling usually leads to better interpretability and higher generalization performance. While great efforts have focused on the convex regularization, recent studies show that nonconvex regularizers can outperform their convex counterparts in many situations. However, the resulting nonconvex optimization problems are still challenging, especially for the structured sparsity-inducing regularizers. In this paper, we propose a splitting method for solving nonconvex structured sparsity optimization problems. The proposed method alternates between a gradient step and an easily solvable proximal step, and thus enjoys low per-iteration computational complexity. We prove that the whole sequence generated by the proposed method converges to a critical point with at least sublinear convergence rate, relying on the Kurdyka-Łojasiewicz inequality. Experiments on both simulated and real-world data sets demonstrate the efficiency and efficacy of the proposed method.

Many randomized heuristic derivative-free optimization methods share a framework that iteratively learns a model for promising search areas and samples solutions from the model. This paper studies a particular setting of such framework, where the model is implemented by a classification model discriminating good solutions from bad ones. This setting allows a general theoretical characterization, where critical factors to the optimization are discovered. We also prove that optimization problems with Local Lipschitz continuity can be solved in polynomial time by proper configurations of this framework. Following the critical factors, we propose the randomized coordinate shrinking classification algorithm to learn the model, forming the RACOS algorithm, for optimization in continuous and discrete domains. Experiments on the testing functions as well as on the machine learning tasks including spectral clustering and classification with Ramp loss demonstrate the effectiveness of RACOS.

Although many handle missing labels and class imbalance jointly. We formulate multi-label learning methods have been proposed in recent the problem as a transductive learning problem that years, a main challenge remains for this problem, i.e., the include five components that are label consistency, instancelevel lack of completely labeled training instances. This is important and class-level label smoothness, and two types of class because in many real life applications, most training cardinality (lower and upper) bounds. The first three components instances are only partially labeled, while other labels are are used to propagate the label information from the not provided or missing. One such example is image annotation, provided labels to missing labels, and the latter two components a human labeler can only feasibly annotates each are included to handle two types of the class imbalance training image with a subset of tags, especially when the problem. We first formulate a unified model that combines number of classes/tags is large. Learning from such partially these components as a constrained submodular minimization labeled instances is referred to as the multi-label learning problem (CSM). However, due to the class cardinality with missing labels (MLML) problem (Wu et al. 2014; constraint, it is a NPhard problem.