Recently, a new convex formulation of IBM Model 2 was introduced. In this paper we develop the theory further and introduce a class of convex relaxations for latent variable models which include IBM Model 2. When applied to IBM Model 2, our relaxation class subsumes the previous relaxation as a special case. As proof of concept, we study a new relaxation of IBM Model 2 which is simpler than the previous algorithm: the new relaxation relies on the use of nothing more than a multinomial EM algorithm, does not require the tuning of a learning rate, and has some favorable comparisons to IBM Model 2 in terms of F-Measure. The ideas presented could be applied to a wide range of NLP and machine learning problems.

Roughly speaking, Interdependent Defense (IDD) games, previously proposed, model the situation where an attacker wants to cause as much damage as possible to a network by attacking one of the sites in the network. Each site must make an investment decision regarding security to protect itself against a direct or indirect attack, the latter due to potential transfer-risk from an unprotected neighboring site. The work introducing IDD games discusses potential applications to model the essence of real-world scenarios such as the 2006 transatlantic aircraft plot. In this paper, our focus is the study of the problem of computing a Nash Equilibrium (NE) in IDD games. We show that an efficient algorithm to determine whether some attacker’s strategy can be a part of a NE in an instance of IDD games is unlikely to exist. Yet, we provide a dynamic programming algorithm to compute an approximate NE when the graph/network structure of the game is a directed tree with a single source, and show that it is an FPTAS. We also introduce an improved heuristic to compute an approximate NE on arbitrary graph structures. Our experiments show that our heuristic is more efficient, and provides better approximations, than best-response-gradient dynamics for the case of Internet games, a class of games introduced and studied in the original work on IDD games.

We describe an optimization-based approach for automatically creating well-edited movies from a 3D animation. While previous work has mostly focused on the problem of placing cameras to produce nice-looking views of the action, the problem of cutting and pasting shots from all available cameras has never been addressed extensively. In this paper, we review the main causes of editing errors in literature and propose an editing model relying on a minimization of such errors. We make a plausible semi-Markov assumption, resulting in a dynamic programming solution which is computationally efficient. We also show that our method can generate movies with different editing rhythms and validate the results through a user study. Combined with state-of-the-art cinematography, our approach therefore promises to significantly extend the expressiveness and naturalness of virtual movie-making.

In emergency medical systems, arriving at the incident locationa few seconds early can save a human life. Thus, this paper is motivated by the need to reduce the response time– time taken to arrive at the incident location after receivingthe emergency call — of Emergency Response Vehicles, ERVs(ex: ambulances, fire rescue vehicles) for as many requests as possible. We expect to achieve this primarily by positioning the ”right” number of ERVs at the ”right” places and at the ”right” times. Given the exponentially large action space(with respect to number of ERVs and their placement) and the stochasticity in location and timing of emergency incidents,this problem is computationally challenging. To that end, ourcontributions building on existing data-driven approaches are three fold:1. Based on real world evaluation metrics, we provide a riskbased optimization criterion to learn from past incident data. Instead of minimizing expected response time, we minimize the largest value of response time such that the risk of finding requests that have a higher value is bounded(ex: Only 10% of requests should have a response time greater than 8 minutes).2. We develop a mixed integer linear optimization formulation to learn and compute an allocation from a set of inputrequests while considering the risk criterion.3. To allow for ”live” reallocation of ambulances, we provide a decomposition method based on Lagrangian Relaxation to significantly reduce the run-time of the optimization formulation.Finally, we provide an exhaustive evaluation on real-world datasets from two asian cities that demonstrates the improvement provided by our approach over current practice and the best known approach from literature.

Mitigating risk in decision-making has been a long-standing problem. Due to the mathematical challenge of its nonlinear nature, especially in adaptive decision-making problems, finding optimal policies is typically intractable. With a focus on efficient algorithms, we ask how well we can approximate the optimal policies for the difficult case of general utility models of risk. Little is known about efficient algorithms beyond the very special cases of linear (risk-neutral) and exponential utilities since general utilities are not separable and preclude the use of traditional dynamic programming techniques. In this paper, we consider general utility functions and investigate efficient computation of approximately optimal routing policies, where the goal is to maximize the expected utility of arriving at a destination around a given deadline. We present an adaptive discretization variant of successive approximation which gives an $\error$-optimal policy in polynomial time. The main insight is to perform discretization at the utility level space, which results in a nonuniform discretization of the domain, and applies for any monotone utility function.

Reinforcement learning for robot control tasks in continuous environments is a challenging problem due to the dimensionality of the state and action spaces, time and resource costs for learning with a real robot as well as constraints imposed for its safe operation. In this paper we propose a model-based reinforcement learning approach for continuous environments with constraints. The approach combines model-based reinforcement learning with recent advances in approximate optimal control. This results in a bounded-rationality agent that makes decisions in real-time by efficiently solving a sequence of constrained optimization problems on learned sparse Gaussian process models. Such a combination has several advantages. No high-dimensional policy needs to be computed or stored while the learning problem often reduces to a set of lower-dimensional models of the dynamics. In addition, hard constraints can easily be included and objectives can also be changed in real-time to allow for multiple or dynamic tasks. The efficacy of the approach is demonstrated on both an extended cart pole domain and a challenging quadcopter navigation task using real data.

Energy consumption in commercial and educational buildings is impacted by group activities such as meetings, workshops, classes and exams, and can be reduced by scheduling these activities to take place at times and locations that are favorable from an energy standpoint. This paper improves on the effectiveness of energy-aware room-booking and occupancy scheduling approaches, by allowing the scheduling decisions to rely on an explicit model of the building's occupancy-based HVAC control. The core component of our approach is a mixed-integer linear programming (MILP) model which optimally solves the joint occupancy scheduling and occupancy-based HVAC control problem. To scale up to realistic problem sizes, we embed this MILP model into a large neighbourhood search (LNS). We obtain substantial energy reduction in comparison with occupancy-based HVAC control using arbitrary schedules or using schedules obtained by existing heuristic energy-aware scheduling approaches.

In the proposed thesis, we study Distributed Constraint Optimization Problems (DCOPs), which are problems where several agents coordinate with each other to optimize a global cost function. The use of DCOPs has gained momentum, due to their capability of addressing complex and naturally distributed problems. A majority of the work in DCOP addresses the resolution problem by detaching the model from the resolution process, where they assume that each agent controls exclusively one variable of the problem (Burke et al. 2006). This assumption often is not reflected in the model specifications, and may lead to inefficient communication requirements. Another limitation of current DCOP resolution methods is their inability to capitalize on the presence of structural information, which may allow incoherent/unnecessary data to reticulate among the agents (Yokoo 2001). The purpose of the proposed dissertation is to study how to adapt and integrate insights gained from centralized solving techniques in order to enhance DCOP performance and scalability, enabling their use for the resolution of real-world complex problems. To do so, we hypothesize that one can exploit the DCOP structure in both problem modeling and problem resolution phases.

I draw the reader's attention to machine teaching, the problem of finding an optimal training set given a machine learning algorithm and a target model. In addition to generating fascinating mathematical questions for computer scientists to ponder, machine teaching holds the promise of enhancing education and personnel training. The Socratic dialogue style aims to stimulate critical thinking.

Multi-view point registration is a relatively less studied problem compared with two-view point registration. Directly applying pairwise registration often leads to matching discrepancy as the mapping between two point sets can be determined either by direct correspondences or by any intermediate point set. Also, the local two-view registration tends to be sensitive to noises. We propose a novel multi-view registration method, where the optimal registration is achieved via an efficient and effective alternating concave minimization process. We further extend our solution to a general case in practice of registration among point sets with different cardinalities. Extensive empirical evaluations of peer methods on both synthetic data and real images suggest our method is robust to large disturbance. In particular, it is shown that our method outperforms peer point matching methods and performs competitively against graph matching approaches. The latter approaches utilize the additional second-order information at the cost of exponentially increased run-time, thus usually being less efficient.