We investigate the use of message-passing algorithms for the problem of finding the max-weight independent set (MWIS) in a graph. First, we study the performance of the classical loopy max-product belief propagation. We show that each fixed point estimate of max-product can be mapped in a natural way to an extreme point of the LP polytope associated with the MWIS problem. However, this extreme point may not be the one that maximizes the value of node weights; the particular extreme point at final convergence depends on the initialization of max-product. We then show that if max-product is started from the natural initialization of uninformative messages, it always solves the correct LP -- if it converges. This result is obtained via a direct analysis of the iterative algorithm, and cannot be obtained by looking only at fixed points. The tightness of the LP relaxation is thus necessary for max-product optimality, but it is not sufficient. Motivated by this observation, we show that a simple modification of max-product becomes gradient descent on (a convexified version of) the dual of the LP, and converges to the dual optimum. We also develop a message-passing algorithm that recovers the primal MWIS solution from the output of the descent algorithm. We show that the MWIS estimate obtained using these two algorithms in conjunction is correct when the graph is bipartite and the MWIS is unique. Finally, we show that any problem of MAP estimation for probability distributions over finite domains can be reduced to an MWIS problem. We believe this reduction will yield new insights and algorithms for MAP estimation.

In the efficient social choice problem, the goal is to assign values, subject to side constraints, to a set of variables to maximize the total utility across a population of agents, where each agent has private information about its utility function. In this paper we model the social choice problem as a distributed constraint optimization problem (DCOP), in which each agent can communicate with other agents that share an interest in one or more variables. Whereas existing DCOP algorithms can be easily manipulated by an agent, either by misreporting private information or deviating from the algorithm, we introduce M-DPOP, the first DCOP algorithm that provides a faithful distributed implementation for efficient social choice. This provides a concrete example of how the methods of mechanism design can be unified with those of distributed optimization. Faithfulness ensures that no agent can benefit by unilaterally deviating from any aspect of the protocol, neither information-revelation, computation, nor communication, and whatever the private information of other agents. We allow for payments by agents to a central bank, which is the only central authoritythat we require. To achieve faithfulness, we carefully integrate the Vickrey-Clarke-Groves (VCG) mechanism with the DPOP algorithm, such that each agent is only asked to perform computation, report information, and send messages that is in its own best interest. Determining agent i's payment requires solving the social choice problem without agent i. Here, we present a method to reuse computation performed in solving the main problem in a way that is robust against manipulation by the excluded agent. Experimental results on structured problems show that as much as 87% of the computation required for solving the marginal problems can be avoided by re-use, providing very good scalability in the number of agents. On unstructured problems, we observe a sensitivity of M-DPOP to the density of the problem, and we show that reusability decreases from almost 100% for very sparse problems to around 20% for highly connected problems. We close with a discussion of the features of DCOP that enable faithful implementations in this problem, the challenge of reusing computation from the main problem to marginal problems in other algorithms such as ADOPT and OptAPO, and the prospect of methods to avoid the welfare loss that can occur because of the transfer of payments to the bank.

Robots reason about abstract actions, such as "go to position `l'", in order to decide what to do or to generate plans for their intended course of action. The use of abstract actions enables robots to employ small action libraries, which reduces the search space for decision making. When executing the actions, however, the robot must tailor the abstract actions to the specific task and situation context at hand. In this article we propose a novel robot action execution system that learns success and performance models for possible specializations of abstract actions. At execution time, the robot uses these models to optimize the execution of abstract actions to the respective task contexts. The robot can so use abstract actions for efficient reasoning, without compromising the performance of action execution. We show the impact of our action execution model in three robotic domains and on two kinds of action execution problems: (1) the instantiation of free action parameters to optimize the expected performance of action sequences; (2) the automatic introduction of additional subgoals to make action sequences more reliable.

Technically the underlying optimization development of online commerce forced problem is either NP or P-space businesses to question the week-plus supply-chain complete (depending on the details of the planning cycles that had been domain). Furthermore, the problem mixes the norm. Finally, the year 2000 (Y2K) a dozen or so classic optimization problems problem caused an across-the-board from AI and operations research (OR), replacement of enterprise software, allowing and much of the expected savings from many businesses to update their global supply-chain optimization are lost if approach to supply-chain planning. The end result of all of these factors was This article describes our experience a huge upswing in demand for supplychain from four years of solving supply-chain planning tools from i2 Technologies planning and optimization problems and other vendors. When I joined i2 in across industries, and some of the lessons 1996 as optimization architect, the company we learned.

We consider the problem of estimating the support of a vector $\beta^* \in \mathbb{R}^{p}$ based on observations contaminated by noise. A significant body of work has studied behavior of $\ell_1$-relaxations when applied to measurement matrices drawn from standard dense ensembles (e.g., Gaussian, Bernoulli). In this paper, we analyze \emph{sparsified} measurement ensembles, and consider the trade-off between measurement sparsity, as measured by the fraction $\gamma$ of non-zero entries, and the statistical efficiency, as measured by the minimal number of observations $n$ required for exact support recovery with probability converging to one. Our main result is to prove that it is possible to let $\gamma \to 0$ at some rate, yielding measurement matrices with a vanishing fraction of non-zeros per row while retaining the same statistical efficiency as dense ensembles. A variety of simulation results confirm the sharpness of our theoretical predictions.

Sentence compression holds promise for many applications ranging from summarization to subtitle generation. Our work views sentence compression as an optimization problem and uses integer linear programming (ILP) to infer globally optimal compressions in the presence of linguistically motivated constraints. We show how previous formulations of sentence compression can be recast as ILPs and extend these models with novel global constraints. Experimental results on written and spoken texts demonstrate improvements over state-of-the-art models.

In this paper we introduce a new selection scheme in cellular genetic algorithms (cGAs). Anisotropic Selection (AS) promotes diversity and allows accurate control of the selective pressure. First we compare this new scheme with the classical rectangular grid shapes solution according to the selective pressure: we can obtain the same takeover time with the two techniques although the spreading of the best individual is different. We then give experimental results that show to what extent AS promotes the emergence of niches that support low coupling and high cohesion. Finally, using a cGA with anisotropic selection on a Quadratic Assignment Problem we show the existence of an anisotropic optimal value for which the best average performance is observed. Further work will focus on the selective pressure self-adjustment ability provided by this new selection scheme.

This paper proposes the incremental Bayesian optimization algorithm (iBOA), which modifies standard BOA by removing the population of solutions and using incremental updates of the Bayesian network. iBOA is shown to be able to learn and exploit unrestricted Bayesian networks using incremental techniques for updating both the structure as well as the parameters of the probabilistic model. This represents an important step toward the design of competent incremental estimation of distribution algorithms that can solve difficult nearly decomposable problems scalably and reliably.

We describe Hidden Semi-Markov Support Vector Machines (SHM SVMs), an extension of HM SVMs to semi-Markov chains. This allows us to predict segmentations of sequences based on segment-based features measuring properties such as the length of the segment. We propose a novel technique to partition the problem into sub-problems. The independently obtained partial solutions can then be recombined in an efficient way, which allows us to solve label sequence learning problems with several thousands of labeled sequences. We have tested our algorithm for predicting gene structures, an important problem in computational biology. Results on a well-known model organism illustrate the great potential of SHM SVMs in computational biology.

We describe a nonnegative variant of the "Sparse PCA" problem. The goal is to create a low dimensional representation from a collection of points which on the one hand maximizes the variance of the projected points and on the other uses only parts of the original coordinates, and thereby creating a sparse representation. What distinguishes our problem from other Sparse PCA formulations is that the projection involves only nonnegative weights of the original coordinates -- a desired quality in various fields, including economics, bioinformatics and computer vision. Adding nonnegativity contributes to sparseness, where it enforces a partitioning of the original coordinates among the new axes. We describe a simple yet efficient iterative coordinate-descent type of scheme which converges to a local optimum of our optimization criteria, giving good results on large real world datasets.