9,559 research outputs found
Cakewalk Sampling
We study the task of finding good local optima in combinatorial optimization
problems. Although combinatorial optimization is NP-hard in general, locally
optimal solutions are frequently used in practice. Local search methods however
typically converge to a limited set of optima that depend on their
initialization. Sampling methods on the other hand can access any valid
solution, and thus can be used either directly or alongside methods of the
former type as a way for finding good local optima. Since the effectiveness of
this strategy depends on the sampling distribution, we derive a robust learning
algorithm that adapts sampling distributions towards good local optima of
arbitrary objective functions. As a first use case, we empirically study the
efficiency in which sampling methods can recover locally maximal cliques in
undirected graphs. Not only do we show how our adaptive sampler outperforms
related methods, we also show how it can even approach the performance of
established clique algorithms. As a second use case, we consider how greedy
algorithms can be combined with our adaptive sampler, and we demonstrate how
this leads to superior performance in k-medoid clustering. Together, these
findings suggest that our adaptive sampler can provide an effective strategy to
combinatorial optimization problems that arise in practice.Comment: Accepted as a conference paper by AAAI-2020 (oral presentation
Gossip Dual Averaging for Decentralized Optimization of Pairwise Functions
In decentralized networks (of sensors, connected objects, etc.), there is an
important need for efficient algorithms to optimize a global cost function, for
instance to learn a global model from the local data collected by each
computing unit. In this paper, we address the problem of decentralized
minimization of pairwise functions of the data points, where these points are
distributed over the nodes of a graph defining the communication topology of
the network. This general problem finds applications in ranking, distance
metric learning and graph inference, among others. We propose new gossip
algorithms based on dual averaging which aims at solving such problems both in
synchronous and asynchronous settings. The proposed framework is flexible
enough to deal with constrained and regularized variants of the optimization
problem. Our theoretical analysis reveals that the proposed algorithms preserve
the convergence rate of centralized dual averaging up to an additive bias term.
We present numerical simulations on Area Under the ROC Curve (AUC) maximization
and metric learning problems which illustrate the practical interest of our
approach
Decision support model for the selection of asphalt wearing courses in highly trafficked roads
The suitable choice of the materials forming the wearing course of highly trafficked roads is a delicate task because of their direct interaction with vehicles. Furthermore, modern roads must be planned according to sustainable development goals, which is complex because some of these might be in conflict. Under this premise, this paper develops a multi-criteria decision support model based on the analytic hierarchy process and the technique for order of preference by similarity to ideal solution to facilitate the selection of wearing courses in European countries. Variables were modelled using either fuzzy logic or Monte Carlo methods, depending on their nature. The views of a panel of experts on the problem were collected and processed using the generalized reduced gradient algorithm and a distance-based aggregation approach. The results showed a clear preponderance by stone mastic asphalt over the remaining alternatives in different scenarios evaluated through sensitivity analysis. The research leading to these results was framed in the European FP7 Project DURABROADS (No. 605404).The research leading to these results has received funding from the European Union Seventh Framework Programme (FP7/2007–2013) under Grant Agreement No. 605404
Algorithmic Foundations of Empirical X-risk Minimization
This manuscript introduces a new optimization framework for machine learning
and AI, named {\bf empirical X-risk minimization (EXM)}. X-risk is a term
introduced to represent a family of compositional measures or objectives, in
which each data point is compared with a large number of items explicitly or
implicitly for defining a risk function. It includes surrogate objectives of
many widely used measures and non-decomposable losses, e.g., AUROC, AUPRC,
partial AUROC, NDCG, MAP, precision/recall at top positions, precision at a
certain recall level, listwise losses, p-norm push, top push, global
contrastive losses, etc. While these non-decomposable objectives and their
optimization algorithms have been studied in the literature of machine
learning, computer vision, information retrieval, and etc, optimizing these
objectives has encountered some unique challenges for deep learning. In this
paper, we present recent rigorous efforts for EXM with a focus on its
algorithmic foundations and its applications. We introduce a class of
algorithmic techniques for solving EXM with smooth non-convex objectives. We
formulate EXM into three special families of non-convex optimization problems
belonging to non-convex compositional optimization, non-convex min-max
optimization and non-convex bilevel optimization, respectively. For each family
of problems, we present some strong baseline algorithms and their complexities,
which will motivate further research for improving the existing results.
Discussions about the presented results and future studies are given at the
end. Efficient algorithms for optimizing a variety of X-risks are implemented
in the LibAUC library at \url{www.libauc.org}
WordRank: Learning Word Embeddings via Robust Ranking
Embedding words in a vector space has gained a lot of attention in recent
years. While state-of-the-art methods provide efficient computation of word
similarities via a low-dimensional matrix embedding, their motivation is often
left unclear. In this paper, we argue that word embedding can be naturally
viewed as a ranking problem due to the ranking nature of the evaluation
metrics. Then, based on this insight, we propose a novel framework WordRank
that efficiently estimates word representations via robust ranking, in which
the attention mechanism and robustness to noise are readily achieved via the
DCG-like ranking losses. The performance of WordRank is measured in word
similarity and word analogy benchmarks, and the results are compared to the
state-of-the-art word embedding techniques. Our algorithm is very competitive
to the state-of-the- arts on large corpora, while outperforms them by a
significant margin when the training set is limited (i.e., sparse and noisy).
With 17 million tokens, WordRank performs almost as well as existing methods
using 7.2 billion tokens on a popular word similarity benchmark. Our multi-node
distributed implementation of WordRank is publicly available for general usage.Comment: Conference on Empirical Methods in Natural Language Processing
(EMNLP), November 1-5, 2016, Austin, Texas, US
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