In many practical cases, we need to generalize a model trained in a source domain to a new target domain.However, the distribution of these two domains may differ very significantly, especially sometimes some crucial target features may not have support in the source domain.This paper proposes a novel locality preserving projection method for domain adaptation task,which can find a linear mapping preserving the 'intrinsic structure' for both source and target domains.We first construct two graphs encoding the neighborhood information for source and target domains separately.We then find linear projection coefficients which have the property of locality preserving for each graph.Instead of combing the two objective terms under compatibility assumption and requiring the user to decide the importance of each objective function,we propose a multi-objective formulation for this problem and solve it simultaneously using Pareto optimization.The Pareto frontier captures all possible good linear projection coefficients that are preferred by one or more objectives.The effectiveness of our approach is justified by both theoretical analysis and empirical results on real world data sets.The new feature representation shows better prediction accuracy as our experiments demonstrate.
We propose Pareto-frontier entropy search (PFES) for multi-objective Bayesian optimization (MBO). Unlike the existing entropy search for MBO which considers the entropy of the input space, we define the entropy of Pareto-frontier in the output space. By using a sampled Pareto-frontier from the current model, PFES provides a simple formula for directly evaluating the entropy. Besides the usual MBO setting, in which all the objectives are simultaneously observed, we also consider the "decoupled" setting, in which the objective functions can be observed separately. PFES can easily derive an acquisition function for the decoupled setting through the entropy of the marginal density for each output variable. For the both settings, by conditioning on the sampled Pareto-frontier, dependence among different objectives arises in the entropy evaluation. PFES can incorporate this dependency into the acquisition function, while the existing information-based MBO employs an independent Gaussian approximation. Our numerical experiments show effectiveness of PFES through synthetic functions and real-world datasets from materials science.
The content ranking problem in a social news website is typically a function that maximizes a scalar metric like dwell-time. However, in most real-world applications we are interested in more than one metric — for instance, simultaneously maximizing click-through rate, monetization metrics, and dwell-time — while also satisfying the constraints from traffic requirements promised to different publishers. The solution needs to be an online algorithm since the data arrives serially. Additionally, the objective function and the constraints can dynamically change. In this paper, we formulate this problem as a constrained, dynamic, multi-objective optimization problem. We propose a novel framework that extends a successful genetic optimization algorithm, NSGA-II, to solve our ranking problem. We evaluate optimization performance using the Hypervolume metric. We demonstrate the application of our framework on a real-world article ranking problem from the Yahoo! News page. We observe that our proposed solution makes considerable improvements in both time and performance over a brute-force baseline technique that is currently in production.
Multi-objective optimization aims at finding trade-off solutions to conflicting objectives. These constitute the Pareto optimal set. In the context of expensive-to-evaluate functions, it is impossible and often non-informative to look for the entire set. As an end-user would typically prefer a certain part of the objective space, we modify the Bayesian multi-objective optimization algorithm which uses Gaussian Processes to maximize the Expected Hypervolume Improvement, to focus the search in the preferred region. The cumulated effects of the Gaussian Processes and the targeting strategy lead to a particularly efficient convergence to the desired part of the Pareto set. To take advantage of parallel computing, a multi-point extension of the targeting criterion is proposed and analyzed.
This paper deals with these problems by using a new decomposition-based algorithm called: "Fractal geometric decomposition base algorithm" (FDA). It is a deterministic metaheuristic developed to solve large-scale continuous optimization problems . It can be noticed, that we call large scale problems those having the dimension greater than 1000. In this research, we are interested in using FDA to deal with MOPs because in the literature decomposition based algorithms have been with more less success applied to solve these problems, their main problem is related to their complexity. In this work, the goal is to deal with this complexity problem by keeping the same level of efficiency. FDA is based on "divide-and-conquer" paradigm where the sub-regions are hyperspheres rather than hypercubes on classical approaches. In order to identify the Pareto optimal solutions, we propose to extend FDA using the scalarization approach. We called the proposed algorithm Mo-FDA.