We consider multi-objective optimization (MOO) of an unknown vector-valued function in the non-parametric Bayesian optimization (BO) setting, with the aim being to learn points on the Pareto front of the objectives. Most existing BO algorithms do not model the fact that the multiple objectives, or equivalently, tasks can share similarities, and even the few that do lack rigorous, finite-time regret guarantees that capture explicitly inter-task structure. In this work, we address this problem by modelling inter-task dependencies using a multi-task kernel and develop two novel BO algorithms based on random scalarizations of the objectives. Our algorithms employ vector-valued kernel regression as a stepping stone and belong to the upper confidence bound class of algorithms. Under a smoothness assumption that the unknown vector-valued function is an element of the reproducing kernel Hilbert space associated with the multi-task kernel, we derive worst-case regret bounds for our algorithms that explicitly capture the similarities between tasks. We numerically benchmark our algorithms on both synthetic and real-life MOO problems, and show the advantages offered by learning with multi-task kernels.

In this paper, we consider the graph alignment problem, which is the problem of recovering, given two graphs, a one-to-one mapping between nodes that maximizes edge overlap. This problem can be viewed as a noisy version of the well-known graph isomorphism problem and appears in many applications, including social network deanonymization and cellular biology. Our focus here is on \emph{partial recovery}, i.e., we look for a one-to-one mapping which is correct on a fraction of the nodes of the graph rather than on all of them, and we assume that the two input graphs to the problem are correlated Erd\H{o}s-R\'enyi graphs of parameters $(n,q,s)$. Our main contribution is then to give necessary and sufficient conditions on $(n,q,s)$ under which partial recovery is possible with high probability as the number of nodes $n$ goes to infinity. In particular, we show that it is possible to achieve partial recovery in the $nqs=\Theta(1)$ regime under certain additional assumptions.

Bayesian geoacoustic inversion problems are conventionally solved by Markov chain Monte Carlo methods or its variants, which are computationally expensive. This paper extends the classic Bayesian geoacoustic inversion framework using the mixture density network (MDN), which provides a much more efficient way to solve geoacoustic inversion problems in Bayesian inference framework. Some important geoacoustic statistics of Bayesian geoacoustic inversion are derived from the multidimensional posterior probability density (PPD) using the MDN theory. These statistics make it convenient to train the network directly on the whole parameter space and get the multidimensional PPD of model parameters. The network is trained on a simulated dataset of surface-wave dispersion curves with shear-wave velocities as labels. The results show that the network gives reliable predictions and has good generalization performance on unseen data. Once trained, the network can rapidly (within seconds) give a fully probabilistic solution which is comparable to Monte Carlo methods. It provides an promissing approach for real-time inversion.

We propose a unifying dynamic-programming framework to compute exact literal-weighted model counts of formulas in conjunctive normal form. At the center of our framework are project-join trees, which specify efficient project-join orders to apply additive projections (variable eliminations) and joins (clause multiplications). In this framework, model counting is performed in two phases. First, the planning phase constructs a project-join tree from a formula. Second, the execution phase computes the model count of the formula, employing dynamic programming as guided by the project-join tree. We empirically evaluate various methods for the planning phase and compare constraint-satisfaction heuristics with tree-decomposition tools. We also investigate the performance of different data structures for the execution phase and compare algebraic decision diagrams with tensors. We show that our dynamic-programming model-counting framework DPMC is competitive with the state-of-the-art exact weighted model counters cachet, c2d, d4, and miniC2D.

Balanced order batching problem (BOBP) arises from the process of warehouse picking in Cainiao, the largest logistics platform in China. Batching orders together in the picking process to form a single picking route, reduces travel distance. The reason for its importance is that order picking is a labor intensive process and, by using good batching methods, substantial savings can be obtained. The BOBP is a NP-hard combinational optimization problem and designing a good problem-specific heuristic under the quasi-real-time system response requirement is non-trivial. In this paper, rather than designing heuristics, we propose an end-to-end learning and optimization framework named Balanced Task-orientated Graph Clustering Network (BTOGCN) to solve the BOBP by reducing it to balanced graph clustering optimization problem. In BTOGCN, a task-oriented estimator network is introduced to guide the type-aware heterogeneous graph clustering networks to find a better clustering result related to the BOBP objective. Through comprehensive experiments on single-graph and multi-graphs, we show: 1) our balanced task-oriented graph clustering network can directly utilize the guidance of target signal and outperforms the two-stage deep embedding and deep clustering method; 2) our method obtains an average 4.57m and 0.13m picking distance ("m" is the abbreviation of the meter (the SI base unit of length)) reduction than the expert-designed algorithm on single and multi-graph set and has a good generalization ability to apply in practical scenario.

We introduce Auto-Surprise, an Automated Recommender System library. Auto-Surprise is an extension of the Surprise recommender system library and eases the algorithm selection and configuration process. Compared to out-of-the-box Surprise library, Auto-Surprise performs better when evaluated with MovieLens, Book Crossing and Jester Datasets. It may also result in the selection of an algorithm with significantly lower runtime. Compared to Surprise's grid search, Auto-Surprise performs equally well or slightly better in terms of RMSE, and is notably faster in finding the optimum hyperparameters.

Machine Learning (ML) algorithms have been successfully employed by a vast range of practitioners with different backgrounds. One of the reasons for ML popularity is the capability to consistently delivers accurate results, which can be further boosted by adjusting hyperparameters (HP). However, part of practitioners has limited knowledge about the algorithms and does not take advantage of suitable HP settings. In general, HP values are defined by trial and error, tuning, or by using default values. Trial and error is very subjective, time costly and dependent on the user experience. Tuning techniques search for HP values able to maximize the predictive performance of induced models for a given dataset, but with the drawback of a high computational cost and target specificity. To avoid tuning costs, practitioners use default values suggested by the algorithm developer or by tools implementing the algorithm. Although default values usually result in models with acceptable predictive performance, different implementations of the same algorithm can suggest distinct default values. To maintain a balance between tuning and using default values, we propose a strategy to generate new optimized default values. Our approach is grounded on a small set of optimized values able to obtain predictive performance values better than default settings provided by popular tools. The HP candidates are estimated through a pool of promising values tuned from a small and informative set of datasets. After performing a large experiment and a careful analysis of the results, we concluded that our approach delivers better default values. Besides, it leads to competitive solutions when compared with the use of tuned values, being easier to use and having a lower cost.Based on our results, we also extracted simple rules to guide practitioners in deciding whether using our new methodology or a tuning approach.

Most recommender systems (RS) research assumes that a user's utility can be maximized independently of the utility of the other agents (e.g., other users, content providers). In realistic settings, this is often not true---the dynamics of an RS ecosystem couple the long-term utility of all agents. In this work, we explore settings in which content providers cannot remain viable unless they receive a certain level of user engagement. We formulate the recommendation problem in this setting as one of equilibrium selection in the induced dynamical system, and show that it can be solved as an optimal constrained matching problem. Our model ensures the system reaches an equilibrium with maximal social welfare supported by a sufficiently diverse set of viable providers. We demonstrate that even in a simple, stylized dynamical RS model, the standard myopic approach to recommendation---always matching a user to the best provider---performs poorly. We develop several scalable techniques to solve the matching problem, and also draw connections to various notions of user regret and fairness, arguing that these outcomes are fairer in a utilitarian sense.

We study the problem of optimizing expensive blackbox functions over combinatorial spaces (e.g., sets, sequences, trees, and graphs). BOCS (Baptista and Poloczek, 2018) is a state-of-the-art Bayesian optimization method for tractable statistical models, which performs semi-definite programming based acquisition function optimization (AFO) to select the next structure for evaluation. Unfortunately, BOCS scales poorly for large number of binary and/or categorical variables. Based on recent advances in submodular relaxation (Ito and Fujimaki, 2016) for solving Binary Quadratic Programs, we study an approach referred as Parametrized Submodular Relaxation (PSR) towards the goal of improving the scalability and accuracy of solving AFO problems for BOCS model. PSR approach relies on two key ideas. First, reformulation of AFO problem as submodular relaxation with some unknown parameters, which can be solved efficiently using minimum graph cut algorithms. Second, construction of an optimization problem to estimate the unknown parameters with close approximation to the true objective. Experiments on diverse benchmark problems show significant improvements with PSR for BOCS model. The source code is available at https://github.com/aryandeshwal/Submodular_Relaxation_BOCS .

Robust low-rank matrix completion (RMC), or robust principal component analysis with partially observed data, has been studied extensively for computer vision, signal processing and machine learning applications. This problem aims to decompose a partially observed matrix into the superposition of a low-rank matrix and a sparse matrix, where the sparse matrix captures the grossly corrupted entries of the matrix. A widely used approach to tackle RMC is to consider a convex formulation, which minimizes the nuclear norm of the low-rank matrix (to promote low-rankness) and the l1 norm of the sparse matrix (to promote sparsity). In this paper, motivated by some recent works on low-rank matrix completion and Riemannian optimization, we formulate this problem as a nonsmooth Riemannian optimization problem over Grassmann manifold. This new formulation is scalable because the low-rank matrix is factorized to the multiplication of two much smaller matrices. We then propose an alternating manifold proximal gradient continuation (AManPGC) method to solve the proposed new formulation. The convergence rate of the proposed algorithm is rigorously analyzed. Numerical results on both synthetic data and real data on background extraction from surveillance videos are reported to demonstrate the advantages of the proposed new formulation and algorithm over several popular existing approaches.