Many machine learning problems involve Monte Carlo gradient estimators. As a prominent example, we focus on Monte Carlo variational inference (MCVI) in this paper. The performance of MCVI crucially depends on the variance of its stochastic gradients. We propose variance reduction by means of Quasi-Monte Carlo (QMC) sampling. QMC replaces N i.i.d. samples from a uniform probability distribution by a deterministic sequence of samples of length N. This sequence covers the underlying random variable space more evenly than i.i.d. draws, reducing the variance of the gradient estimator. With our novel approach, both the score function and the reparameterization gradient estimators lead to much faster convergence. We also propose a new algorithm for Monte Carlo objectives, where we operate with a constant learning rate and increase the number of QMC samples per iteration. We prove that this way, our algorithm can converge asymptotically at a faster rate than SGD. We furthermore provide theoretical guarantees on QMC for Monte Carlo objectives that go beyond MCVI, and support our findings by several experiments on large-scale data sets from various domains.

Bayesian optimization offers the possibility of optimizing black-box operations not accessible through traditional techniques. The success of Bayesian optimization methods such as Expected Improvement (EI) are significantly affected by the degree of trade-off between exploration and exploitation. Too much exploration can lead to inefficient optimization protocols, whilst too much exploitation leaves the protocol open to strong initial biases, and a high chance of getting stuck in a local minimum. Typically, a constant margin is used to control this trade-off, which results in yet another hyper-parameter to be optimized. We propose contextual improvement as a simple, yet effective heuristic to counter this - achieving a one-shot optimization strategy. Our proposed heuristic can be swiftly calculated and improves both the speed and robustness of discovery of optimal solutions. We demonstrate its effectiveness on both synthetic and real world problems and explore the unaccounted for uncertainty in the pre-determination of search hyperparameters controlling explore-exploit trade-off.

Many real-world optimization problems require significant resources for objective function evaluations. This is a challenge to evolutionary algorithms, as it limits the number of available evaluations. One solution are surrogate models, which replace the expensive objective. A particular issue in this context are hierarchical variables. Hierarchical variables only influence the objective function if other variables satisfy some condition. We study how this kind of hierarchical structure can be integrated into the model based optimization framework. We discuss an existing kernel and propose alternatives. An artificial test function is used to investigate how different kernels and assumptions affect model quality and search performance.

We introduce a framework based on bilevel programming that unifies gradient-based hyperparameter optimization and meta-learning. We show that an approximate version of the bilevel problem can be solved by taking into explicit account the optimization dynamics for the inner objective. Depending on the specific setting, the outer variables take either the meaning of hyperparameters in a supervised learning problem or parameters of a meta-learner. We provide sufficient conditions under which solutions of the approximate problem converge to those of the exact problem. We instantiate our approach for meta-learning in the case of deep learning where representation layers are treated as hyperparameters shared across a set of training episodes. In experiments, we confirm our theoretical findings, present encouraging results for few-shot learning and contrast the bilevel approach against classical approaches for learning-to-learn.

In compressed sensing, a small number of linear measurements can be used to reconstruct an unknown signal. Existing approaches leverage assumptions on the structure of these signals, such as sparsity or the availability of a generative model. A domain-specific generative model can provide a stronger prior and thus allow for recovery with far fewer measurements. However, unlike sparsity-based approaches, existing methods based on generative models guarantee exact recovery only over their support, which is typically only a small subset of the space on which the signals are defined. We propose Sparse-Gen, a framework that allows for sparse deviations from the support set, thereby achieving the best of both worlds by using a domain specific prior and allowing reconstruction over the full space of signals. Theoretically, our framework provides a new class of signals that can be acquired using compressed sensing, reducing classic sparse vector recovery to a special case and avoiding the restrictive support due to a generative model prior. Empirically, we observe consistent improvements in reconstruction accuracy over competing approaches, especially in the more practical setting of transfer compressed sensing where a generative model for a data-rich, source domain aids sensing on a data-scarce, target domain.

What is the relationship between machine learning and optimization? On the other hand, what happens when machine learning is used to solve optimization problems? Consider this: a UPS driver with 25 packages has 15 trillion possible routes to choose from. And if each driver drives just one more mile each day than necessary, the company would be losing $30 million a year. While UPS would have all the data for their trucks and routes, there is no way they can run 15 trillion computations per each driver with 25 packages.

Bayesian optimization has emerged as a strong candidate tool for global optimization of functions with expensive evaluation costs. However, due to the dynamic nature of research in Bayesian approaches, and the evolution of computing technology, using Bayesian optimization in a parallel computing environment remains a challenge for the non-expert. In this report, I review the state-of-the-art in parallel and scalable Bayesian optimization methods. In addition, I propose practical ways to avoid a few of the pitfalls of Bayesian optimization, such as oversampling of edge parameters and over-exploitation of high performance parameters. Finally, I provide relatively simple, heuristic algorithms, along with their open source software implementations, that can be immediately and easily deployed in any computing environment.

Risk assessment is the process where we identify hazards, analyze or evaluate the risk associated with that hazard, and determine appropriate ways to eliminate or control the hazard. Risk assessment techniques have been widely applied in many area including quantitative financial engineering (Krokhmal et al. 2002), health and environment study (Zhang and Wang 2012; Van Asselt et al. 2013), transportation science (Liu et al. 2017), etc. Paltrinieri et al. (2014) point out that traditional risk assessment methods are often limited by static, onetime processes performed during the design phase of industrial processes. As such they often use older data or generic data on potential hazards and failure rates of equipment and processes and cannot be easily updated in order to take into account new information, giving a more complete view of the related risks. This failure to account for new information can lead to unrecognized hazards, or misunderstandings about the real probability of their occurrence under current management and safety precautions. With the rapid development of computational intelligence and corresponding decision support system, as well as the launch of "Big data" era, nowadays, new risk assessment technique should allow decision maker to update the assessment results by observing new information or data and realize quick response to dynamic environment. In this paper, we develop a satisficing measure based model to assess, compare and ranking random outcomes, and propose both online and offline data-driven computational frameworks.

Metastasis is the migration of cancerous cells from a primary tumor to other anatomical sites. Although metastasis was long thought to result from monoclonal seeding, or single cellular migrations, recent phylogenetic analyses of metastatic cancers have reported complex patterns of cellular migrations between sites, including polyclonal migrations and reseeding. However, accurate determination of migration patterns from somatic mutation data is complicated by intratumor heterogeneity and discordance between clonal lineage and cellular migration. We introduce MACHINA, a multi-objective optimization algorithm that jointly infers clonal lineages and parsimonious migration histories of metastatic cancers from DNA sequencing data. MACHINA analysis of data from multiple cancers shows that migration patterns are often not uniquely determined from sequencing data alone and that complicated migration patterns among primary tumors and metastases may be less prevalent than previously reported.

Machine learning (ML) problems are often posed as highly nonlinear and nonconvex unconstrained optimization problems. Methods for solving ML problems based on stochastic gradient descent are easily scaled for very large problems but may involve fine-tuning many hyper-parameters. Quasi-Newton approaches based on the limited-memory Broyden-Fletcher-Goldfarb-Shanno (BFGS) update typically do not require manually tuning hyper-parameters but suffer from approximating a potentially indefinite Hessian with a positive-definite matrix. Hessian-free methods leverage the ability to perform Hessian-vector multiplication without needing the entire Hessian matrix, but each iteration's complexity is significantly greater than quasi-Newton methods. In this paper we propose an alternative approach for solving ML problems based on a quasi-Newton trust-region framework for solving large-scale optimization problems that allow for indefinite Hessian approximations. Numerical experiments on a standard testing data set show that with a fixed computational time budget, the proposed methods achieve better results than the traditional limited-memory BFGS and the Hessian-free methods.