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Register a new userOptimization under Uncertainty in the Era of Big Data and Deep Learning: When Machine Learning Meets Mathematical Programming
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Added by
Fengqi You
Publication date
2019
fields
Informatics Engineering
and research's language is
English
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This paper reviews recent advances in the field of optimization under uncertainty via a modern data lens, highlights key research challenges and promise of data-driven optimization that organically integrates machine learning and mathematical programming for decision-making under uncertainty, and identifies potential research opportunities. A brief review of classical mathematical programming techniques for hedging against uncertainty is first presented, along with their wide spectrum of applications in Process Systems Engineering. A comprehensive review and classification of the relevant publications on data-driven distributionally robust optimization, data-driven chance constrained program, data-driven robust optimization, and data-driven scenario-based optimization is then presented. This paper also identifies fertile avenues for future research that focuses on a closed-loop data-driven optimization framework, which allows the feedback from mathematical programming to machine learning, as well as scenario-based optimization leveraging the power of deep learning techniques. Perspectives on online learning-based data-driven multistage optimization with a learning-while-optimizing scheme is presented.
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A novel data-driven stochastic robust optimization (DDSRO) framework is proposed for optimization under uncertainty leveraging labeled multi-class uncertainty data. Uncertainty data in large datasets are often collected from various conditions, which are encoded by class labels. Machine learning methods including Dirichlet process mixture model and maximum likelihood estimation are employed for uncertainty modeling. A DDSRO framework is further proposed based on the data-driven uncertainty model through a bi-level optimization structure. The outer optimization problem follows a two-stage stochastic programming approach to optimize the expected objective across different data classes; adaptive robust optimization is nested as the inner problem to ensure the robustness of the solution while maintaining computational tractability. A decomposition-based algorithm is further developed to solve the resulting multi-level optimization problem efficiently. Case studies on process network design and planning are presented to demonstrate the applicability of the proposed framework and algorithm.
Bilevel optimization has become a powerful framework in various machine learning applications including meta-learning, hyperparameter optimization, and network architecture search. There are generally two classes of bilevel optimization formulations for machine learning: 1) problem-based bilevel optimization, whose inner-level problem is formulated as finding a minimizer of a given loss function; and 2) algorithm-based bilevel optimization, whose inner-level solution is an output of a fixed algorithm. For the first class, two popular types of gradient-based algorithms have been proposed for hypergradient estimation via approximate implicit differentiation (AID) and iterative differentiation (ITD). Algorithms for the second class include the popular model-agnostic meta-learning (MAML) and almost no inner loop (ANIL). However, the convergence rate and fundamental limitations of bilevel optimization algorithms have not been well explored. This thesis provides a comprehensive convergence rate analysis for bilevel algorithms in the aforementioned two classes. We further propose principled algorithm designs for bilevel optimization with higher efficiency and scalability. For the problem-based formulation, we provide a convergence rate analysis for AID- and ITD-based bilevel algorithms. We then develop acceleration bilevel algorithms, for which we provide shaper convergence analysis with relaxed assumptions. We also provide the first lower bounds for bilevel optimization, and establish the optimality by providing matching upper bounds under certain conditions. We finally propose new stochastic bilevel optimization algorithms with lower complexity and higher efficiency in practice. For the algorithm-based formulation, we develop a theoretical convergence for general multi-step MAML and ANIL, and characterize the impact of parameter selections and loss geometries on the their complexities.
Optimization in machine learning, both theoretical and applied, is presently dominated by first-order gradient methods such as stochastic gradient descent. Second-order optimization methods, that involve second derivatives and/or second order statistics of the data, are far less prevalent despite strong theoretical properties, due to their prohibitive computation, memory and communication costs. In an attempt to bridge this gap between theoretical and practical optimization, we present a scalable implementation of a second-order preconditioned method (concretely, a variant of full-matrix Adagrad), that along with several critical algorithmic and numerical improvements, provides significant convergence and wall-clock time improvements compared to conventional first-order methods on state-of-the-art deep models. Our novel design effectively utilizes the prevalent heterogeneous hardware architecture for training deep models, consisting of a multicore CPU coupled with multiple accelerator units. We demonstrate superior performance compared to state-of-the-art on very large learning tasks such as machine translation with Transformers, language modeling with BERT, click-through rate prediction on Criteo, and image classification on ImageNet with ResNet-50.
We present SmartChoices, an approach to making machine learning (ML) a first class citizen in programming languages which we see as one way to lower the entrance cost to applying ML to problems in new domains. There is a growing divide in approaches to building systems: on the one hand, programming leverages human experts to define a system while on the other hand behavior is learned from data in machine learning. We propose to hybridize these two by providing a 3-call API which we expose through an object called SmartChoice. We describe the SmartChoices-interface, how it can be used in programming with minimal code changes, and demonstrate that it is an easy to use but still powerful tool by demonstrating improvements over not using ML at all on three algorithmic problems: binary search, QuickSort, and caches. In these three examples, we replace the commonly used heuristics with an ML model entirely encapsulated within a SmartChoice and thus requiring minimal code changes. As opposed to previous work applying ML to algorithmic problems, our proposed approach does not require to drop existing implementations but seamlessly integrates into the standard software development workflow and gives full control to the software developer over how ML methods are applied. Our implementation relies on standard Reinforcement Learning (RL) methods. To learn faster, we use the heuristic function, which they are replacing, as an initial function. We show how this initial function can be used to speed up and stabilize learning while providing a safety net that prevents performance to become substantially worse -- allowing for a safe deployment in critical applications in real life.
Labeling training datasets has become a key barrier to building medical machine learning models. One strategy is to generate training labels programmatically, for example by applying natural language processing pipelines to text reports associated with imaging studies. We propose cross-modal data programming, which generalizes this intuitive strategy in a theoretically-grounded way that enables simpler, clinician-driven input, reduces required labeling time, and improves with additional unlabeled data. In this approach, clinicians generate training labels for models defined over a target modality (e.g. images or time series) by writing rules over an auxiliary modality (e.g. text reports). The resulting technical challenge consists of estimating the accuracies and correlations of these rules; we extend a recent unsupervised generative modeling technique to handle this cross-modal setting in a provably consistent way. Across four applications in radiography, computed tomography, and electroencephalography, and using only several hours of clinician time, our approach matches or exceeds the efficacy of physician-months of hand-labeling with statistical significance, demonstrating a fundamentally faster and more flexible way of building machine learning models in medicine.
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