We study methods for estimating model uncertainty for neural networks (NNs) in regression. To isolate the effect of model uncertainty, we focus on a noiseless setting with scarce training data. We introduce five important desiderata regarding model uncertainty that any method should satisfy. However, we find that established benchmarks often fail to reliably capture some of these desiderata, even those that are required by Bayesian theory. To address this, we introduce a new approach for capturing model uncertainty for NNs, which we call Neural Optimization-based Model Uncertainty (NOMU). The main idea of NOMU is to design a network architecture consisting of two connected sub-NNs, one for model prediction and one for model uncertainty, and to train it using a carefully-designed loss function. Importantly, our design enforces that NOMU satisfies our five desiderata. Due to its modular architecture, NOMU can provide model uncertainty for any given (previously trained) NN if given access to its training data. We evaluate NOMU in various regressions tasks and noiseless Bayesian optimization (BO) with costly evaluations. In regression, NOMU performs at least as well as state-of-the-art methods. In BO, NOMU even outperforms all considered benchmarks.
Bayesian optimization is a popular tool for data-efficient optimization of expensive objective functions. In real-life applications like engineering design, the designer often wants to take multiple objectives as well as input uncertainty into account to find a set of robust solutions. While this is an active topic in single-objective Bayesian optimization, it is less investigated in the multi-objective case. We introduce a novel Bayesian optimization framework to efficiently perform multi-objective optimization considering input uncertainty. We propose a robust Gaussian Process model to infer…
Our goal is to build robust optimization problems for making decisions based on complex data from the past. In robust optimization (RO) generally, the goal is to create a policy for decision-making that is robust to our uncertainty about the future. In particular, we want our policy to best handle the the worst possible situation that could arise, out of an uncertainty set of possible situations. Classically, the uncertainty set is simply chosen by the user, or it might be estimated in overly simplistic ways with strong assumptions; whereas in this work, we learn the uncertainty set from data …
We consider the problem of constrained multi-objective (MO) blackbox optimization using expensive function evaluations, where the goal is to approximate the true Pareto set of solutions satisfying a set of constraints while minimizing the number of function evaluations. We propose a novel framework named Uncertainty-aware Search framework for Multi-Objective Optimization with Constraints (USeMOC) to efficiently select the sequence of inputs for evaluation to solve this problem. The selection method of USeMOC consists of solving a cheap constrained MO optimization problem via surrogate models o…
We consider the problem of multi-objective (MO) blackbox optimization using expensive function evaluations, where the goal is to approximate the true Pareto set of solutions while minimizing the number of function evaluations. For example, in hardware design optimization, we need to find the designs that trade-off performance, energy, and area overhead using expensive simulations. We propose a novel uncertainty-aware search framework referred to as USeMO to efficiently select the sequence of inputs for evaluation to solve this problem. The selection method of USeMO consists of solving a cheap …
Nagoya Institute of Technology（名古屋工业大学）；RIKEN Center for Advanced Intelligence Project（理化学研究所革新智能综合研究中心）
We consider active learning (AL) in an uncertain environment in which trade-off between multiple risk measures need to be considered. As an AL problem in such an uncertain environment, we study Mean-Variance Analysis in Bayesian Optimization (MVA-BO) setting. Mean-variance analysis was developed in the field of financial engineering and has been used to make decisions that take into account the trade-off between the average and variance of investment uncertainty. In this paper, we specifically focus on BO setting with an uncertain component and consider multi-task, multi-objective, and constra…
Sequential model-based optimization sequentially selects a candidate point by constructing a surrogate model with the history of evaluations, to solve a black-box optimization problem. Gaussian process (GP) regression is a popular choice as a surrogate model, because of its capability of calculating prediction uncertainty analytically. On the other hand, an ensemble of randomized trees is another option and has practical merits over GPs due to its scalability and easiness of handling continuous/discrete mixed variables. In this paper we revisit various ensembles of randomized trees to investig…
Particle swarm optimization for online sparse streaming feature selection under uncertainty
Chongqing University of Posts and Telecommunications（重庆邮电大学）；Chongqing Institute of Green and Intelligent Technology, Chinese Academy of Sciences（中国科学院重庆绿色智能技术研究院）
Optimization of expensive computer models with the help of Gaussian process emulators in now commonplace. However, when several (competing) objectives are considered, choosing an appropriate sampling strategy remains an open question. We present here a new algorithm based on stepwise uncertainty reduction principles to address this issue. Optimization is seen as a sequential reduction of the volume of the excursion sets below the current best solutions, and our sampling strategy chooses the points that give the highest expected reduction. Closed-form formulae are provided to compute the sampli…
Optimizing management practices and selecting the best cultivar for planting play a significant role in increasing agricultural food production and decreasing environmental footprint. In this study, we develop optimization frameworks under uncertainty using conditional value-at-risk in the stochastic programming objective function. We integrate the crop model, APSIM, and a parallel Bayesian optimization algorithm to optimize the management practices and select the best cultivar at different levels of risk aversion. This approach integrates the power of optimization in determining the best deci…
The problem of establishing out-of-sample bounds for the values of an unkonwn ground-truth function is considered. Kernels and their associated Hilbert spaces are the main formalism employed herein along with an observational model where outputs are corrupted by bounded measurement noise. The noise can originate from any compactly supported distribution and no independence assumptions are made on the available data. In this setting, we show how computing tight, finite-sample uncertainty bounds amounts to solving parametric quadratically constrained linear programs. Next, properties of our appr…
We propose a Bayesian uncertainty quantification method for large-scale imaging inverse problems. Our method applies to all Bayesian models that are log-concave, where maximum-a-posteriori (MAP) estimation is a convex optimization problem. The method is a framework to analyse the confidence in specific structures observed in MAP estimates (e.g., lesions in medical imaging, celestial sources in astronomical imaging), to enable using them as evidence to inform decisions and conclusions. Precisely, following Bayesian decision theory, we seek to assert the structures under scrutiny by performing a…
In order for reinforcement learning techniques to be useful in real-world decision making processes, they must be able to produce robust performance from limited data. Deep policy optimization methods have achieved impressive results on complex tasks, but their real-world adoption remains limited because they often require significant amounts of data to succeed. When combined with small sample sizes, these methods can result in unstable learning due to their reliance on high-dimensional sample-based estimates. In this work, we develop techniques to control the uncertainty introduced by these e…
University of Science and Technology of China（中国科学技术大学）
Model-based reinforcement learning algorithms tend to achieve higher sample efficiency than model-free methods. However, due to the inevitable errors of learned models, model-based methods struggle to achieve the same asymptotic performance as model-free methods. In this paper, We propose a Policy Optimization method with Model-Based Uncertainty (POMBU)---a novel model-based approach---that can effectively improve the asymptotic performance using the uncertainty in Q-values. We derive an upper bound of the uncertainty, based on which we can approximate the uncertainty accurately and efficientl…
Virginia Tech（弗吉尼亚理工大学）；University of Oslo（奥斯陆大学）；DEVCOM Army Research Laboratory（DEVCOM陆军研究实验室）；University of Texas at Dallas（德克萨斯大学达拉斯分校）；University of the District of Columbia（哥伦比亚特区大学）
Proximal Policy Optimization (PPO) is a highly popular policy-based deep reinforcement learning (DRL) approach. However, we observe that the homogeneous exploration process in PPO could cause an unexpected stability issue in the training phase. To address this issue, we propose PPO-UE, a PPO variant equipped with self-adaptive uncertainty-aware explorations (UEs) based on a ratio uncertainty level. The proposed PPO-UE is designed to improve convergence speed and performance with an optimized ratio uncertainty level. Through extensive sensitivity analysis by varying the ratio uncertainty level,…
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 publ…
The performance of any Machine Learning (ML) algorithm is impacted by the choice of its hyperparameters. As training and evaluating a ML algorithm is usually expensive, the hyperparameter optimization (HPO) method needs to be computationally efficient to be useful in practice. Most of the existing approaches on multi-objective HPO use evolutionary strategies and metamodel-based optimization. However, few methods have been developed to account for uncertainty in the performance measurements. This paper presents results on multi-objective hyperparameter optimization with uncertainty on the evalu…
University of Oxford（牛津大学）；University of Cambridge（剑桥大学）
Optimization in the latent space of variational autoencoders is a promising approach to generate high-dimensional discrete objects that maximize an expensive black-box property (e.g., drug-likeness in molecular generation, function approximation with arithmetic expressions). However, existing methods lack robustness as they may decide to explore areas of the latent space for which no data was available during training and where the decoder can be unreliable, leading to the generation of unrealistic or invalid objects. We propose to leverage the epistemic uncertainty of the decoder to guide the…
In many contemporary applications such as healthcare, finance, robotics, and recommendation systems, continuous deployment of new policies for data collection and online learning is either cost ineffective or impractical. We consider a setting that lies between pure offline reinforcement learning (RL) and pure online RL called deployment constrained RL in which the number of policy deployments for data sampling is limited. To solve this challenging task, we propose a new algorithmic learning framework called Model-based Uncertainty regularized and Sample Efficient Batch Optimization (MUSBO). O…
Model based predictions of future trajectories of a dynamical system often suffer from inaccuracies, forcing model based control algorithms to re-plan often, thus being computationally expensive, suboptimal and not reliable. In this work, we propose a model agnostic method for estimating the uncertainty of a model?s predictions based on reconstruction error, using it in control and exploration. As our experiments show, this uncertainty estimation can be used to improve control performance on a wide variety of environments by choosing predictions of which the model is confident. It can also be …
Obtaining reliable and accurate quantification of uncertainty estimates from deep neural networks is important in safety-critical applications. A well-calibrated model should be accurate when it is certain about its prediction and indicate high uncertainty when it is likely to be inaccurate. Uncertainty calibration is a challenging problem as there is no ground truth available for uncertainty estimates. We propose an optimization method that leverages the relationship between accuracy and uncertainty as an anchor for uncertainty calibration. We introduce a differentiable accuracy versus uncert…
University at Buffalo（布法罗大学）；Penn State Erie（宾夕法尼亚州立大学伊利分校）
Deep Neural Networks (DNNs), despite their tremendous success in recent years, could still cast doubts on their predictions due to the intrinsic uncertainty associated with their learning process. Ensemble techniques and post-hoc calibrations are two types of approaches that have individually shown promise in improving the uncertainty calibration of DNNs. However, the synergistic effect of the two types of methods has not been well explored. In this paper, we propose a truth discovery framework to integrate ensemble-based and post-hoc calibration methods. Using the geometric variance of the en…
We investigate a data-driven approach to constructing uncertainty sets for robust optimization problems, where the uncertain problem parameters are modeled as random variables whose joint probability distribution is not known. Relying only on independent samples drawn from this distribution, we provide a nonparametric method to estimate uncertainty sets whose probability mass is guaranteed to approximate a given target mass within a given tolerance with high confidence. The nonparametric estimators that we consider are also shown to obey distribution-free finite-sample performance bounds that …
VNU University of Engineering and Technology（越南国立大学工程技术大学）；Microsoft Research（微软研究院）
Model-based reinforcement learning has the potential to be more sample efficient than model-free approaches. However, existing model-based methods are vulnerable to model bias, which leads to poor generalization and asymptotic performance compared to model-free counterparts. In addition, they are typically based on the model predictive control (MPC) framework, which not only is computationally inefficient at decision time but also does not enable policy transfer due to the lack of an explicit policy representation. In this paper, we propose a novel uncertainty-aware model-based policy optimiza…
Reliable uncertainty quantification in deep neural networks is very crucial in safety-critical applications such as automated driving for trustworthy and informed decision-making. Assessing the quality of uncertainty estimates is challenging as ground truth for uncertainty estimates is not available. Ideally, in a well-calibrated model, uncertainty estimates should perfectly correlate with model error. We propose a novel error aligned uncertainty optimization method and introduce a trainable loss function to guide the models to yield good quality uncertainty estimates aligning with the model e…
ETH Zürich（苏黎世联邦理工学院）；University of Konstanz（康斯坦茨大学）；ETH AI Center（苏黎世联邦理工学院人工智能中心）
While deep reinforcement learning (RL) agents have showcased strong results across many domains, a major concern is their inherent opaqueness and the safety of such systems in real-world use cases. To overcome these issues, we need agents that can quantify their uncertainty and detect out-of-distribution (OOD) states. Existing uncertainty estimation techniques, like Monte-Carlo Dropout or Deep Ensembles, have not seen widespread adoption in on-policy deep RL. We posit that this is due to two reasons: concepts like uncertainty and OOD states are not well defined compared to supervised learning,…
Paul G. Allen School of Computer Science & Engineering（保罗·G·艾伦计算机科学与工程学院）；University of Washington（华盛顿大学）
Addressing uncertainty is critical for autonomous systems to robustly adapt to the real world. We formulate the problem of model uncertainty as a continuous Bayes-Adaptive Markov Decision Process (BAMDP), where an agent maintains a posterior distribution over latent model parameters given a history of observations and maximizes its expected long-term reward with respect to this belief distribution. Our algorithm, Bayesian Policy Optimization, builds on recent policy optimization algorithms to learn a universal policy that navigates the exploration-exploitation trade-off to maximize the Bayesia…
University College London（伦敦大学学院）；Universidad Nacional Autónoma de México（墨西哥国立自治大学）；Norwegian University of Science and Technology（挪威科技大学）；The University of Manchester（曼彻斯特大学）；Imperial College London（帝国理工学院）
Dynamic real-time optimization (DRTO) is a challenging task due to the fact that optimal operating conditions must be computed in real time. The main bottleneck in the industrial application of DRTO is the presence of uncertainty. Many stochastic systems present the following obstacles: 1) plant-model mismatch, 2) process disturbances, 3) risks in violation of process constraints. To accommodate these difficulties, we present a constrained reinforcement learning (RL) based approach. RL naturally handles the process uncertainty by computing an optimal feedback policy. However, no state constrai…
Robust portfolio optimization for recommender systems considering uncertainty of estimated statistics
Graduate School of Science and Technology, University of Tsukuba（筑波大学科学技术研究科）；Institute of Systems and Information Engineering, University of Tsukuba（筑波大学系统与信息工程研究所）
Lancaster University（兰卡斯特大学）；University of Siegen（锡根大学）
In robust optimization, the uncertainty set is used to model all possible outcomes of uncertain parameters. In the classic setting, one assumes that this set is provided by the decision maker based on the data available to her. Only recently it has been recognized that the process of building useful uncertainty sets is in itself a challenging task that requires mathematical support. In this paper, we propose an approach to go beyond the classic setting, by assuming multiple uncertainty sets to be prepared, each with a weight showing the degree of belief that the set is a "true" model of uncert…
Multi-level informed optimization via decomposed Kriging for large design problems under uncertainty
Reliability and Risk Engineering Laboratory, Institute of Energy and Process Engineering, Department of Mechanical and Process Engineering, ETH Zurich（可靠性与风险工程实验室，能源与过程工程研究所，机械与过程工程系，苏黎世联邦理工学院）
Robust optimization has been established as a leading methodology to approach decision problems under uncertainty. To derive a robust optimization model, a central ingredient is to identify a suitable model for uncertainty, which is called the uncertainty set. An ongoing challenge in the recent literature is to derive uncertainty sets from given historical data that result in solutions that are robust regarding future scenarios. In this paper we use an unsupervised deep learning method to learn and extract hidden structures from data, leading to non-convex uncertainty sets and better robust so…
Iowa State University（爱荷华州立大学）；The Hong Kong Polytechnic University（香港理工大学）；Swiss Federal Institute of Technology Lausanne（洛桑联邦理工学院）；National Institute of Standards and Technology（美国国家标准与技术研究院）；GE Research（通用电气研究中心）；Seoul National University（首尔国立大学）；University of California, San Diego（加州大学圣地亚哥分校）；Vanderbilt University（范德堡大学）
As an emerging technology in the era of Industry 4.0, digital twin is gaining unprecedented attention because of its promise to further optimize process design, quality control, health monitoring, decision and policy making, and more, by comprehensively modeling the physical world as a group of interconnected digital models. In a two-part series of papers, we examine the fundamental role of different modeling techniques, twinning enabling technologies, and uncertainty quantification and optimization methods commonly used in digital twins. This second paper presents a literature review of key e…
