We consider robust optimization problems, where the goal is to optimize an unknown objective function against the worst-case realization of an uncertain parameter. For this setting, we design a novel sample-efficient algorithm GP-MRO, which sequentially learns about the unknown objective from noisy point evaluations. GP-MRO seeks to discover a robust and randomized mixed strategy, that maximizes the worst-case expected objective value. To achieve this, it combines techniques from online learning with nonparametric confidence bounds from Gaussian processes. Our theoretical results characterize the number of samples required by GP-MRO to discover a robust near-optimal mixed strategy for different GP kernels of interest. We experimentally demonstrate the performance of our algorithm on synthetic datasets and on human-assisted trajectory planning tasks for autonomous vehicles. In our simulations, we show that robust deterministic strategies can be overly conservative, while the mixed strategies found by GP-MRO significantly improve the overall performance.
We consider the problem of mixed linear regression (MLR), where each observed sample belongs to one of $K$ unknown linear models. In practical applications, the proportions of the $K$ components are often imbalanced. Unfortunately, most MLR methods do not perform well in such settings. Motivated by this practical challenge, in this work we propose Mix-IRLS, a novel, simple and fast algorithm for MLR with excellent performance on both balanced and imbalanced mixtures. In contrast to popular approaches that recover the $K$ models simultaneously, Mix-IRLS does it sequentially using tools from rob…
This paper studies the high-dimensional mixed linear regression (MLR) where the output variable comes from one of the two linear regression models with an unknown mixing proportion and an unknown covariance structure of the random covariates. Building upon a high-dimensional EM algorithm, we propose an iterative procedure for estimating the two regression vectors and establish their rates of convergence. Based on the iterative estimators, we further construct debiased estimators and establish their asymptotic normality. For individual coordinates, confidence intervals centered at the debiased …
We present new results for consistency of maximum likelihood estimators with a focus on multivariate mixed models. Our theory builds on the idea of using subsets of the full data to establish consistency of estimators based on the full data. It requires neither that the data consist of independent observations, nor that the observations can be modeled as a stationary stochastic process. Compared to existing asymptotic theory using the idea of subsets we substantially weaken the assumptions, bringing them closer to what suffices in classical settings. We apply our theory in two multivariate mix…
Modeling of longitudinal data often requires diffusion models that incorporate overall time-dependent, nonlinear dynamics of multiple components and provide sufficient flexibility for subject-specific modeling. This complexity challenges parameter inference and approximations are inevitable. We propose a method for approximate maximum-likelihood parameter estimation in multivariate time-inhomogeneous diffusions, where subject-specific flexibility is accounted for by incorporation of multidimensional mixed effects and covariates. We consider $N$ multidimensional independent diffusions $X^i = (X…
The University of Hong Kong（香港大学）；Nanjing University（南京大学）
Popular crowdsourcing techniques mostly focus on evaluating workers' labeling quality before adjusting their weights during label aggregation. Recently, another cohort of models regard crowdsourced annotations as incomplete tensors and recover unfilled labels by tensor completion. However, mixed strategies of the two methodologies have never been comprehensively investigated, leaving them as rather independent approaches. In this work, we propose $\textit{MiSC}$ ($\textbf{Mi}$xed $\textbf{S}$trategies $\textbf{C}$rowdsourcing), a versatile framework integrating arbitrary conventional crowdsour…
Development of Hybrid Artificial Intelligence Training on Real and Synthetic Data: Benchmark on Two Mixed Training Strategies
Faculty of Engineering and Computer Science（工程与计算机科学学院）；Osnabrück University of Applied Sciences（奥斯纳布鲁克应用科学大学）；Institute of Cognitive Science（认知科学研究所）；Osnabrück University（奥斯纳布鲁克大学）
Spurious credit card transactions are a significant source of financial losses and urge the development of accurate fraud detection algorithms. In this paper, we use machine learning strategies for such an aim. First, we apply a mixed learning technique that uses K-means preprocessing before trained classification to the problem at hand. Next, we introduce an adapted detector ensemble technique that uses OR-logic algorithm aggregation to enhance the detection rate. Then, both strategies are deployed in tandem in numerical simulations using real-world transactions data. We observed from simulat…
Imperial College London（帝国理工学院）；KTH Royal Institute of Technology（瑞典皇家理工学院）
This paper introduces a class of mixed-integer formulations for trained ReLU neural networks. The approach balances model size and tightness by partitioning node inputs into a number of groups and forming the convex hull over the partitions via disjunctive programming. At one extreme, one partition per input recovers the convex hull of a node, i.e., the tightest possible formulation for each node. For fewer partitions, we develop smaller relaxations that approximate the convex hull, and show that they outperform existing formulations. Specifically, we propose strategies for partitioning variab…
Solver-Guided Reasoning for Mixed-Equilibrium Strategies
Shanghai Jiao Tong University（上海交通大学）；GTO Wizard；Tsinghua University（清华大学）；The Chinese University of Hong Kong, Shenzhen（香港中文大学（深圳））；Vector Institute（向量研究所）
In this work we focus on improving the efficiency and generalisation of learned navigation strategies when transferred from its training environment to previously unseen ones. We present an extension of the residual reinforcement learning framework from the robotic manipulation literature and adapt it to the vast and unstructured environments that mobile robots can operate in. The concept is based on learning a residual control effect to add to a typical sub-optimal classical controller in order to close the performance gap, whilst guiding the exploration process during training for improved d…
Models notoriously suffer from dataset biases which are detrimental to robustness and generalization. The identify-emphasize paradigm shows a promising effect in dealing with unknown biases. However, we find that it is still plagued by two challenges: A, the quality of the identified bias-conflicting samples is far from satisfactory; B, the emphasizing strategies just yield suboptimal performance. In this work, for challenge A, we propose an effective bias-conflicting scoring method to boost the identification accuracy with two practical strategies -- peer-picking and epoch-ensemble. For chall…
Generalization Performance of Deep Learning models trained using Empirical Risk Minimization can be improved significantly by using Data Augmentation strategies such as simple transformations, or using Mixed Samples. We attempt to empirically analyze the impact of such strategies on the transfer of generalization between teacher and student models in a distillation setup. We observe that if a teacher is trained using any of the mixed sample augmentation strategies, such as MixUp or CutMix, the student model distilled from it is impaired in its generalization capabilities. We hypothesize that s…
University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）
Markovian jump linear systems (MJLS) are an important class of dynamical systems that arise in many control applications. In this paper, we introduce the problem of controlling unknown (discrete-time) MJLS as a new benchmark for policy-based reinforcement learning of Markov decision processes (MDPs) with mixed continuous/discrete state variables. Compared with the traditional linear quadratic regulator (LQR), our proposed problem leads to a special hybrid MDP (with mixed continuous and discrete variables) and poses significant new challenges due to the appearance of an underlying Markov jump p…
