Machine learning models are often required to perform well across several pre-defined settings, such as a set of user groups. Worst-case performance is a common metric to capture this requirement, and is the objective of group distributionally robust optimization (group DRO). Unfortunately, these methods struggle when the loss is non-convex in the parameters, or the model class is non-parametric. Here, we make a classical move to address this: we reparameterize group DRO from parameter space to function space, which results in a number of advantages. First, we show that group DRO over the space of bounded functions admits a minimax theorem. Second, for cross-entropy and mean squared error, we show that the minimax optimal mixture distribution is the solution of a simple convex optimization problem. Thus, provided one is working with a model class of universal function approximators, group DRO can be solved by a convex optimization problem followed by a classical risk minimization problem. We call our method MixMax. In our experi ments, we found that MixMax matched or outperformed the standard group DRO baselines, and in particular, MixMax improved the performance of XGBoost over the only baseline, data balancing, for variations of the ACSIncome and CelebA annotations datasets.
In this paper, we study communication efficient distributed algorithms for distributionally robust federated learning via periodic averaging with adaptive sampling. In contrast to standard empirical risk minimization, due to the minimax structure of the underlying optimization problem, a key difficulty arises from the fact that the global parameter that controls the mixture of local losses can only be updated infrequently on the global stage. To compensate for this, we propose a Distributionally Robust Federated Averaging (DRFA) algorithm that employs a novel snapshotting scheme to approximate…
We propose a novel data-driven method to learn a mixture of multiple kernels with random features that is certifiabaly robust against adverserial inputs. Specifically, we consider a distributionally robust optimization of the kernel-target alignment with respect to the distribution of training samples over a distributional ball defined by the Kullback-Leibler (KL) divergence. The distributionally robust optimization problem can be recast as a min-max optimization whose objective function includes a log-sum term. We develop a mini-batch biased stochastic primal-dual proximal method to solve the…
We present neural mixture distributional regression (NMDR), a holistic framework to estimate complex finite mixtures of distributional regressions defined by flexible additive predictors. Our framework is able to handle a large number of mixtures of potentially different distributions in high-dimensional settings, allows for efficient and scalable optimization and can be applied to recent concepts that combine structured regression models with deep neural networks. While many existing approaches for mixture models address challenges in optimization of such and provide results for convergence u…
Linear Independent Component Analysis via Optimal Transport
University of Tübingen（图宾根大学）；Max Planck Institute for Intelligent Systems, Tübingen（图宾根马克斯·普朗克智能系统研究所）；Institute of Artificial Intelligence TU Braunschweig（布伦瑞克工业大学人工智能研究所）
We show how any PAC learning algorithm that works under the uniform distribution can be transformed, in a blackbox fashion, into one that works under an arbitrary and unknown distribution $\mathcal{D}$. The efficiency of our transformation scales with the inherent complexity of $\mathcal{D}$, running in $\mathrm{poly}(n, (md)^d)$ time for distributions over $\{\pm 1\}^n$ whose pmfs are computed by depth-$d$ decision trees, where $m$ is the sample complexity of the original algorithm. For monotone distributions our transformation uses only samples from $\mathcal{D}$, and for general ones it use…
Samsung AI center（三星人工智能中心）；National Research University Higher School of Economics（国立研究型大学高等经济学院）
The overestimation bias is one of the major impediments to accurate off-policy learning. This paper investigates a novel way to alleviate the overestimation bias in a continuous control setting. Our method---Truncated Quantile Critics, TQC,---blends three ideas: distributional representation of a critic, truncation of critics prediction, and ensembling of multiple critics. Distributional representation and truncation allow for arbitrary granular overestimation control, while ensembling provides additional score improvements. TQC outperforms the current state of the art on all environments from…
Distributional Determinantal Point Process for Repulsive Clustering of Distributions
Department of Statistics and Data Sciences, University of Texas at Austin（统计与数据科学系，德克萨斯大学奥斯汀分校）；Department of Mathematics, University of Texas at Austin（数学系，德克萨斯大学奥斯汀分校）；Department of Biostatistics and Informatics, University of Colorado Anschutz（生物统计学与信息学系，科罗拉多大学安舒茨分校）
Optimal transport (OT) based data analysis is often faced with the issue that the underlying cost function is (partially) unknown. This paper is concerned with the derivation of distributional limits for the empirical OT value when the cost function and the measures are estimated from data. For statistical inference purposes, but also from the viewpoint of a stability analysis, understanding the fluctuation of such quantities is paramount. Our results find direct application in the problem of goodness-of-fit testing for group families, in machine learning applications where invariant transport…
Brown University（布朗大学）；IAS（高等研究院）；Purdue University（普渡大学）
Given a mixture between two populations of coins, "positive" coins that each have -- unknown and potentially different -- bias $\geq\frac{1}{2}+Δ$ and "negative" coins with bias $\leq\frac{1}{2}-Δ$, we consider the task of estimating the fraction $ρ$ of positive coins to within additive error $ε$. We achieve an upper and lower bound of $Θ(\fracρ{ε^2Δ^2}\log\frac{1}δ)$ samples for a $1-δ$ probability of success, where crucially, our lower bound applies to all fully-adaptive algorithms. Thus, our sample complexity bounds have tight dependence for every relevant problem parameter. A crucial compo…
FDR-SVM: A Federated Distributionally Robust Support Vector Machine via a Mixture of Wasserstein Balls Ambiguity Set
H. Milton Stewart School of Industrial and Systems Engineering（H. Milton Stewart工业与系统工程学院）；Georgia Institute of Technology（佐治亚理工学院）；Department of Electrical Engineering（电气工程系）；University of Chile（智利大学）
National Tsing Hua University（台湾清华大学）；NVIDIA Corporation（英伟达公司）
In fully cooperative multi-agent reinforcement learning (MARL) settings, the environments are highly stochastic due to the partial observability of each agent and the continuously changing policies of the other agents. To address the above issues, we integrate distributional RL and value function factorization methods by proposing a Distributional Value Function Factorization (DFAC) framework to generalize expected value function factorization methods to their DFAC variants. DFAC extends the individual utility functions from deterministic variables to random variables, and models the quantile …
This manuscript investigates unconditional and conditional-on-stopping maximum likelihood estimators (MLEs), information measures and information loss associated with conditioning in group sequential designs (GSDs). The possibility of early stopping brings truncation to the distributional form of MLEs; sequentially, GSD decisions eliminate some events from the sample space. Multiple testing induces mixtures on the adapted sample space. Distributions of MLEs are mixtures of truncated distributions. Test statistics that are asymptotically normal without GSD, have asymptotic distributions, under …
Actor-critic algorithms that make use of distributional policy evaluation have frequently been shown to outperform their non-distributional counterparts on many challenging control tasks. Examples of this behavior include the D4PG and DMPO algorithms as compared to DDPG and MPO, respectively [Barth-Maron et al., 2018; Hoffman et al., 2020]. However, both agents rely on the C51 critic for value estimation.One major drawback of the C51 approach is its requirement of prior knowledge about the minimum andmaximum values a policy can attain as well as the number of bins used, which fixes the resolut…
Carnegie Mellon University（卡内基梅隆大学）；Columbia University（哥伦比亚大学）；University of Illinois Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）
One key challenge for multi-task Reinforcement learning (RL) in practice is the absence of task indicators. Robust RL has been applied to deal with task ambiguity, but may result in over-conservative policies. To balance the worst-case (robustness) and average performance, we propose Group Distributionally Robust Markov Decision Process (GDR-MDP), a flexible hierarchical MDP formulation that encodes task groups via a latent mixture model. GDR-MDP identifies the optimal policy that maximizes the expected return under the worst-possible qualified belief over task groups within an ambiguity set. …
One of the major shortcomings of variational autoencoders is the inability to produce generations from the individual modalities of data originating from mixture distributions. This is primarily due to the use of a simple isotropic Gaussian as the prior for the latent code in the ancestral sampling procedure for the data generations. We propose a novel formulation of variational autoencoders, conditional prior VAE (CP-VAE), which learns to differentiate between the individual mixture components and therefore allows for generations from the distributional data clusters. We assume a two-level ge…
University of Science and Technology of China（中国科学技术大学）；Huawei Cloud（华为云）
In cooperative multi-agent tasks, a team of agents jointly interact with an environment by taking actions, receiving a team reward and observing the next state. During the interactions, the uncertainty of environment and reward will inevitably induce stochasticity in the long-term returns and the randomness can be exacerbated with the increasing number of agents. However, such randomness is ignored by most of the existing value-based multi-agent reinforcement learning (MARL) methods, which only model the expectation of Q-value for both individual agents and the team. Compared to using the expe…
Machine Learning Research, Morgan Stanley, New York, NY（机器学习研究部，摩根士丹利，纽约，纽约）；School of Electrical and Computer Engineering, Cornell University, Ithaca, NY（电气与计算机工程学院，康奈尔大学，伊萨卡，纽约）
Recently proposed adversarial training methods show the robustness to both adversarial and original examples and achieve state-of-the-art results in supervised and semi-supervised learning. All the existing adversarial training methods consider only how the worst perturbed examples (i.e., adversarial examples) could affect the model output. Despite their success, we argue that such setting may be in lack of generalization, since the output space (or label space) is apparently less informative.In this paper, we propose a novel method, called Manifold Adversarial Training (MAT). MAT manages to b…
Sorbonne Université, LPSM Paris, France（索邦大学，巴黎LPSM分校，法国）；EPFL, Institute of Mathematics Lausanne, Switzerland（苏黎世联邦理工学院，数学研究所，瑞士）；Laboratoire de Mathématiques d’Orsay Université Paris Saclay（奥赛数学实验室，巴黎萨克雷大学）；Institut Universitaire de France（法国国家科学研究中心）
This paper focuses on stochastic saddle point problems with decision-dependent distributions. These are problems whose objective is the expected value of a stochastic payoff function and whose data distribution drifts in response to decision variables--a phenomenon represented by a distributional map. A common approach to accommodating distributional shift is to retrain optimal decisions once a new distribution is revealed, or repeated retraining. We introduce the notion of equilibrium points, which are the fixed points of this repeated retraining procedure, and provide sufficient conditions f…
Certified Robustness from Approximate Gaussian Mixture Structures in Pretrained Latent Spaces
CS & MINDS Johns Hopkins University（计算机科学与MINDS约翰霍普金斯大学）；CIS University of Pennsylvania（计算机与信息科学宾夕法尼亚大学）；AMS & MINDS Johns Hopkins University（人工智能与机器学习系约翰霍普金斯大学）；ESE, Radiology & IDEAS University of Pennsylvania（工程科学与放射学系及IDEAS宾夕法尼亚大学）
RoME: Domain-Robust Mixture-of-Experts for MILP Solution Prediction across Domains
Laboratory for Big Data and Decision, College of Systems Engineering, National University of Defense Technology（大数据与决策实验室，系统工程学院，国防科技大学）；MoE Key Laboratory of Brain-inspired Intelligent Perception and Cognition, University of Science and Technology of China（脑启发智能感知与认知关键实验室，中国科学技术大学）；College of Computer Science and Technology, National University of Defense Technology（计算机科学与技术学院，国防科技大学）
