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We construct a Wasserstein gradient flow of the maximum mean discrepancy (MMD) and study its convergence properties. The MMD is an integral probability metric defined for a reproducing kernel Hilbert space (RKHS), and serves as a metric on…

Machine Learning · Statistics 2019-12-04 Michael Arbel , Anna Korba , Adil Salim , Arthur Gretton

In recent years, $Q$-learning has become indispensable for model-free reinforcement learning (MFRL). However, it suffers from well-known problems such as under- and overestimation bias of the value, which may adversely affect the policy…

Machine Learning · Computer Science 2021-02-09 Youngmin Oh , Jinwoo Shin , Eunho Yang , Sung Ju Hwang

Although distributional reinforcement learning (DRL) has been widely examined in the past few years, very few studies investigate the validity of the obtained Q-function estimator in the distributional setting. To fully understand how the…

Machine Learning · Computer Science 2023-08-01 Qi Kuang , Zhoufan Zhu , Liwen Zhang , Fan Zhou

Score-based and flow-based generative models exhibit remarkable expressive capacity in capturing complex distributions, and have been extensively deployed in tasks ranging from image generation to reinforcement learning. Nevertheless, these…

Machine Learning · Computer Science 2026-05-29 Yiyan , Liang , Sifei Liu , Weitong Zhang

Likelihood-free inference methods typically make use of a distance between simulated and real data. A common example is the maximum mean discrepancy (MMD), which has previously been used for approximate Bayesian computation, minimum…

Methodology · Statistics 2023-05-11 Ayush Bharti , Masha Naslidnyk , Oscar Key , Samuel Kaski , François-Xavier Briol

The exploration-exploitation dilemma has been a central challenge in reinforcement learning (RL) with complex model classes. In this paper, we propose a new algorithm, Monotonic Q-Learning with Upper Confidence Bound (MQL-UCB) for RL with…

Machine Learning · Computer Science 2025-10-06 Heyang Zhao , Jiafan He , Quanquan Gu

We introduce a (de)-regularization of the Maximum Mean Discrepancy (DrMMD) and its Wasserstein gradient flow. Existing gradient flows that transport samples from source distribution to target distribution with only target samples, either…

This paper is motivated by addressing open questions in distributionally robust chance-constrained programs (DRCCP) using the popular Wasserstein ambiguity sets. Specifically, the computational techniques for those programs typically place…

Optimization and Control · Mathematics 2022-04-26 Yassine Nemmour , Heiner Kremer , Bernhard Schölkopf , Jia-Jie Zhu

We investigate the training and performance of generative adversarial networks using the Maximum Mean Discrepancy (MMD) as critic, termed MMD GANs. As our main theoretical contribution, we clarify the situation with bias in GAN loss…

Machine Learning · Statistics 2021-01-15 Mikołaj Bińkowski , Danica J. Sutherland , Michael Arbel , Arthur Gretton

Off-policy, value-based reinforcement learning methods such as Q-learning are appealing because they can learn from arbitrary experience, including data collected by older policies or other agents. In practice, however, bootstrapping makes…

Artificial Intelligence · Computer Science 2026-05-12 Armaan A. Abraham , Lucy Xiaoyang Shi , Chelsea Finn

There has been an increasing surge of interest on development of advanced Reinforcement Learning (RL) systems as intelligent approaches to learn optimal control policies directly from smart agents' interactions with the environment.…

Machine Learning · Computer Science 2020-06-02 Parvin Malekzadeh , Mohammad Salimibeni , Arash Mohammadi , Akbar Assa , Konstantinos N. Plataniotis

Comparing probability distributions is at the crux of many machine learning algorithms. Maximum Mean Discrepancies (MMD) and Wasserstein distances are two classes of distances between probability distributions that have attracted abundant…

Machine Learning · Statistics 2023-06-01 Titouan Vayer , Rémi Gribonval

The maximum mean discrepancy and Wasserstein distance are popular distance measures between distributions and play important roles in many machine learning problems such as metric learning, generative modeling, domain adaption, and…

Machine Learning · Computer Science 2025-01-22 Dong Qiao , Jicong Fan

Distributionally robust reinforcement learning (DRRL) focuses on designing policies that achieve good performance under model uncertainties. The goal is to maximize the worst-case long-term discounted reward, where the data for RL comes…

Machine Learning · Computer Science 2026-03-17 Saptarshi Mandal , Yashaswini Murthy , R. Srikant

Traditional deep learning (DL) models are powerful classifiers, but many approaches do not provide uncertainties for their estimates. Uncertainty quantification (UQ) methods for DL models have received increased attention in the literature…

Machine Learning · Computer Science 2023-08-14 Daniel Ries , Joshua Michalenko , Tyler Ganter , Rashad Imad-Fayez Baiyasi , Jason Adams

Deep Q-learning Network (DQN) is a successful way which combines reinforcement learning with deep neural networks and leads to a widespread application of reinforcement learning. One challenging problem when applying DQN or other…

Machine Learning · Computer Science 2022-09-19 Zhe Zhang , Yukun Zou , Junjie Lai , Qing Xu

Q-Learning is a fundamental off-policy reinforcement learning (RL) algorithm that has the objective of approximating action-value functions in order to learn optimal policies. Nonetheless, it has difficulties in reconciling bias with…

Machine Learning · Computer Science 2024-11-22 Mahammad Humayoo

Temporal-difference and Q-learning play a key role in deep reinforcement learning, where they are empowered by expressive nonlinear function approximators such as neural networks. At the core of their empirical successes is the learned…

Machine Learning · Computer Science 2024-04-02 Yufeng Zhang , Qi Cai , Zhuoran Yang , Yongxin Chen , Zhaoran Wang

Deep Q-Learning (DQL), a family of temporal difference algorithms for control, employs three techniques collectively known as the `deadly triad' in reinforcement learning: bootstrapping, off-policy learning, and function approximation.…

Machine Learning · Computer Science 2019-03-22 Joshua Achiam , Ethan Knight , Pieter Abbeel

Detecting changes is of fundamental importance when analyzing data streams and has many applications, e.g., in predictive maintenance, fraud detection, or medicine. A principled approach to detect changes is to compare the distributions of…

Machine Learning · Computer Science 2025-02-13 Florian Kalinke , Marco Heyden , Georg Gntuni , Edouard Fouché , Klemens Böhm
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