130 citations · 187 across the 21 of their papers we have counts for
22 papers
Improved Stochastic Optimization of LogSumExp
Egor Gladin, Alexey Kroshnin, Jia-Jie Zhu +1
The LogSumExp function, dual to the Kullback-Leibler (KL) divergence, plays a central role in many important optimization problems, including entropy-regularized optimal transport…
Evolution of Gaussians in the Hellinger-Kantorovich-Boltzmann gradient flow
Matthias Liero, Alexander Mielke, Oliver Tse +1
This study leverages the basic insight that the gradient-flow equation associated with the relative Boltzmann entropy, in relation to a Gaussian reference measure within the Hellin…
Hellinger-Kantorovich Gradient Flows: Global Exponential Decay of Entropy Functionals
Alexander Mielke, Jia-Jie Zhu
We investigate a family of gradient flows of positive and probability measures, focusing on the Hellinger-Kantorovich (HK) geometry, which unifies transport mechanism of Otto-Wasse…
Inclusive KL Gradient Flows: Otto-Wasserstein, Fisher-Rao-Gaussian, and Local-Estimator Dynamics
Jia-Jie Zhu
Otto's Wasserstein gradient flow of the inclusive (forward) Kullback--Leibler (KL) divergence offers a principled framework for analyzing statistical inference algorithms, yet algo…
Kernel Approximation of Fisher-Rao Gradient Flows
Jia-Jie Zhu, Alexander Mielke
The purpose of this paper is to answer a few open questions in the interface of kernel methods and PDE gradient flows. Motivated by recent advances in machine learning, particularl…
Interaction-Force Transport Gradient Flows
Egor Gladin, Pavel Dvurechensky, Alexander Mielke +1
This paper presents a new gradient flow dissipation geometry over non-negative and probability measures. This is motivated by a principled construction that combines the unbalanced…
Analysis of Kernel Mirror Prox for Measure Optimization
Pavel Dvurechensky, Jia-Jie Zhu
By choosing a suitable function space as the dual to the non-negative measure cone, we study in a unified framework a class of functional saddle-point optimization problems, which…
An Inexact Halpern Iteration with Application to Distributionally Robust Optimization
Ling Liang, Zusen Xu, Kim-Chuan Toh +1
The Halpern iteration for solving monotone inclusion problems has gained increasing interests in recent years due to its simple form and appealing convergence properties. In this p…
Propagating Kernel Ambiguity Sets in Nonlinear Data-driven Dynamics Models
Jia-Jie Zhu
This paper provides answers to an open problem: given a nonlinear data-driven dynamical system model, e.g., kernel conditional mean embedding (CME) and Koopman operator, how can on…
Distributionally Robust Trajectory Optimization Under Uncertain Dynamics via Relative Entropy Trust-Regions
Hany Abdulsamad, Tim Dorau, Boris Belousov +2
Trajectory optimization and model predictive control are essential techniques underpinning advanced robotic applications, ranging from autonomous driving to full-body humanoid cont…
Kernel Distributionally Robust Optimization
Jia-Jie Zhu, Wittawat Jitkrittum, Moritz Diehl +1
We propose kernel distributionally robust optimization (Kernel DRO) using insights from the robust optimization theory and functional analysis. Our method uses reproducing kernel H…
Worst-Case Risk Quantification under Distributional Ambiguity using Kernel Mean Embedding in Moment Problem
Jia-Jie Zhu, Wittawat Jitkrittum, Moritz Diehl +1
In order to anticipate rare and impactful events, we propose to quantify the worst-case risk under distributional ambiguity using a recent development in kernel methods -- the kern…
A Kernel Mean Embedding Approach to Reducing Conservativeness in Stochastic Programming and Control
Jia-Jie Zhu, Moritz Diehl, Bernhard Schölkopf
We apply kernel mean embedding methods to sample-based stochastic optimization and control. Specifically, we use the reduced-set expansion method as a way to discard sampled scenar…
A New Distribution-Free Concept for Representing, Comparing, and Propagating Uncertainty in Dynamical Systems with Kernel Probabilistic Programming
Jia-Jie Zhu, Krikamol Muandet, Moritz Diehl +1
This work presents the concept of kernel mean embedding and kernel probabilistic programming in the context of stochastic systems. We propose formulations to represent, compare, an…
Fast Non-Parametric Learning to Accelerate Mixed-Integer Programming for Online Hybrid Model Predictive Control
Jia-Jie Zhu, Georg Martius
Today's fast linear algebra and numerical optimization tools have pushed the frontier of model predictive control (MPC) forward, to the efficient control of highly nonlinear and hy…
Robust Humanoid Locomotion Using Trajectory Optimization and Sample-Efficient Learning
Mohammad Hasan Yeganegi, Majid Khadiv, S. Ali A. Moosavian +3
Trajectory optimization (TO) is one of the most powerful tools for generating feasible motions for humanoid robots. However, including uncertainties and stochasticity in the TO pro…
Trajectory Optimization for Robust Humanoid Locomotion with Sample-Efficient Learning
Majid Khadiv, Mohammad Hasan Yeganegi, S. Ali A. Moosavian +2
Trajectory optimization (TO) is one of the most powerful tools for generating feasible motions for humanoid robots. However, including uncertainties and stochasticity in the TO pro…
Deep Reinforcement Learning for Event-Triggered Control
Dominik Baumann, Jia-Jie Zhu, Georg Martius +1
Event-triggered control (ETC) methods can achieve high-performance control with a significantly lower number of samples compared to usual, time-triggered methods. These frameworks…
Generative Adversarial Active Learning
Jia-Jie Zhu, José Bento
We propose a new active learning by query synthesis approach using Generative Adversarial Networks (GAN). Different from regular active learning, the resulting algorithm adaptively…
A metric for sets of trajectories that is practical and mathematically consistent
José Bento, Jia Jie Zhu
Metrics on the space of sets of trajectories are important for scientists in the field of computer vision, machine learning, robotics, and general artificial intelligence. However,…
A Decentralized Multi-block ADMM for Demand-side Primary Frequency Control using Local Frequency Measurements
Jonathan Brooks, William Hager, Jiajie Zhu
We consider demand-side primary frequency control in the power grid provided by smart and flexible loads: loads change consumption to match generation and help the grid while minim…
Projection Algorithms for Non-Convex Minimization with Application to Sparse Principal Component Analysis
William W. Hager, Dzung T. Phan, Jia-Jie Zhu
We consider concave minimization problems over non-convex sets.Optimization problems with this structure arise in sparse principal component analysis. We analyze both a gradient pr…