# Research interests

My overall goal is to advance the research of computational and learning algorithms, using principles in applied mathematics and physics, to change the world for the better. In general, I am interested in optimization, machine learning, dynamical systems, and control theory.

On one hand, I am motivated by addressing the lack of robustness and data distribution shift issues in modern learning algorithms. This lack of robustness can be the consequence of biases or unfairness in training data, adversarial attacks, offline data in RL, or causal confounding. For example, I have worked on the theory and computation algorithm to robustly learn ML models by optimizing the risk

$\min_\theta \sup _ {P\in \mathcal M}\mathbb E_{X,Y\sim P} l(f_\theta(X), Y),$

where the underlying data distribution $$P$$ is not the typical empirical average distribution used in statistical learning risk minimization $$\min_\theta \frac1N\sum_{i=1}^N l(\theta, \xi_i)$$, but selected from an ambiguity set $$\mathcal M$$ to endow robustness to the learning model.

On the other hand, I am interested in interfacing dynamical systems and machine learning (e.g., gradient flow, optimal transport, feedback control theory, robustness of deep learning models, generative models), aiming at building robust and scalable optimization and learning algorithms. The dynamics perspective of ML and computation is distinct from a static one in that it views quantities as time-evolutionary processes. For example, the aforementioned data distribution can be described by an evolutionary differential equation

$\partial _t P_t(x) \in G(P_t(x)),$

where just as in continuous optimization, the differential equation can be driven forward by the gradient of certain system energy encoded in the functional $$G$$ above. Our goal is then to study this time evolution of the data distribution $$P_t(x)$$ for large-scale computation and learning.

All those research topics call for a new generation of computational algorithms that can manipulate probability distributions and large-scale data structures robustly. Some example technical topics include

• robust machine learning, learning under distribution shift
• distributionally robust optimization, optimization under uncertainty
• numerical optimization, numerical methods
• data-driven modeling of dynamical systems and physics
• control, multi-stage decision-making
• generative models, machine learning applications of optimal transport and kernel methods

# Previous projects

• Kernel machine learning for distributionally robust optimization, Empirical Inference Department, Max Planck Institute for Intelligent Systems, Tübingen
• Marie Skołodowska-Curie Individual Fellowship on learning-control algorithms, Max Planck Institute for Intelligent Systems, Tübingen
• (More under construction …)

# Publications, preprints, code

Functional Generalized Empirical Likelihood Estimation for Conditional Moment Restrictions. Heiner Kremer, Jia-Jie Zhu, Krikamol Muandet, and Bernard Schölkopf. In the Proceedings of the 39th International Conference on Machine Learning (ICML). PMLR, 2022. paper poster

Maximum Mean Discrepancy Distributionally Robust Nonlinear Chance-Constrained Optimization with Finite-Sample Guarantee Yassine Nemmour, Heiner Kremer, Bernhard Schölkopf, Jia-Jie Zhu. To appear in the 61st IEEE Conference on Decision and Control (CDC). preprint code (summer school exercises) slides (summer school)

• Note: there is an issue with the proof in this paper. We will update with a fix soon.

Adversarially Robust Kernel Smoothing. Jia-Jie Zhu, Christina Kouridi, Yassine Nemmour, Bernhard Schölkopf. Proceedings of The 25th International Conference on Artificial Intelligence and Statistics, volume 151 of Proceedings of Machine Learning Research, pages 4972–4994. PMLR, 28–30 Mar 2022. paper code slides (oral) poster

Learning Random Feature Dynamics for Uncertainty Quantification. Diego Agudelo-Espana, Yassine Nemmour, Bernhard Schölkopf, Jia-Jie Zhu. To appear in the 61st IEEE Conference on Decision and Control (CDC). preprint

Distributionally Robust Trajectory Optimization Under Uncertain Dynamics via Relative-Entropy Trust Regions. Hany Abdulsamad, Tim Dorau, Boris Belousov, Jia-Jie Zhu and Jan Peters. preprint

Distributional Robustness Regularized Scenario Optimization with Application to Model Predictive Control. Yassine Nemmour, Bernhard Schölkopf, Jia-Jie Zhu, 2021. Proceedings of the Conference on Learning for Dynamics and Control (L4DC). paper

Kernel Distributionally Robust Optimization. Jia-Jie Zhu, Wittawat Jitkrittum, Moritz Diehl, Bernhard Schölkopf, 2020. The conference version of this paper appeared in the Proceedings of the 24th International Conference on Artificial Intelligence and Statistics (AISTATS) 2021, San Diego, California, USA. PMLR: Volume 130. paper code slides (shorter version) (longer version)

Worst-Case Risk Quantification under Distributional Ambiguity using Kernel Mean Embedding in Moment Problem. Jia-Jie Zhu, Wittawat Jitkrittum, Moritz Diehl, Bernhard Schölkopf, 2020. In the 59th IEEE Conference on Decision and Control (CDC)), 2020. paper slides

Projection Algorithms for Non-Convex Minimization with Application to Sparse Principal Component Analysis. J.J. Zhu, D. Phan, W. Hager, 2015. Journal of Global Optimization, 65(4):657–676, 2016. paper code

A Kernel Mean Embedding Approach to Reducing Conservativeness in Stochastic Programming and Control. Zhu, Jia-Jie, Moritz Diehl and Bernhard Schölkopf. 2nd Annual Conference on Learning for Dynamics and Control (L4DC). In Proceedings of Machine Learning Research vol 120:1–9, 2020. paper slides

A New Distribution-Free Concept for Representing, Comparing, and Propagating Uncertainty in Dynamical Systems with Kernel Probabilistic Programming. Zhu, Jia-Jie, Krikamol Muandet, Moritz Diehl, and Bernhard Schölkopf. 21st IFAC World Congress. In IFAC-PapersOnLine proceedings, 2020. paper slides

Fast Non-Parametric Learning to Accelerate Mixed-Integer Programming for Online Hybrid Model Predictive Control. Zhu, Jia-Jie, and Martius, Georg. 21st IFAC World Congress. In IFAC-PapersOnLine proceedings, 2020. paper slides

Robust Humanoid Locomotion Using Trajectory Optimization and Sample-Efficient Learning. Yeganegi, Mohammad Hasan, Majid Khadiv, S Ali A Moosavian, Jia-Jie Zhu, Andrea Del Prete, and Ludovic Righetti. IEEE Humanoids, 2019. paper

Generative Adversarial Active Learning. J.J. Zhu, J. Bento, 2017. NIPS 2017 Workshop on Teaching Machines, Robots, and Humans. paper

Control What You Can: Intrinsically Motivated Task-Planning Agent. Blaes, Sebastian, Marin Vlastelica Pogančić, JJ Zhu, and Georg Martius. In Advances in Neural Information Processing Systems (NeurIPS) 32, pages 12541– 12552. Curran Associates, Inc., 2019. paper

Deep Reinforcement Learning for Resource-Aware Control. D. Baumann, J.J. Zhu, G. Martius, S. Trimpe, 2018. IEEE CDC 2018. paper code

A Metric for Sets of Trajectories that is Practical and Mathematically Consistent. J. Bento, J.J. Zhu, 2016. paper

A Decentralized Multi-Block Algorithm for Demand-Side Primary Frequency Control Using Local Frequency Measurements. J. Brooks, W. Hager, J.J. Zhu, 2015. paper