Minghui Zhu

Siyuan Xu, Minghui Zhu

Bilevel optimization has been developed for many machine learning tasks with large-scale and high-dimensional data. This paper considers a constrained bilevel optimization problem, where the lower-level optimization problem is convex with equality and inequality constraints and the upper-level optimization problem is non-convex. The overall objective function is non-convex and non-differentiable. To solve the problem, we develop a gradient-based approach, called gradient approximation method, which determines the descent direction by computing several representative gradients of the objective function inside a neighborhood of the current estimate. We show that the algorithm asymptotically converges to the set of Clarke stationary points, and demonstrate the efficacy of the algorithm by the experiments on hyperparameter optimization and meta-learning.

Shicheng Liu, Minghui Zhu

Inverse reinforcement learning (IRL) aims to learn a reward function and a corresponding policy that best fit the demonstrated trajectories of an expert. However, current IRL works cannot learn incrementally from an ongoing trajectory because they have to wait to collect at least one complete trajectory to learn. To bridge the gap, this paper considers the problem of learning a reward function and a corresponding policy while observing the initial state-action pair of an ongoing trajectory and keeping updating the learned reward and policy when new state-action pairs of the ongoing trajectory are observed. We formulate this problem as an online bi-level optimization problem where the upper level dynamically adjusts the learned reward according to the newly observed state-action pairs with the help of a meta-regularization term, and the lower level learns the corresponding policy. We propose a novel algorithm to solve this problem and guarantee that the algorithm achieves sub-linear local regret $O(\sqrt{T}+\log T+\sqrt{T}\log T)$. If the reward function is linear, we prove that the proposed algorithm achieves sub-linear regret $O(\log T)$. Experiments are used to validate the proposed algorithm.

Sze Zheng Yong, Minghui Zhu, Emilio Frazzoli

In this paper, we consider the problem of attack-resilient state estimation, that is to reliably estimate the true system states despite two classes of attacks: (i) attacks on the switching mechanisms and (ii) false data injection attacks on actuator and sensor signals, in the presence of unbounded stochastic process and measurement noise signals. We model the systems under attack as hidden mode stochastic switched linear systems with unknown inputs and propose the use of a multiple-model inference algorithm to tackle these security issues. Moreover, we characterize fundamental limitations to resilient estimation (e.g., upper bound on the number of tolerable signal attacks) and discuss the topics of attack detection, identification and mitigation under this framework. Simulation examples of switching and false data injection attacks on a benchmark system and an IEEE 68-bus test system show the efficacy of our approach to recover resilient (i.e., asymptotically unbiased) state estimates as well as to identify and mitigate the attacks.

Sze Zheng Yong, Minghui Zhu, Emilio Frazzoli

In this paper, we propose a filtering algorithm for simultaneously estimating the mode, input and state of hidden mode switched linear stochastic systems with unknown inputs. Using a multiple-model approach with a bank of linear input and state filters for each mode, our algorithm relies on the ability to find the most probable model as a mode estimate, which we show is possible with input and state filters by identifying a key property, that a particular residual signal we call generalized innovation is a Gaussian white noise. We also provide an asymptotic analysis for the proposed algorithm and provide sufficient conditions for asymptotically achieving convergence to the true model (consistency), or to the 'closest' model according to an information-theoretic measure (convergence). A simulation example of intention-aware vehicles at an intersection is given to demonstrate the effectiveness of our approach.