Adaptive Online Learning of Quantum States

In the fundamental problem of shadow tomography, the goal is to efficiently learn an unknown $d$-dimensional quantum state using projective measurements. However, it is rarely the case that the underlying state remains stationary: changes may occur due to measurements, environmental noise, or an underlying Hamiltonian state evolution. In this paper we adopt tools from adaptive online learning to learn a changing state, giving adaptive and dynamic regret bounds for online shadow tomography that are polynomial in the number of qubits and sublinear in the number of measurements. Our analysis utilizes tools from complex matrix analysis to cope with complex numbers, which may be of independent interest in online learning. In addition, we provide numerical experiments that corroborate our theoretical results.

Machine Learning for Mechanical Ventilation Control (Extended Abstract)

Mechanical ventilation is one of the most widely used therapies in the ICU. However, despite broad application from anaesthesia to COVID-related life support, many injurious challenges remain. We frame these as a control problem: ventilators must let air in and out of the patient's lungs according to a prescribed trajectory of airway pressure. Industry-standard controllers, based on the PID method, are neither optimal nor robust. Our data-driven approach learns to control an invasive ventilator by training on a simulator itself trained on data collected from the ventilator. This method outperforms popular reinforcement learning algorithms and even controls the physical ventilator more accurately and robustly than PID. These results underscore how effective data-driven methodologies can be for invasive ventilation and suggest that more general forms of ventilation (e.g., non-invasive, adaptive) may also be amenable.

Provable Regret Bounds for Deep Online Learning and Control

The use of deep neural networks has been highly successful in reinforcement learning and control, although few theoretical guarantees for deep learning exist for these problems. There are two main challenges for deriving performance guarantees: a) control has state information and thus is inherently online and b) deep networks are non-convex predictors for which online learning cannot provide provable guarantees in general. Building on the linearization technique for overparameterized neural networks, we derive provable regret bounds for efficient online learning with deep neural networks. Specifically, we show that over any sequence of convex loss functions, any low-regret algorithm can be adapted to optimize the parameters of a neural network such that it competes with the best net in hindsight. As an application of these results in the online setting, we obtain provable bounds for online episodic control with deep neural network controllers.

Control of Pneumatic Artificial Muscles with SNN-based Cerebellar-like Model

Soft robotics technologies have gained growing interest in recent years, which allows various applications from manufacturing to human-robot interaction. Pneumatic artificial muscle (PAM), a typical soft actuator, has been widely applied to soft robots. The compliance and resilience of soft actuators allow soft robots to behave compliant when interacting with unstructured environments, while the utilization of soft actuators also introduces nonlinearity and uncertainty. Inspired by Cerebellum's vital functions in control of human's physical movement, a neural network model of Cerebellum based on spiking neuron networks (SNNs) is designed. This model is used as a feed-forward controller in controlling a 1-DOF robot arm driven by PAMs. The simulation results show that this Cerebellar-based system achieves good performance and increases the system's response.

Robust Online Control with Model Misspecification

We study online control of an unknown nonlinear dynamical system that is approximated by a time-invariant linear system with model misspecification. Our study focuses on robustness, which measures how much deviation from the assumed linear approximation can be tolerated while maintaining a bounded $\ell_2$-gain compared to the optimal control in hindsight. Some models cannot be stabilized even with perfect knowledge of their coefficients: the robustness is limited by the minimal distance between the assumed dynamics and the set of unstabilizable dynamics. Therefore it is necessary to assume a lower bound on this distance. Under this assumption, and with full observation of the $d$ dimensional state, we describe an efficient controller that attains $\Omega(\frac{1}{\sqrt{d}})$ robustness together with an $\ell_2$-gain whose dimension dependence is near optimal. We also give an inefficient algorithm that attains constant robustness independent of the dimension, with a finite but sub-optimal $\ell_2$-gain.

A Deep Reinforcement Learning Approach towards Pendulum Swing-up Problem based on TF-Agents

Adapting the idea of training CartPole with Deep Q-learning agent, we are able to find a promising result that prevent the pole from falling down. The capacity of reinforcement learning (RL) to learn from the interaction between the environment and agent provides an optimal control strategy. In this paper, we aim to solve the classic pendulum swing-up problem that making the learned pendulum to be in upright position and balanced. Deep Deterministic Policy Gradient algorithm is introduced to operate over continuous action domain in this problem. Salient results of optimal pendulum are proved with increasing average return, decreasing loss, and live video in the code part.

Unsupervised 3D Shape Completion through GAN Inversion

Most 3D shape completion approaches rely heavily on partial-complete shape pairs and learn in a fully supervised manner. Despite their impressive performances on in-domain data, when generalizing to partial shapes in other forms or real-world partial scans, they often obtain unsatisfactory results due to domain gaps. In contrast to previous fully supervised approaches, in this paper we present ShapeInversion, which introduces Generative Adversarial Network (GAN) inversion to shape completion for the first time. ShapeInversion uses a GAN pre-trained on complete shapes by searching for a latent code that gives a complete shape that best reconstructs the given partial input. In this way, ShapeInversion no longer needs paired training data, and is capable of incorporating the rich prior captured in a well-trained generative model. On the ShapeNet benchmark, the proposed ShapeInversion outperforms the SOTA unsupervised method, and is comparable with supervised methods that are learned using paired data. It also demonstrates remarkable generalization ability, giving robust results for real-world scans and partial inputs of various forms and incompleteness levels. Importantly, ShapeInversion naturally enables a series of additional abilities thanks to the involvement of a pre-trained GAN, such as producing multiple valid complete shapes for an ambiguous partial input, as well as shape manipulation and interpolation.

Variational Relational Point Completion Network

Real-scanned point clouds are often incomplete due to viewpoint, occlusion, and noise. Existing point cloud completion methods tend to generate global shape skeletons and hence lack fine local details. Furthermore, they mostly learn a deterministic partial-to-complete mapping, but overlook structural relations in man-made objects. To tackle these challenges, this paper proposes a variational framework, Variational Relational point Completion network (VRCNet) with two appealing properties: 1) Probabilistic Modeling. In particular, we propose a dual-path architecture to enable principled probabilistic modeling across partial and complete clouds. One path consumes complete point clouds for reconstruction by learning a point VAE. The other path generates complete shapes for partial point clouds, whose embedded distribution is guided by distribution obtained from the reconstruction path during training. 2) Relational Enhancement. Specifically, we carefully design point self-attention kernel and point selective kernel module to exploit relational point features, which refines local shape details conditioned on the coarse completion. In addition, we contribute a multi-view partial point cloud dataset (MVP dataset) containing over 100,000 high-quality scans, which renders partial 3D shapes from 26 uniformly distributed camera poses for each 3D CAD model. Extensive experiments demonstrate that VRCNet outperforms state-of-theart methods on all standard point cloud completion benchmarks. Notably, VRCNet shows great generalizability and robustness on real-world point cloud scans.