The past decade has witnessed significant advancements in quantum hardware, encompassing improvements in speed, qubit quantity, and quantum volume-a metric defining the maximum size of a quantum circuit effectively implementable on near-term quantum devices. This progress has led to a surge in Quantum Machine Learning (QML) applications on real hardware, aiming to achieve quantum advantage over classical approaches. This survey focuses on selected supervised and unsupervised learning applications executed on quantum hardware, specifically tailored for real-world scenarios. The exploration includes a thorough analysis of current QML implementation limitations on quantum hardware, covering techniques like encoding, ansatz structure, error mitigation, and gradient methods to address these challenges. Furthermore, the survey evaluates the performance of QML implementations in comparison to classical counterparts. In conclusion, we discuss existing bottlenecks related to applying QML on real quantum devices and propose potential solutions to overcome these challenges in the future.

Recently, estimation of causal effects with high-dimensional observational data has drawn much attention in many research fields such as economics, epidemiology and genomics. The instrumental variable (IV) method is widely used when the treatment variable of interest is endogenous. As shown in Figure 1, the ideal IV needs to be correlated with the endogenous treatment variable (C1), it should not have a direct effect on the outcome (C2) and should not be related to unobserved confounders that affect both outcome and treatment (C3). Figure 1: Relevance and Validity of IVs Our research is motivated by the difficulty of finding IVs that satisfy all the above conditions. In applications, invalid IVs (violation of C2 or C3) (Davey Smith and Ebrahim, 2003; Kang et al., 2016; Windmeijer et al., 2019) and weak IVs (concerning the weak correlation in C1) (Bound et al., 1995; Staiger and Stock, 1997) are prevalent. A strand of literature studies the "many weak IVs" problem (Stock et al., 2002; Chao and Swanson, 2005). With the increasing availability of large datasets, IV models are often high-dimensional (Belloni et al., 2012; Lin et al., 2015; Fan and Zhong, 2018), and have potentially weak IVs (Andrews et al., 2018), and invalid IVs (Guo et al., 2018; Windmeijer et al., 2021). Among those problems, we mainly focus on the invalid IV problem, while allowing for potential high-dimensionality and weak signals.

This work uses game theory as a mathematical framework to address interaction modeling in multi-agent motion forecasting and control. Despite its interpretability, applying game theory to real-world robotics, like automated driving, faces challenges such as unknown game parameters. To tackle these, we establish a connection between differential games, optimal control, and energy-based models, demonstrating how existing approaches can be unified under our proposed Energy-based Potential Game formulation. Building upon this, we introduce a new end-to-end learning application that combines neural networks for game-parameter inference with a differentiable game-theoretic optimization layer, acting as an inductive bias. The analysis provides empirical evidence that the game-theoretic layer adds interpretability and improves the predictive performance of various neural network backbones using two simulations and two real-world driving datasets.

Flow fields are often partitioned into data blocks for massively parallel computation and analysis based on blockwise relationships. However, most of the previous techniques only consider the first-order dependencies among blocks, which is insufficient in describing complex flow patterns. In this work, we present FlowHON, an approach to construct higher-order networks (HONs) from flow fields. FlowHON captures the inherent higher-order dependencies in flow fields as nodes and estimates the transitions among them as edges. We formulate the HON construction as an optimization problem with three linear transformations. The first two layers correspond to the node generation and the third one corresponds to edge estimation. Our formulation allows the node generation and edge estimation to be solved in a unified framework. With FlowHON, the rich set of traditional graph algorithms can be applied without any modification to analyze flow fields, while leveraging the higher-order information to understand the inherent structure and manage flow data for efficiency. We demonstrate the effectiveness of FlowHON using a series of downstream tasks, including estimating the density of particles during tracing, partitioning flow fields for data management, and understanding flow fields using the node-link diagram representation of networks.

Inferring unknown constraints is a challenging and crucial problem in many robotics applications. When only expert demonstrations are available, it becomes essential to infer the unknown domain constraints to deploy additional agents effectively. In this work, we propose an approach to infer affine constraints in control tasks after observing expert demonstrations. We formulate the constraint inference problem as an inverse optimization problem, and we propose an alternating optimization scheme that infers the unknown constraints by minimizing a KKT residual objective. We demonstrate the effectiveness of our method in a number of simulations, and show that our method can infer less conservative constraints than a recent baseline method, while maintaining comparable safety guarantees.

A pose-graph-based optimization technique is widely used to estimate robot poses using various sensor measurements from devices such as laser scanners and cameras. The global navigation satellite system (GNSS) has recently been used to estimate the absolute 3D position of outdoor mobile robots. However, since the accuracy of GNSS single-point positioning is only a few meters, the GNSS is not used for the loop closure of a pose graph. The main purpose of this study is to generate a loop closure of a pose graph using a time-relative real-time kinematic GNSS (TR-RTK-GNSS) technique. The proposed TR-RTK-GNSS technique uses time-differential carrier phase positioning, which is based on carrier-phase-based differential GNSS with a single GNSS receiver. Unlike a conventional RTK-GNSS, we can directly compute the robot's relative position using only a stand-alone GNSS receiver. The initial pose graph is generated from the accumulated velocity computed from GNSS Doppler measurements. To reduce the accumulated error of velocity, we use the TR-RTK-GNSS technique for the loop closure in the graph-based optimization framework. The kinematic positioning tests were performed using an unmanned aerial vehicle to confirm the effectiveness of the proposed technique. From the tests, we can estimate the vehicle's trajectory with approximately 3 cm accuracy using only a stand-alone GNSS receiver.

Indirect experiments provide a valuable framework for estimating treatment effects in situations where conducting randomized control trials (RCTs) is impractical or unethical. Unlike RCTs, indirect experiments estimate treatment effects by leveraging (conditional) instrumental variables, enabling estimation through encouragement and recommendation rather than strict treatment assignment. However, the sample efficiency of such estimators depends not only on the inherent variability in outcomes but also on the varying compliance levels of users with the instrumental variables and the choice of estimator being used, especially when dealing with numerous instrumental variables. While adaptive experiment design has a rich literature for direct experiments, in this paper we take the initial steps towards enhancing sample efficiency for indirect experiments by adaptively designing a data collection policy over instrumental variables. Our main contribution is a practical computational procedure that utilizes influence functions to search for an optimal data collection policy, minimizing the mean-squared error of the desired (non-linear) estimator. Through experiments conducted in various domains inspired by real-world applications, we showcase how our method can significantly improve the sample efficiency of indirect experiments.

This paper proposes a highly accurate trajectory estimation method for outdoor mobile robots using global navigation satellite system (GNSS) time differences of carrier phase (TDCP) measurements. By using GNSS TDCP, the relative 3D position can be estimated with millimeter precision. However, when a phenomenon called cycle slip occurs, wherein the carrier phase measurement jumps and becomes discontinuous, it is impossible to accurately estimate the relative position using TDCP. Although previous studies have eliminated the effect of cycle slip using a robust optimization technique, it was difficult to completely eliminate the effect of outliers. In this paper, we propose a method to detect GNSS carrier phase cycle slip, estimate the amount of cycle slip, and modify the observed TDCP to calculate the relative position using the factor graph optimization framework. The estimated relative position acts as a loop closure in graph optimization and contributes to the reduction in the integration error of the relative position. Experiments with an unmanned aerial vehicle showed that by modifying the cycle slip using the proposed method, the vehicle trajectory could be estimated with an accuracy of 5 to 30 cm using only a single GNSS receiver, without using any other external data or sensors.

De novo drug design requires simultaneously generating novel molecules outside of training data and predicting their target properties, making it a hard task for generative models. To address this, we propose Joint Transformer that combines a Transformer decoder, Transformer encoder, and a predictor in a joint generative model with shared weights. We formulate a probabilistic black-box optimization algorithm that employs Joint Transformer to generate novel molecules with improved target properties and outperforms other SMILES-based optimization methods in de novo drug design.

Selecting the best hyperparameters for a particular optimization instance, such as the learning rate and momentum, is an important but nonconvex problem. As a result, iterative optimization methods such as hypergradient descent lack global optimality guarantees in general. We propose an online nonstochastic control methodology for mathematical optimization. First, we formalize the setting of meta-optimization, an online learning formulation of learning the best optimization algorithm from a class of methods. The meta-optimization problem over gradient-based methods can be framed as a feedback control problem over the choice of hyperparameters, including the learning rate, momentum, and the preconditioner. Although the original optimal control problem is nonconvex, we show how recent methods from online nonstochastic control using convex relaxations can be used to overcome the challenge of nonconvexity, and obtain regret guarantees against the best offline solution. This guarantees that in meta-optimization, given a sequence of optimization problems, we can learn a method that attains convergence comparable to that of the best optimization method in hindsight from a class of methods.