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In this paper, we consider two paradigms that are developed to account for uncertainty in optimization models: robust optimization (RO) and joint estimation-optimization (JEO). We examine recent developments on efficient and scalable iterative first-order methods for these problems, and show that these iterative methods can be viewed through the lens of online convex optimization (OCO). The standard OCO framework has seen much success for its ability to handle decision-making in dynamic, uncertain, and even adversarial environments. Nevertheless, our applications of interest present further flexibility in OCO via three simple modifications to standard OCO assumptions: we introduce two new concepts of weighted regret and online saddle point problems and study the possibility of making lookahead (anticipatory) decisions. Our analyses demonstrate that these flexibilities introduced into the OCO framework have significant consequences whenever they are applicable. For example, in the strongly convex case, minimizing unweighted regret has a proven optimal bound of O(log(T)/T), whereas we show that a bound of O(1 / T) is possible when we consider weighted regret. Similarly, for the smooth case, considering 1-lookahead decisions results in a O(1 / T) bound, compared to O(1/T) in the standard OCO setting. Consequently, these OCO tools are instrumental in exploiting structural properties of functions and results in improved convergence rates for RO and JEO. In certain cases, our results for RO and JEO match the best known or optimal rates in the corresponding problem classes without data uncertainty.

Continuous quantum error correction has been found to have certain advantages over discrete quantum error correction, such as a reduction in hardware resources and the elimination of error mechanisms introduced by having entangling gates and ancilla qubits. We propose a machine learning algorithm for continuous quantum error correction that is based on the use of a recurrent neural network to identify bit-flip errors from continuous noisy syndrome measurements. The algorithm is designed to operate on measurement signals deviating from the ideal behavior in which the mean value corresponds to a code syndrome value and the measurement has white noise. We analyze continuous measurements taken from a superconducting architecture using three transmon qubits to identify three significant practical examples of non-ideal behavior, namely auto-correlation at temporal short lags, transient syndrome dynamics after each bit-flip, and drift in the steady-state syndrome values over the course of many experiments. Based on these real-world imperfections, we generate synthetic measurement signals from which to train the recurrent neural network, and then test its proficiency when implementing active error correction, comparing this with a traditional double threshold scheme and a discrete Bayesian classifier. The results show that our machine learning protocol is able to outperform the double threshold protocol across all tests, achieving a final state fidelity comparable to the discrete Bayesian classifier.

Background The health workforce (HW) plays an important role in patient care, and in rural Australia its distribution varies substantially. This paper explores trends in Australia’s HW full-time equivalent (HW–FTE) rates and estimates the risk of HW attrition phenomena using data from local government areas (LGAs) during 2013–2021. Methods Trends and spatial analyses were used to understand HW–FTE rates for allied health professionals, medical practitioners, and nurses and midwives in four major types of Australian Statistical Geography Standard (ASGS) remoteness areas. The time-to-event modelling was used to identify HW retention times and probability of HW attrition, by remoteness areas and major states in Australia. Results On average the HW–FTE rate at the granular geo-spatial LGA level exhibits variation in trends between States, rurality, LGA and health professional groups over the study period. The increase in the HW–FTE rate over time for medical practitioners and allied health professionals is lower for outer regional, remote, and very remote Australia compared to inner regional Australia. The HW–FTE rate is also consistently lower for rural Australia compared to major cities irrespective of HW professions. The average HW retention time estimated for allied health was highest in major cities (5 years), and lowest in outer regional areas (3 years). States such as NSW and QLD had more than 4 years of HW retention time for medical practitioners. For nurses and midwives, the average retention time was less than 3 years for all states in Australia. There is variation in trends in HW–FTE rate between LGAs within and between States, including markedly contrasting trends between geographically adjacent LGAs. Conclusions Our results provide new insight into variation in HW availability, and trends in availability, between major health professional groupings between States, degrees of rurality and local government areas across Australia. This presents new opportunities for understanding and addressing factors that underly the variation in trends for the purpose of refining policy and programs that aim to address the persistent maldistribution and shortages in health worker availability between major cities and regional and remote parts of Australia.

The utility of a quantum computer is highly dependent on the ability to reliably perform accurate quantum logic operations. For finding optimal control solutions, it is of particular interest to explore model-free approaches, since their quality is not constrained by the limited accuracy of theoretical models for the quantum processor—in contrast to many established gate implementation strategies. In this work, we utilize a continuous control reinforcement learning algorithm to design entangling two-qubit gates for superconducting qubits; specifically, our agent constructs cross-resonance and CNOT gates without any prior information about the physical system. Using a simulated environment of fixed-frequency fixed-coupling transmon qubits, we demonstrate the capability to generate novel pulse sequences that outperform the standard cross-resonance gates in both fidelity and gate duration, while maintaining a comparable susceptibility to stochastic unitary noise. We further showcase an augmentation in training and input information that allows our agent to adapt its pulse design abilities to drifting hardware characteristics, importantly, with little to no additional optimization. Our results exhibit clearly the advantages of unbiased adaptive-feedback learning-based optimization methods for transmon gate design.

Assortment optimization has received significant attention in recent revenue management and combinatorial optimization literature. In “The Approximability of Assortment Optimization Under Ranking Preferences,” A. Aouad, V. Farias, R. Levi, and D. Segev provide best-possible approximability bounds for this problem under an almost general model specification, where preferences are expressed as a distribution over rankings. This paper shows how this optimization problem relates to the computational task of detecting large independent sets in graphs, allowing the establishment of strong complexity lower bounds with respect to various problem parameters. These findings are complemented by a number of algorithms that attain essentially best-possible approximation factors, proving that the hardness results are tight up to lower-order terms. Surprisingly, their results imply that a simple and widely studied policy, known as revenue-ordered assortments, achieves the best possible performance guarantee with respect to prices. The main contribution of this paper is to provide best-possible approximability bounds for assortment planning under a general choice model, where customer choices are modeled through an arbitrary distribution over ranked lists of their preferred products, subsuming most random utility choice models of interest. From a technical perspective, we show how to relate this optimization problem to the computational task of detecting large independent sets in graphs, allowing us to argue that general ranking preferences are extremely hard to approximate with respect to various problem parameters. These findings are complemented by a number of approximation algorithms that attain essentially best-possible factors, proving that our hardness results are tight up to lower-order terms. Surprisingly, our results imply that a simple and widely studied policy, known as revenue-ordered assortments, achieves the best possible performance guarantee with respect to the price parameters.

Robust optimization (RO) is a technique to tractably model uncertain parameters in optimization problems. More recently, it has attracted interest in applications from machine learning and statistics. These recent applications present algorithmic challenges in which the scalability of RO algorithms with problem dimension becomes crucial. The traditional solution method for RO is to transform it into an equivalent—yet more complex—deterministic problem. The alternate solution technique is to iteratively solve sequences of the underlying deterministic model with different values of the uncertain parameters. However, such iterative approaches have been rather prohibitive in practice, especially when solving even the underlying deterministic model is expensive. In “Online First-Order Framework for Robust Convex Optimization,” by analyzing the structure of an underlying convex–nonconcave saddle point problem, N. Ho-Nguyen and F. Kılınç-Karzan develop an iterative framework for RO in which the cost of each iteration can be remarkably reduced. In particular, they show that, without scarifying from the guarantees on the number of iterations needed, it is possible to use cheap first-order updates instead of deterministic optimization solvers in each iteration. Robust optimization (RO) has emerged as one of the leading paradigms to efficiently model parameter uncertainty. The recent connections between RO and problems in statistics and machine learning domains demand for solving RO problems in ever larger scales. However, the traditional approaches for solving RO formulations based on building and solving robust counterparts or the iterative approaches utilizing nominal feasibility oracles can be prohibitively expensive and thus significantly hinder the scalability of the RO paradigm. In this paper, we present a general and flexible iterative framework to approximately solve robust convex optimization problems that is built on a fully online first-order paradigm. In comparison with the existing literature, a key distinguishing feature of our approach is that it requires access to only first-order oracles that are remarkably cheaper than pessimization or nominal feasibility oracles, while maintaining the same convergence rates. This, in particular, makes our approach much more scalable and hence preferable in large-scale applications, specifically those from machine learning and statistics domains. We also provide new interpretations of existing iterative approaches in our framework and illustrate our framework on robust quadratic programming. The e-companion is available at https://doi.org/10.1287/opre.2018.1764 .

Abstract Continuous quantum error correction has been found to have certain advantages over discrete quantum error correction, such as a reduction in hardware resources and the elimination of error mechanisms introduced by having entangling gates and ancilla qubits. We propose a machine learning algorithm for continuous quantum error correction that is based on the use of a recurrent neural network to identify bit-flip errors from continuous noisy syndrome measurements. The algorithm is designed to operate on measurement signals deviating from the ideal behavior in which the mean value corresponds to a code syndrome value and the measurement has white noise. We analyze continuous measurements taken from a superconducting architecture using three transmon qubits to identify three significant practical examples of non-ideal behavior, namely auto-correlation at temporal short lags, transient syndrome dynamics after each bit-flip, and drift in the steady-state syndrome values over the course of many experiments. Based on these real-world imperfections, we generate synthetic measurement signals from which to train the recurrent neural network, and then test its proficiency when implementing active error correction, comparing this with a traditional double threshold scheme and a discrete Bayesian classifier. The results show that our machine learning protocol is able to outperform the double threshold protocol across all tests, achieving a final state fidelity comparable to the discrete Bayesian classifier.

The utility of a quantum computer depends heavily on the ability to reliably perform accurate quantum logic operations. For finding optimal control solutions, it is of particular interest to explore model-free approaches, since their quality is not constrained by the limited accuracy of theoretical models for the quantum processor - in contrast to many established gate implementation strategies. In this work, we utilize a continuous-control reinforcement learning algorithm to design entangling two-qubit gates for superconducting qubits; specifically, our agent constructs cross-resonance and CNOT gates without any prior information about the physical system. Using a simulated environment of fixed-frequency, fixed-coupling transmon qubits, we demonstrate the capability to generate novel pulse sequences that outperform the standard cross-resonance gates in both fidelity and gate duration, while maintaining a comparable susceptibility to stochastic unitary noise. We further showcase an augmentation in training and input information that allows our agent to adapt its pulse design abilities to drifting hardware characteristics, importantly with little to no additional optimization. Our results exhibit clearly the advantages of unbiased adaptive-feedback learning-based optimization methods for transmon gate design.

Continuous quantum error correction has been found to have certain advantages over discrete quantum error correction, such as a reduction in hardware resources and the elimination of error mechanisms introduced by having entangling gates and ancilla qubits. We propose a machine learning algorithm for continuous quantum error correction that is based on the use of a recurrent neural network to identify bit-flip errors from continuous noisy syndrome measurements. The algorithm is designed to operate on measurement signals deviating from the ideal behavior in which the mean value corresponds to a code syndrome value and the measurement has white noise. We analyze continuous measurements taken from a superconducting architecture using three transmon qubits to identify three significant practical examples of non-ideal behavior, namely auto-correlation at temporal short lags, transient syndrome dynamics after each bit-flip, and drift in the steady-state syndrome values over the course of many experiments. Based on these real-world imperfections, we generate synthetic measurement signals from which to train the recurrent neural network, and then test its proficiency when implementing active error correction, comparing this with a traditional double threshold scheme and a discrete Bayesian classifier. The results show that our machine learning protocol is able to outperform the double threshold protocol across all tests, achieving a final state fidelity comparable to the discrete Bayesian classifier.

We present a method to measure the small-scale matter power spectrum using high-resolution measurements of the gravitational lensing of the Cosmic Microwave Background (CMB). To determine whether small-scale structure today is suppressed on scales below 10 kiloparsecs (corresponding to M < 10^9 M_sun), one needs to probe CMB-lensing modes out to L ~ 35,000, requiring a CMB experiment with about 20 arcsecond resolution or better. We show that a CMB survey covering 4,000 square degrees of sky, with an instrumental sensitivity of 0.5 uK-arcmin at 18 arcsecond resolution, could distinguish between cold dark matter and an alternative, such as 1 keV warm dark matter or 10^(-22) eV fuzzy dark matter with about 4-sigma significance. A survey of the same resolution with 0.1 uK-arcmin noise could distinguish between cold dark matter and these alternatives at better than 20-sigma significance; such high-significance measurements may also allow one to distinguish between a suppression of power due to either baryonic effects or the particle nature of dark matter, since each impacts the shape of the lensing power spectrum differently. CMB temperature maps yield higher signal-to-noise than polarization maps in this small-scale regime; thus, systematic effects, such as from extragalactic astrophysical foregrounds, need to be carefully considered. However, these systematic concerns can likely be mitigated with known techniques. Next-generation CMB lensing may thus provide a robust and powerful method of measuring the small-scale matter power spectrum.