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Quantum Annealing (QA) holds great potential for solving combinatorial optimization problems efficiently. However, the effectiveness of QA algorithms heavily relies on the embedding of problem instances, represented as logical graphs, into the quantum unit processing (QPU) whose topology is in form of a limited connectivity graph, known as the minor embedding Problem. Existing methods for the minor embedding problem suffer from scalability issues when confronted with larger problem sizes. In this paper, we propose a novel approach utilizing Reinforcement Learning (RL) techniques to address the minor embedding problem, named CHARME. CHARME includes three key components: a Graph Neural Network (GNN) architecture for policy modeling, a state transition algorithm ensuring solution validity, and an order exploration strategy for effective training. Through comprehensive experiments on synthetic and real-world instances, we demonstrate that the efficiency of our proposed order exploration strategy as well as our proposed RL framework, CHARME. In details, CHARME yields superior solutions compared to fast embedding methods such as Minorminer and ATOM. Moreover, our method surpasses the OCT-based approach, known for its slower runtime but high-quality solutions, in several cases. In addition, our proposed exploration enhances the efficiency of the training of the CHARME framework by providing better solutions compared to the greedy strategy.

This paper introduces the Orthogonal Polynomials Quadrature Algorithm for Survival Analysis (OPSurv), a new method providing time-continuous functional outputs for both single and competing risks scenarios in survival analysis. OPSurv utilizes the initial zero condition of the Cumulative Incidence function and a unique decomposition of probability densities using orthogonal polynomials, allowing it to learn functional approximation coefficients for each risk event and construct Cumulative Incidence Function estimates via Gauss--Legendre quadrature. This approach effectively counters overfitting, particularly in competing risks scenarios, enhancing model expressiveness and control. The paper further details empirical validations and theoretical justifications of OPSurv, highlighting its robust performance as an advancement in survival analysis with competing risks.

Score-based generative models (SGMs) is a recent class of deep generative models with state-of-the-art performance in many applications. In this paper, we establish convergence guarantees for a general class of SGMs in 2-Wasserstein distance, assuming accurate score estimates and smooth log-concave data distribution. We specialize our result to several concrete SGMs with specific choices of forward processes modelled by stochastic differential equations, and obtain an upper bound on the iteration complexity for each model, which demonstrates the impacts of different choices of the forward processes. We also provide a lower bound when the data distribution is Gaussian. Numerically, we experiment SGMs with different forward processes, some of which are newly proposed in this paper, for unconditional image generation on CIFAR-10. We find that the experimental results are in good agreement with our theoretical predictions on the iteration complexity, and the models with our newly proposed forward processes can outperform existing models.

Network motif identification problem aims to find topological patterns in biological networks. Identifying non-overlapping motifs is a computationally challenging problem using classical computers. Quantum computers enable solving high complexity problems which do not scale using classical computers. In this paper, we develop the first quantum solution, called QOMIC (Quantum Optimization for Motif IdentifiCation), to the motif identification problem. QOMIC transforms the motif identification problem using a integer model, which serves as the foundation to develop our quantum solution. We develop and implement the quantum circuit to find motif locations in the given network using this model. Our experiments demonstrate that QOMIC outperforms the existing solutions developed for the classical computer, in term of motif counts. We also observe that QOMIC can efficiently find motifs in human regulatory networks associated with five neurodegenerative diseases: Alzheimers, Parkinsons, Huntingtons, Amyotrophic Lateral Sclerosis (ALS), and Motor Neurone Disease (MND).

A technique is proposed that uses a multi-scale approach to calculate transport properties of compressed felts using only image analysis and numerical calculations. From the image analysis fiber diameter distribution and fiber orientation are determined. From a known porosity and the latter two characteristics, two representative elementary volumes (REV) are constructed: one based on the volume-weighted average diameter and one on an inverse volume-weighted average diameter. Numerical calculations on the former showed that it correctly estimates viscous and thermal permeabilities, while the latter correctly estimates tortuosity and viscous and thermal characteristic lengths. From these calculations, micro-macro analytical expressions are developed to estimate the transport properties of polydisperse composite felts based solely on open porosity, fiber diameter polydiversity, and fiber orientation. Good agreements are obtained between analytical predictions and measurements of transport properties. The predicted transport properties are also used in the Johnson-Champoux-Allard-Lafarge (JCAL) equivalent fluid model to predict the sound absorption coefficient of the felts. Excellent agreements are obtained with impedance tube measurements., Comment: 29 pages, 17 figures

Shape estimation of sweetpotato (SP) storage roots is inherently challenging due to their varied size and shape characteristics. Even measuring "simple" metrics, such as length and width, requires significant time investments either directly in-field or afterward using automated graders. In this paper, we present the results of a model that can perform grading and provide yield estimates directly in the field quicker than manual measurements. Detectron2, a library consisting of deep-learning object detection algorithms, was used to implement Mask R-CNN, an instance segmentation model. This model was deployed for in-field grade estimation of SPs and evaluated against an optical sorter. Storage roots from various clones imaged with a cellphone during trials between 2019 and 2020, were used in the model's training and validation to fine-tune a model to detect SPs. Our results showed that the model could distinguish individual SPs in various environmental conditions including variations in lighting and soil characteristics. RMSE for length, width, and weight, from the model compared to a commercial optical sorter, were 0.66 cm, 1.22 cm, and 74.73 g, respectively, while the RMSE of root counts per plot was 5.27 roots, with r^2 = 0.8. This phenotyping strategy has the potential enable rapid yield estimates in the field without the need for sophisticated and costly optical sorters and may be more readily deployed in environments with limited access to these kinds of resources or facilities., Comment: 21 pages, 11 figures

Quantum annealing (QA) has emerged as a powerful technique to solve optimization problems by taking advantages of quantum physics. In QA process, a bottleneck that may prevent QA to scale up is minor embedding step in which we embed optimization problems represented by a graph, called logical graph, to Quantum Processing Unit (QPU) topology of quantum computers, represented by another graph, call hardware graph. Existing methods for minor embedding require a significant amount of running time in a large-scale graph embedding. To overcome this problem, in this paper, we introduce a novel notion of adaptive topology which is an expandable subgraph of the hardware graph. From that, we develop a minor embedding algorithm, namely Adaptive TOpology eMbedding (ATOM). ATOM iteratively selects a node from the logical graph, and embeds it to the adaptive topology of the hardware graph. Our experimental results show that ATOM is able to provide a feasible embedding in much smaller running time than that of the state-of-the-art without compromising the quality of resulting embedding.

Cameras and image-editing software often process images in the wide-gamut ProPhoto color space, encompassing 90% of all visible colors. However, when images are encoded for sharing, this color-rich representation is transformed and clipped to fit within the small-gamut standard RGB (sRGB) color space, representing only 30% of visible colors. Recovering the lost color information is challenging due to the clipping procedure. Inspired by neural implicit representations for 2D images, we propose a method that optimizes a lightweight multi-layer-perceptron (MLP) model during the gamut reduction step to predict the clipped values. GamutMLP takes approximately 2 seconds to optimize and requires only 23 KB of storage. The small memory footprint allows our GamutMLP model to be saved as metadata in the sRGB image -- the model can be extracted when needed to restore wide-gamut color values. We demonstrate the effectiveness of our approach for color recovery and compare it with alternative strategies, including pre-trained DNN-based gamut expansion networks and other implicit neural representation methods. As part of this effort, we introduce a new color gamut dataset of 2200 wide-gamut/small-gamut images for training and testing. Our code and dataset can be found on the project website: https://gamut-mlp.github.io.

Target Identification by Enzymes (TIE) problem aims to identify the set of enzymes in a given metabolic network, such that their inhibition eliminates a given set of target compounds associated with a disease while incurring minimum damage to the rest of the compounds. This is an NP-complete problem, and thus optimal solutions using classical computers fail to scale to large metabolic networks. In this paper, we consider the TIE problem for identifying drug targets in metabolic networks. We develop the first quantum optimization solution, called QuTIE (Quantum optimization for Target Identification by Enzymes), to this NP-complete problem. We do that by developing an equivalent formulation of the TIE problem in Quadratic Unconstrained Binary Optimization (QUBO) form, then mapping it to a logical graph, which is then embedded on a hardware graph on a quantum computer. Our experimental results on 27 metabolic networks from Escherichia coli, Homo sapiens, and Mus musculus show that QuTIE yields solutions which are optimal or almost optimal. Our experiments also demonstrate that QuTIE can successfully identify enzyme targets already verified in wet-lab experiments for 14 major disease classes.

We study the problem of policy optimization (PO) with linear temporal logic (LTL) constraints. The language of LTL allows flexible description of tasks that may be unnatural to encode as a scalar cost function. We consider LTL-constrained PO as a systematic framework, decoupling task specification from policy selection, and as an alternative to the standard of cost shaping. With access to a generative model, we develop a model-based approach that enjoys a sample complexity analysis for guaranteeing both task satisfaction and cost optimality (through a reduction to a reachability problem). Empirically, our algorithm can achieve strong performance even in low-sample regimes.

Robust control is a core approach for controlling systems with performance guarantees that are robust to modeling error, and is widely used in real-world systems. However, current robust control approaches can only handle small system uncertainty, and thus require significant effort in system identification prior to controller design. We present an online approach that robustly controls a nonlinear system under large model uncertainty. Our approach is based on decomposing the problem into two sub-problems, "robust control design" (which assumes small model uncertainty) and "chasing consistent models", which can be solved using existing tools from control theory and online learning, respectively. We provide a learning convergence analysis that yields a finite mistake bound on the number of times performance requirements are not met and can provide strong safety guarantees, by bounding the worst-case state deviation. To the best of our knowledge, this is the first approach for online robust control of nonlinear systems with such learning theoretic and safety guarantees. We also show how to instantiate this framework for general robotic systems, demonstrating the practicality of our approach., Comment: 58 pages, 5 figures

We offer an experimental benchmark and empirical study for off-policy policy evaluation (OPE) in reinforcement learning, which is a key problem in many safety critical applications. Given the increasing interest in deploying learning-based methods, there has been a flurry of recent proposals for OPE method, leading to a need for standardized empirical analyses. Our work takes a strong focus on diversity of experimental design to enable stress testing of OPE methods. We provide a comprehensive benchmarking suite to study the interplay of different attributes on method performance. We distill the results into a summarized set of guidelines for OPE in practice. Our software package, the Caltech OPE Benchmarking Suite (COBS), is open-sourced and we invite interested researchers to further contribute to the benchmark.

We study the problem of programmatic reinforcement learning, in which policies are represented as short programs in a symbolic language. Programmatic policies can be more interpretable, generalizable, and amenable to formal verification than neural policies; however, designing rigorous learning approaches for such policies remains a challenge. Our approach to this challenge -- a meta-algorithm called PROPEL -- is based on three insights. First, we view our learning task as optimization in policy space, modulo the constraint that the desired policy has a programmatic representation, and solve this optimization problem using a form of mirror descent that takes a gradient step into the unconstrained policy space and then projects back onto the constrained space. Second, we view the unconstrained policy space as mixing neural and programmatic representations, which enables employing state-of-the-art deep policy gradient approaches. Third, we cast the projection step as program synthesis via imitation learning, and exploit contemporary combinatorial methods for this task. We present theoretical convergence results for PROPEL and empirically evaluate the approach in three continuous control domains. The experiments show that PROPEL can significantly outperform state-of-the-art approaches for learning programmatic policies., Comment: Published in Advances in Neural Information Processing Systems (NeurIPS) 2019

When learning policies for real-world domains, two important questions arise: (i) how to efficiently use pre-collected off-policy, non-optimal behavior data; and (ii) how to mediate among different competing objectives and constraints. We thus study the problem of batch policy learning under multiple constraints, and offer a systematic solution. We first propose a flexible meta-algorithm that admits any batch reinforcement learning and online learning procedure as subroutines. We then present a specific algorithmic instantiation and provide performance guarantees for the main objective and all constraints. To certify constraint satisfaction, we propose a new and simple method for off-policy policy evaluation (OPE) and derive PAC-style bounds. Our algorithm achieves strong empirical results in different domains, including in a challenging problem of simulated car driving subject to multiple constraints such as lane keeping and smooth driving. We also show experimentally that our OPE method outperforms other popular OPE techniques on a standalone basis, especially in a high-dimensional setting.

The goal of this paper is to understand the impact of learning on control synthesis from a Lyapunov function perspective. In particular, rather than consider uncertainties in the full system dynamics, we employ Control Lyapunov Functions (CLFs) as low-dimensional projections. To understand and characterize the uncertainty that these projected dynamics introduce in the system, we introduce a new notion: Projection to State Stability (PSS). PSS can be viewed as a variant of Input to State Stability defined on projected dynamics, and enables characterizing robustness of a CLF with respect to the data used to learn system uncertainties. We use PSS to bound uncertainty in affine control, and demonstrate that a practical episodic learning approach can use PSS to characterize uncertainty in the CLF for robust control synthesis.

Many modern nonlinear control methods aim to endow systems with guaranteed properties, such as stability or safety, and have been successfully applied to the domain of robotics. However, model uncertainty remains a persistent challenge, weakening theoretical guarantees and causing implementation failures on physical systems. This paper develops a machine learning framework centered around Control Lyapunov Functions (CLFs) to adapt to parametric uncertainty and unmodeled dynamics in general robotic systems. Our proposed method proceeds by iteratively updating estimates of Lyapunov function derivatives and improving controllers, ultimately yielding a stabilizing quadratic program model-based controller. We validate our approach on a planar Segway simulation, demonstrating substantial performance improvements by iteratively refining on a base model-free controller.

We study how to effectively leverage expert feedback to learn sequential decision-making policies. We focus on problems with sparse rewards and long time horizons, which typically pose significant challenges in reinforcement learning. We propose an algorithmic framework, called hierarchical guidance, that leverages the hierarchical structure of the underlying problem to integrate different modes of expert interaction. Our framework can incorporate different combinations of imitation learning (IL) and reinforcement learning (RL) at different levels, leading to dramatic reductions in both expert effort and cost of exploration. Using long-horizon benchmarks, including Montezuma's Revenge, we demonstrate that our approach can learn significantly faster than hierarchical RL, and be significantly more label-efficient than standard IL. We also theoretically analyze labeling cost for certain instantiations of our framework., Comment: Proceedings of the 35th International Conference on Machine Learning (ICML 2018)

We study the problem of imitation learning from demonstrations of multiple coordinating agents. One key challenge in this setting is that learning a good model of coordination can be difficult, since coordination is often implicit in the demonstrations and must be inferred as a latent variable. We propose a joint approach that simultaneously learns a latent coordination model along with the individual policies. In particular, our method integrates unsupervised structure learning with conventional imitation learning. We illustrate the power of our approach on a difficult problem of learning multiple policies for fine-grained behavior modeling in team sports, where different players occupy different roles in the coordinated team strategy. We show that having a coordination model to infer the roles of players yields substantially improved imitation loss compared to conventional baselines., Comment: International Conference on Machine Learning 2017

We study the problem of smooth imitation learning for online sequence prediction, where the goal is to train a policy that can smoothly imitate demonstrated behavior in a dynamic and continuous environment in response to online, sequential context input. Since the mapping from context to behavior is often complex, we take a learning reduction approach to reduce smooth imitation learning to a regression problem using complex function classes that are regularized to ensure smoothness. We present a learning meta-algorithm that achieves fast and stable convergence to a good policy. Our approach enjoys several attractive properties, including being fully deterministic, employing an adaptive learning rate that can provably yield larger policy improvements compared to previous approaches, and the ability to ensure stable convergence. Our empirical results demonstrate significant performance gains over previous approaches., Comment: ICML 2016