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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.

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.

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 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.

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

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 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.

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.

Off-policy policy evaluation (OPE) is the problem of estimating the online performance of a policy using only pre-collected historical data generated by another policy. Given the increasing interest in deploying learning-based methods for safety-critical applications, many recent OPE methods have recently been proposed. Due to disparate experimental conditions from recent literature, the relative performance of current OPE methods is not well understood. In this work, we present the first comprehensive empirical analysis of a broad suite of OPE methods. Based on thousands of experiments and detailed empirical analyses, we offer a summarized set of guidelines for effectively using OPE in practice, and suggest directions for future research.

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)

Cancer is a major cause of death in children worldwide, and the recorded incidence tends to increase with time. Internationally comparable data on childhood cancer incidence in the past two decades are scarce. This study aimed to provide internationally comparable local data on the incidence of childhood cancer to promote research of causes and implementation of childhood cancer control. This population-based registry study, devised by the International Agency for Research on Cancer in collaboration with the International Association of Cancer Registries, collected data on all malignancies and non-malignant neoplasms of the CNS diagnosed before age 20 years in populations covered by high-quality cancer registries with complete data for 2001-10. Incidence rates per million person-years for the 0-14 years and 0-19 years age groups were age-adjusted using the world standard population to provide age-standardised incidence rates (WSRs), using the age-specific incidence rates (ASR) for individual age groups (0-4 years, 5-9 years, 10-14 years, and 15-19 years). All rates were reported for 19 geographical areas or ethnicities by sex, age group, and cancer type. The regional WSRs for children aged 0-14 years were compared with comparable data obtained in the 1980s. Of 532 invited cancer registries, 153 registries from 62 countries, departments, and territories met quality standards, and contributed data for the entire decade of 2001-10. 385 509 incident cases in children aged 0-19 years occurring in 2·64 billion person-years were included. The overall WSR was 140·6 per million person-years in children aged 0-14 years (based on 284 649 cases), and the most common cancers were leukaemia (WSR 46·4), followed by CNS tumours (WSR 28·2), and lymphomas (WSR 15·2). In children aged 15-19 years (based on 100 860 cases), the ASR was 185·3 per million person-years, the most common being lymphomas (ASR 41·8) and the group of epithelial tumours and melanoma (ASR 39·5). Incidence varied

Current state-of-the-art sports metrics such as “Wins-above-Replacement” in baseball, “Expected Point Value” in basketball, and “Expected Goal Value” in soccer and hockey are now commonplace in performance analysis. These measures have enhanced our ability to compare and value performance in sport. But they are inherently limited because they are tied to a discrete outcome of a specific event. With the widespread (and growing) availability of player and ball tracking data comes the potential to quantitatively analyze and compare fine-grain movement patterns. An excellent example of this was the “ghosting” system developed by the Toronto Raptors to analyze player decision-making in STATS SportVU tracking data. Specifically, the Raptors created software to predict what a defensive player should have done instead of what they actually did. Motivated by the original “ghosting” work, we showcase an automatic “data-driven ghosting” method using advanced machine learning methodologies called “deep imitation learning”, applied to a season’s worth of tracking data from a recent professional league in soccer. Our ghosting method, which avoids substantial manual human annotation, results in a data-driven system that allows us to answer the question “how should this player or team have played in a given game situation compare to the league average?”. In addition, by “fine-tuning” our league average model to the tracking data from a particular team, our ghosting technique can estimate how each team might have approached the situation. Our method enables counterfactual analysis of effectiveness of defensive positioning as both a measurable and viewable quantity for the first time.

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 online prediction for realtime camera planning, where the goal is to predict smooth trajectories that correctly track and frame objects of interest (e.g., players in a basketball game). The conventional approach for training predictors does not directly consider temporal consistency, and often produces undesirable jitter. Although post-hoc smoothing (e.g., via a Kalman filter) can mitigate this issue to some degree, it is not ideal due to overly stringent modeling assumptions (e.g., Gaussian noise). We propose a recurrent decision tree framework that can directly incorporate temporal consistency into a data-driven predictor, as well as a learning algorithm that can efficiently learn such temporally smooth models. Our approach does not require any post-processing, making online smooth predictions much easier to generate when the noise model is unknown. We apply our approach to sports broadcasting: given noisy player detections, we learn where the camera should look based on human demonstrations. Our experiments exhibit significant improvements over conventional baselines and showcase the practicality of our approach.

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

In this paper we present a formal verification approach for abstract SystemC models. The approach allows checking expressive properties and lifts induction known from bounded model checking to a higher level, to cope with the large state space of abstract SystemC programs. The technique is tightly integrated with our SystemC to C transformation and generation of monitoring logic to form a complete and efficient method. Properties specifying both hardware and software aspects, e.g. pre- and post-conditions as well as temporal relations of transactions and events, can be specified. As shown by experiments modern proof techniques allow verifying important non-trivial behavior. Moreover, our inductive technique gives significant speed-ups in comparison to simple methods.

In this paper we present a formal verification approach for abstract SystemC models. The approach allows checking expressive properties and lifts induction known from bounded model checking to a higher level, to cope with the large state space of abstract SystemC programs. The technique is tightly integrated with our SystemC to C transformation and generation of monitoring logic to form a complete and efficient method. Properties specifying both hardware and software aspects, e.g. pre- and post-conditions as well as temporal relations of transactions and events, can be specified. As shown by experiments modern proof techniques allow verifying important non-trivial behavior. Moreover, our inductive technique gives significant speed-ups in comparison to simple methods.