Enabling More Accurate and Efficient Structured Prediction

Machine learning practitioners often face a fundamental trade-off between expressiveness and computation time: on average, more accurate, expressive models tend to be more computationally intensive both at training and test time. While this trade-off is always applicable, it is acutely present in the setting of structured prediction, where the joint prediction of multiple output variables often creates two primary, inter-related bottlenecks: inference and feature computation time. In this thesis, we address this trade-off at test-time by presenting frameworks that enable more accurate and efficient structured prediction by addressing each of the bottlenecks specifically. First, we develop a framework based on a cascade of models, where the goal is to control test-time complexity even as features are added that increase inference time (even exponentially). We call this framework Structured Prediction Cascades (SPC); we develop SPC in the context of exact inference and then extend the framework to handle the approximate case. Next, we develop a framework for the setting where the feature computation is explicitly the bottleneck, in which we learn to selectively evaluate features within an instance of the mode. This second framework is referred to as Dynamic Structured Model Selection (DMS), and is once again developed for a simpler, restricted model before being extended to handle a much more complex setting. For both cases, we evaluate our methods on several benchmark datasets, and we find that it is possible to dramatically improve the efficiency and accuracy of structured prediction

Nonlinear Dynamic Systems Parameterization Using Interval-Based Global Optimization: Computing Lipschitz Constants and Beyond

Numerous state-feedback and observer designs for nonlinear dynamic systems (NDS) have been developed in the past three decades. These designs assume that NDS nonlinearities satisfy one of the following function set classifications: bounded Jacobian, Lipschitz continuity, one-sided Lipschitz, quadratic inner-boundedness, and quadratic boundedness. These function sets are characterized by constant scalars or matrices bounding the NDS' nonlinearities. These constants (i) depend on the NDS' operating region, topology, and parameters, and (ii) are utilized to synthesize observer/controller gains. Unfortunately, there is a near-complete absence of algorithms to compute such bounding constants. In this paper, we develop analytical then computational methods to compute such constants. First, for every function set classification, we derive analytical expressions for these bounding constants through global maximization formulations. Second, we utilize a derivative-free, interval-based global maximization algorithm based on branch-and-bound framework to numerically obtain the bounding constants. Third, we showcase the effectiveness of our approaches to compute the corresponding parameters on some NDS such as highway traffic networks and synchronous generator models.Comment: IEEE Transactions on Automatic Contro

Data-driven Invariance for Reference Governors

This paper presents a novel approach to synthesizing positive invariant sets for unmodeled nonlinear systems using direct data-driven techniques. The data-driven invariant sets are used to design a data-driven reference governor that selects a reference for the closed-loop system to enforce constraints. Using kernel-basis functions, we solve a semi-definite program to learn a sum-of-squares Lyapunov-like function whose unity level-set is a constraint admissible positive invariant set, which determines the constraint admissible states as well as reference inputs. Leveraging Lipschitz properties of the system, we prove that tightening the model-based design ensures robustness of the data-driven invariant set to the inherent plant uncertainty in a data-driven framework. To mitigate the curse-of-dimensionality, we repose the semi-definite program into a linear program. We validate our approach through two examples: First, we present an illustrative example where we can analytically compute the maximum positive invariant set and compare with the presented data-driven invariant set. Second, we present a practical autonomous driving scenario to demonstrate the utility of the presented method for nonlinear systems

Safety-Aware Learning-Based Control of Systems with Uncertainty Dependent Constraints (extended version)

The problem of safely learning and controlling a dynamical system - i.e., of stabilizing an originally (partially) unknown system while ensuring that it does not leave a prescribed 'safe set' - has recently received tremendous attention in the controls community. Further complexities arise, however, when the structure of the safe set itself depends on the unknown part of the system's dynamics. In particular, a popular approach based on control Lyapunov functions (CLF), control barrier functions (CBF) and Gaussian processes (to build confidence set around the unknown term), which has proved successful in the known-safe set setting, becomes inefficient as-is, due to the introduction of higher-order terms to be estimated and bounded with high probability using only system state measurements. In this paper, we build on the recent literature on GPs and reproducing kernels to perform this latter task, and show how to correspondingly modify the CLF-CBF-based approach to obtain safety guarantees. Namely, we derive exponential CLF and second relative order exponential CBF constraints whose satisfaction guarantees stability and forward in-variance of the partially unknown safe set with high probability. To overcome the intractability of verification of these conditions on the continuous domain, we apply discretization of the state space and use Lipschitz continuity properties of dynamics to derive equivalent CLF and CBF certificates in discrete state space. Finally, we present an algorithm for the control design aim using the derived certificates

Online Learning for the Control of Human Standing via Spinal Cord Stimulation

Many applications in recommender systems or experimental design need to make decisions online. Each decision leads to a stochastic reward with initially unknown distribution, while new decisions are made based on the observations of previous rewards. To maximize the total reward, one needs to balance between exploring different strategies and exploiting currently optimal strategies within a given set of strategies. This is the underlying trade-off of a number of clinical neural engineering problems, including brain-computer interface, deep brain stimulation, and spinal cord injury therapy. In these systems, complex electronic and computational systems interact with the human central nervous system. A critical issue is how to control the agents to produce results which are optimal under some measure, for example, efficiently decoding the user's intention in a brain-computer interface or performs temporal and spatial specific stimulation in deep brain stimulation. This dissertation is motivated by electrical sipnal cord stimulation with high dimensional inputs(multi-electrode arrays). The stimulation is applied to promote the function and rehabilitation of the remaining neural circuitry below the spinal cord injury, and enable complex motor behaviors such as stepping and standing. To enable the careful tuning of these stimuli for each patient, the electrode arrays which deliver these stimuli have become increasingly more sophisticated, with a corresponding increase in the number of free parameters over which the stimuli need to be optimized. Since the number of stimuli is growing exponentially with the number of electrodes, algorithmic methods of selecting stimuli is necessary, particularly when the feedback is expensive to get. In many online learning settings, particularly those that involve human feedback, reliable feedback is often limited to pairwise preferences instead of real valued feedback. Examples include implicit or subjective feedback for information retrieval and recommender systems, such as clicks on search results, and subjective feedback on the quality of recommended care. Sometimes with real valued feedback, we require that the sampled function values exceed some prespecified ``safety'' threshold, a requirement that existing algorithms fail to meet. Examples include medical applications where the patients' comfort must be guaranteed; recommender systems aiming to avoid user dissatisfaction; and robotic control, where one seeks to avoid controls that cause physical harm to the platform. This dissertation provides online learning algorithms for several specific online decision-making problems. \selfsparring optimizes the cumulative reward with relative feedback. RankComparison deals with ranking feedback. \safeopt considers the optimization with real valued feedback and safety constraints. \cduel is designed for specific spinal cord injury therapy. A variant of \cduel was implemented in closed-loop human experiments, controlling which epidural stimulating electrodes are used in the spinal cord of SCI patients. The results obtained are compared with concurrent stimulus tuning carried out by human experimenter. These experiments show that this algorithm is at least as effective as the human experimenter, suggesting that this algorithm can be applied to the more challenging problems of enabling and optimizing complex, sensory-dependent behaviors, such as stepping and standing in SCI patients. In order to get reliable quantitative measurements besides comparisons, the standing behaviors of paralyzed patients under spinal cord stimulation are evaluated. The potential of quantifying the quality of bipedal standing in an automatic approach is also shown in this work.</p