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Register a new userScalable Identification of Partially Observed Systems with Certainty-Equivalent EM
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Added by
Jayesh Gupta
Publication date
2020
fields
Informatics Engineering
and research's language is
English
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System identification is a key step for model-based control, estimator design, and output prediction. This work considers the offline identification of partially observed nonlinear systems. We empirically show that the certainty-equivalent approximation to expectation-maximization can be a reliable and scalable approach for high-dimensional deterministic systems, which are common in robotics. We formulate certainty-equivalent expectation-maximization as block coordinate-ascent, and provide an efficient implementation. The algorithm is tested on a simulated system of coupled Lorenz attractors, demonstrating its ability to identify high-dimensional systems that can be intractable for particle-based approaches. Our approach is also used to identify the dynamics of an aerobatic helicopter. By augmenting the state with unobserved fluid states, a model is learned that predicts the acceleration of the helicopter better than state-of-the-art approaches. The codebase for this work is available at https://github.com/sisl/CEEM.
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In order to certify performance and safety, feedback control requires precise characterization of sensor errors. In this paper, we provide guarantees on such feedback systems when sensors are characterized by solving a supervised learning problem. We show a uniform error bound on nonparametric kernel regression under a dynamically-achievable dense sampling scheme. This allows for a finite-time convergence rate on the sub-optimality of using the regressor in closed-loop for waypoint tracking. We demonstrate our results in simulation with simplified unmanned aerial vehicle and autonomous driving examples.
We present a new method of learning control policies that successfully operate under unknown dynamic models. We create such policies by leveraging a large number of training examples that are generated using a physical simulator. Our system is made of two components: a Universal Policy (UP) and a function for Online System Identification (OSI). We describe our control policy as universal because it is trained over a wide array of dynamic models. These variations in the dynamic model may include differences in mass and inertia of the robots components, variable friction coefficients, or unknown mass of an object to be manipulated. By training the Universal Policy with this variation, the control policy is prepared for a wider array of possible conditions when executed in an unknown environment. The second part of our system uses the recent state and action history of the system to predict the dynamics model parameters mu. The value of mu from the Online System Identification is then provided as input to the control policy (along with the system state). Together, UP-OSI is a robust control policy that can be used across a wide range of dynamic models, and that is also responsive to sudden changes in the environment. We have evaluated the performance of this system on a variety of tasks, including the problem of cart-pole swing-up, the double inverted pendulum, locomotion of a hopper, and block-throwing of a manipulator. UP-OSI is effective at these tasks across a wide range of dynamic models. Moreover, when tested with dynamic models outside of the training range, UP-OSI outperforms the Universal Policy alone, even when UP is given the actual value of the model dynamics. In addition to the benefits of creating more robust controllers, UP-OSI also holds out promise of narrowing the Reality Gap between simulated and real physical systems.
In this work, we study the problem of learning partially observed linear dynamical systems from a single sample trajectory. A major practical challenge in the existing system identification methods is the undesirable dependency of their required sample size on the system dimension: roughly speaking, they presume and rely on sample sizes that scale linearly with respect to the system dimension. Evidently, in high-dimensional regime where the system dimension is large, it may be costly, if not impossible, to collect as many samples from the unknown system. In this paper, we will remedy this undesirable dependency on the system dimension by introducing an $ell_1$-regularized estimation method that can accurately estimate the Markov parameters of the system, provided that the number of samples scale logarithmically with the system dimension. Our result significantly improves the sample complexity of learning partially observed linear dynamical systems: it shows that the Markov parameters of the system can be learned in the high-dimensional setting, where the number of samples is significantly smaller than the system dimension. Traditionally, the $ell_1$-regularized estimators have been used to promote sparsity in the estimated parameters. By resorting to the notion of weak sparsity, we show that, irrespective of the true sparsity of the system, a similar regularized estimator can be used to reduce the sample complexity of learning partially observed linear systems, provided that the true system is inherently stable.
Applications from finance to epidemiology and cyber-security require accurate forecasts of dynamic phenomena, which are often only partially observed. We demonstrate that a systems predictability degrades as a function of temporal sampling, regardless of the adopted forecasting model. We quantify the loss of predictability due to sampling, and show that it cannot be recovered by using external signals. We validate the generality of our theoretical findings in real-world partially observed systems representing infectious disease outbreaks, online discussions, and software development projects. On a variety of prediction tasks---forecasting new infections, the popularity of topics in online discussions, or interest in cryptocurrency projects---predictability irrecoverably decays as a function of sampling, unveiling fundamental predictability limits in partially observed systems.
We propose a theoretical framework for approximate planning and learning in partially observed systems. Our framework is based on the fundamental notion of information state. We provide two equivalent definitions of information state -- i) a function of history which is sufficient to compute the expected reward and predict its next value; ii) equivalently, a function of the history which can be recursively updated and is sufficient to compute the expected reward and predict the next observation. An information state always leads to a dynamic programming decomposition. Our key result is to show that if a function of the history (called approximate information state (AIS)) approximately satisfies the properties of the information state, then there is a corresponding approximate dynamic program. We show that the policy computed using this is approximately optimal with bounded loss of optimality. We show that several approximations in state, observation and action spaces in literature can be viewed as instances of AIS. In some of these cases, we obtain tighter bounds. A salient feature of AIS is that it can be learnt from data. We present AIS based multi-time scale policy gradient algorithms. and detailed numerical experiments with low, moderate and high dimensional environments.
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