Hierarchical Decomposition of Nonlinear Dynamics and Control for System Identification and Policy Distillation

The control of nonlinear dynamical systems remains a major challenge for autonomous agents. Current trends in reinforcement learning (RL) focus on complex representations of dynamics and policies, which have yielded impressive results in solving a variety of hard control tasks. However, this new sophistication and extremely over-parameterized models have come with the cost of an overall reduction in our ability to interpret the resulting policies. In this paper, we take inspiration from the control community and apply the principles of hybrid switching systems in order to break down complex dynamics into simpler components. We exploit the rich representational power of probabilistic graphical models and derive an expectation-maximization (EM) algorithm for learning a sequence model to capture the temporal structure of the data and automatically decompose nonlinear dynamics into stochastic switching linear dynamical systems. Moreover, we show how this framework of switching models enables extracting hierarchies of Markovian and auto-regressive locally linear controllers from nonlinear experts in an imitation learning scenario.Comment: 2nd Annual Conference on Learning for Dynamics and Contro

Variational Gaussian filtering via Wasserstein gradient flows

In this article, we present a variational approach to Gaussian and mixture-of-Gaussians assumed filtering. Our method relies on an approximation stemming from the gradient-flow representations of a Kullback--Leibler discrepancy minimization. We outline the general method and show its competitiveness in parameter estimation and posterior representation for two models for which Gaussian approximations typically fail: a multiplicative noise and a multi-modal model.Comment: 5 pages, 2 figures, double colum

Model-Based Reinforcement Learning for Stochastic Hybrid Systems

Optimal control of general nonlinear systems is a central challenge in automation. Enabled by powerful function approximators, data-driven approaches to control have recently successfully tackled challenging robotic applications. However, such methods often obscure the structure of dynamics and control behind black-box over-parameterized representations, thus limiting our ability to understand closed-loop behavior. This paper adopts a hybrid-system view of nonlinear modeling and control that lends an explicit hierarchical structure to the problem and breaks down complex dynamics into simpler localized units. We consider a sequence modeling paradigm that captures the temporal structure of the data and derive an expectation-maximization (EM) algorithm that automatically decomposes nonlinear dynamics into stochastic piecewise affine dynamical systems with nonlinear boundaries. Furthermore, we show that these time-series models naturally admit a closed-loop extension that we use to extract local polynomial feedback controllers from nonlinear experts via behavioral cloning. Finally, we introduce a novel hybrid relative entropy policy search (Hb-REPS) technique that incorporates the hierarchical nature of hybrid systems and optimizes a set of time-invariant local feedback controllers derived from a local polynomial approximation of a global state-value function

Statistical Machine Learning for Modeling and Control of Stochastic Structured Systems

Machine learning and its various applications have driven innovation in robotics, synthetic perception, and data analytics. The last decade especially has experienced an explosion in interest in the research and development of artificial intelligence with successful adoption and deployment in some domains. A significant force behind these advances has been an abundance of data and the evolution of simple computational models and tools with a capacity to scale up to massive learning automata. Monolithic neural networks with billions of parameters that rely on automatic differentiation are a prime example of the significant role efficient computation has had on supercharging the ability of well-established representations to extract intelligent patterns from unstructured data. Nonetheless, despite the strides taken in the digital domains of vision and natural language processing, applications of optimal control and robotics significantly trail behind and have not been able to capitalize as much on the latest trends of machine learning. This discrepancy can be explained by the limited transferability of learning concepts that rely on full differentiability to the heavily structured physical and human interaction environments, not to mention the substantial cost of data generation on real physical systems. Therefore, these factors severely limit the application scope of loosely-structured over-parameterized data-crunching machines in the mechanical realm of robot learning and control. This thesis investigates modeling paradigms of hierarchical and switching systems to tackle some of the previously highlighted issues. This research direction is motivated by insights into universal function approximation via local cooperating units and the promise of inherently regularized representations through explicit structural design. Moreover, we explore ideas from robust optimization that address model mismatch issues in statistical models and outline how related methods may be used to improve the tractability of state filtering in stochastic hybrid systems. In Chapter 2, we consider hierarchical modeling for general regression problems. The presented approach is a generative probabilistic interpretation of local regression techniques that approximate nonlinear functions through a set of local linear or polynomial units. The number of available units is crucial in such models, as it directly balances representational power with the parametric complexity. This ambiguity is addressed by using principles from Bayesian nonparametrics to formulate flexible models that adapt their complexity to the data and can potentially encompass an infinite number of components. To learn these representations, we present two efficient variational inference techniques that scale well with data and highlight the advantages of hierarchical infinite local regression models, such as dealing with non-smooth functions, mitigating catastrophic forgetting, and enabling parameter sharing and fast predictions. Finally, we validate this approach on a set of large inverse dynamics datasets and test the learned models in real-world control scenarios. Chapter 3 addresses discrete-continuous hybrid modeling and control for stochastic dynamical systems, which implies dealing with time-series data. In this scenario, we develop an automatic system identification technique that decomposes nonlinear systems into hybrid automata and leverages the resulting structure to learn switching feedback control via hierarchical reinforcement learning. In the process, we rely on an augmented closed-loop hidden Markov model architecture that captures time correlations over long horizons and provides a principled Bayesian inference framework for learning hybrid representations and filtering the hidden discrete states to apply control accordingly. Finally, we embed this structure explicitly into a novel hybrid relative entropy policy search algorithm that optimizes a set of local polynomial feedback controllers and value functions. We validate the overall switching-system perspective by benchmarking the open-loop predictive performance against popular black-box representations. We also provide qualitative empirical results for hybrid reinforcement learning on common nonlinear control tasks. In Chapter 4, we attend to a general and fundamental problem in learning for control, namely robustness in data-driven stochastic optimization. The question of sensitivity has a strong priority, given the rising popularity of embedding statistical models into stochastic control frameworks. However, data from dynamical, especially mechanical, systems is often scarce due to a high extraction cost and limited coverage of the state-action space. The result is usually poor models with narrow validity and brittle control laws, particularly in an ill-posed over-parameterized learning example. We propose to robustify stochastic control by finding the worst-case distribution over the dynamics and optimizing a corresponding robust policy that minimizes the probability of catastrophic failures. We achieve this goal by formulating a two-stage iterative minimax optimization problem that finds the most pessimistic adversary in a trust region around a nominal model and uses it to optimize a robust optimal controller. We test this approach on a set of linear and nonlinear stochastic systems and supply empirical evidence of its practicality. Finally, we provide an outlook on how similar multi-stage distributional optimization techniques can be applied in approximate filtering of stochastic switching systems in order to tackle the issue of exponential explosion in state mixture components. In summation, the individual contributions of this thesis are a collection of interconnected principles for structured and robust learning for control. Although many challenges remain ahead, this research lays a foundation for reflecting on future structured learning questions that strive to combine optimal control and statistical machine learning perspectives for the automatic decomposition and optimization of hierarchical models

State-regularized policy search for linearized dynamical systems

Trajectory-Centric Reinforcement Learning and Trajectory Optimization methods optimize a sequence of feedbackcontrollers by taking advantage of local approximations of model dynamics and cost functions. Stability of the policy update is a major issue for these methods, rendering them hard to apply for highly nonlinear systems. Recent approaches combine classical Stochastic Optimal Control methods with information-theoretic bounds to control the step-size of the policy update and could even be used to train nonlinear deep control policies. These methods bound the relative entropy between the new and the old policy to ensure a stable policy update. However, despite the bound in policy space, the state distributions of two consecutive policies can still differ significantly, rendering the used local approximate models invalid. To alleviate this issue we propose enforcing a relative entropy constraint not only on the policy update, but also on the update of the state distribution, around which the dynamics and cost are being approximated. We present a derivation of the closed-form policy update and show that our approach outperforms related methods on two nonlinear and highly dynamic simulated systems