arXiv subjects

Evangelos Theodorou

Publications and source records attributed to Evangelos Theodorou.

29 records · Page 2Linked to original sources

arXiv2018

Model-Based Stochastic Search for Large Scale Optimization of Multi-Agent UAV Swarms

Recent work from the reinforcement learning community has shown that Evolution Strategies are a fast and scalable alternative to other reinforcement learning methods. In this paper we show that Evolution Strategies are a special case of model-based stochastic search methods. This class of algorithms has nice asymptotic convergence properties and known convergence rates. We show how these methods can be used to solve both cooperative and competitive multi-agent problems in an efficient manner. We demonstrate the effectiveness of this approach on two complex multi-agent UAV swarm combat scenarios: where a team of fixed wing aircraft must attack a well-defended base, and where two teams of agents go head to head to defeat each other.

cs.MA↗

arXiv2018

Propagating Uncertainty through the tanh Function with Application to Reservoir Computing

Many neural networks use the tanh activation function, however when given a probability distribution as input, the problem of computing the output distribution in neural networks with tanh activation has not yet been addressed. One important example is the initialization of the echo state network in reservoir computing, where random initialization of the reservoir requires time to wash out the initial conditions, thereby wasting precious data and computational resources. Motivated by this problem, we propose a novel solution utilizing a moment based approach to propagate uncertainty through an Echo State Network to reduce the washout time. In this work, we contribute two new methods to propagate uncertainty through the tanh activation function and propose the Probabilistic Echo State Network (PESN), a method that is shown to have better average performance than deterministic Echo State Networks given the random initialization of reservoir states. Additionally we test single and multi-step uncertainty propagation of our method on two regression tasks and show that we are able to recover similar means and variances as computed by Monte-Carlo simulations.

stat.ML↗

arXiv2018

A Stochastic Differential Equation Framework for Guiding Online User Activities in Closed Loop

Recently, there is a surge of interest in using point processes to model continuous-time user activities. This framework has resulted in novel models and improved performance in diverse applications. However, most previous works focus on the "open loop" setting where learned models are used for predictive tasks. Typically, we are interested in the "closed loop" setting where a policy needs to be learned to incorporate user feedbacks and guide user activities to desirable states. Although point processes have good predictive performance, it is not clear how to use them for the challenging closed loop activity guiding task. In this paper, we propose a framework to reformulate point processes into stochastic differential equations, which allows us to extend methods from stochastic optimal control to address the activity guiding problem. We also design an efficient algorithm, and show that our method guides user activities to desired states more effectively than the state of the art.

cs.SI↗

arXiv2018

MPC-Inspired Neural Network Policies for Sequential Decision Making

In this paper we investigate the use of MPC-inspired neural network policies for sequential decision making. We introduce an extension to the DAgger algorithm for training such policies and show how they have improved training performance and generalization capabilities. We take advantage of this extension to show scalable and efficient training of complex planning policy architectures in continuous state and action spaces. We provide an extensive comparison of neural network policies by considering feed forward policies, recurrent policies, and recurrent policies with planning structure inspired by the Path Integral control framework. Our results suggest that MPC-type recurrent policies have better robustness to disturbances and modeling error.

cs.LG↗

arXiv2017

Variational Policy for Guiding Point Processes

Temporal point processes have been widely applied to model event sequence data generated by online users. In this paper, we consider the problem of how to design the optimal control policy for point processes, such that the stochastic system driven by the point process is steered to a target state. In particular, we exploit the key insight to view the stochastic optimal control problem from the perspective of optimal measure and variational inference. We further propose a convex optimization framework and an efficient algorithm to update the policy adaptively to the current system state. Experiments on synthetic and real-world data show that our algorithm can steer the user activities much more accurately and efficiently than other stochastic control methods.

cs.LG↗

arXiv2017

Pseudospectral Model Predictive Control under Partially Learned Dynamics

Trajectory optimization of a controlled dynamical system is an essential part of autonomy, however many trajectory optimization techniques are limited by the fidelity of the underlying parametric model. In the field of robotics, a lack of model knowledge can be overcome with machine learning techniques, utilizing measurements to build a dynamical model from the data. This paper aims to take the middle ground between these two approaches by introducing a semi-parametric representation of the underlying system dynamics. Our goal is to leverage the considerable information contained in a traditional physics based model and combine it with a data-driven, non-parametric regression technique known as a Gaussian Process. Integrating this semi-parametric model with model predictive pseudospectral control, we demonstrate this technique on both a cart pole and quadrotor simulation with unmodeled damping and parametric error. In order to manage parametric uncertainty, we introduce an algorithm that utilizes Sparse Spectrum Gaussian Processes (SSGP) for online learning after each rollout. We implement this online learning technique on a cart pole and quadrator, then demonstrate the use of online learning and obstacle avoidance for the dubin vehicle dynamics.

eess.SY↗

arXiv2016

Adaptive Probabilistic Trajectory Optimization via Efficient Approximate Inference

Robotic systems must be able to quickly and robustly make decisions when operating in uncertain and dynamic environments. While Reinforcement Learning (RL) can be used to compute optimal policies with little prior knowledge about the environment, it suffers from slow convergence. An alternative approach is Model Predictive Control (MPC), which optimizes policies quickly, but also requires accurate models of the system dynamics and environment. In this paper we propose a new approach, adaptive probabilistic trajectory optimization, that combines the benefits of RL and MPC. Our method uses scalable approximate inference to learn and updates probabilistic models in an online incremental fashion while also computing optimal control policies via successive local approximations. We present two variations of our algorithm based on the Sparse Spectrum Gaussian Process (SSGP) model, and we test our algorithm on three learning tasks, demonstrating the effectiveness and efficiency of our approach.

cs.RO↗

arXiv2016

Nonparametric Infinite Horizon Kullback-Leibler Stochastic Control

We present two nonparametric approaches to Kullback-Leibler (KL) control, or linearly-solvable Markov decision problem (LMDP) based on Gaussian processes (GP) and Nyström approximation. Compared to recently developed parametric methods, the proposed data-driven frameworks feature accurate function approximation and efficient on-line operations. Theoretically, we derive the mathematical connection of KL control based on dynamic programming with earlier work in control theory which relies on information theoretic dualities for the infinite time horizon case. Algorithmically, we give explicit optimal control policies in nonparametric forms, and propose on-line update schemes with budgeted computational costs. Numerical results demonstrate the effectiveness and usefulness of the proposed frameworks.

eess.SY↗

arXiv2015

Model Predictive Path Integral Control using Covariance Variable Importance Sampling

In this paper we develop a Model Predictive Path Integral (MPPI) control algorithm based on a generalized importance sampling scheme and perform parallel optimization via sampling using a Graphics Processing Unit (GPU). The proposed generalized importance sampling scheme allows for changes in the drift and diffusion terms of stochastic diffusion processes and plays a significant role in the performance of the model predictive control algorithm. We compare the proposed algorithm in simulation with a model predictive control version of differential dynamic programming.

eess.SY↗

arXiv2015

Model Based Reinforcement Learning with Final Time Horizon Optimization

We present one of the first algorithms on model based reinforcement learning and trajectory optimization with free final time horizon. Grounded on the optimal control theory and Dynamic Programming, we derive a set of backward differential equations that propagate the value function and provide the optimal control policy and the optimal time horizon. The resulting policy generalizes previous results in model based trajectory optimization. Our analysis shows that the proposed algorithm recovers the theoretical optimal solution on linear low dimensional problem. Finally we provide application results on nonlinear systems.

eess.SY↗

arXiv2014

Information-Theoretic Stochastic Optimal Control via Incremental Sampling-based Algorithms

This paper considers optimal control of dynamical systems which are represented by nonlinear stochastic differential equations. It is well-known that the optimal control policy for this problem can be obtained as a function of a value function that satisfies a nonlinear partial differential equation, namely, the Hamilton-Jacobi-Bellman equation. This nonlinear PDE must be solved backwards in time, and this computation is intractable for large scale systems. Under certain assumptions, and after applying a logarithmic transformation, an alternative characterization of the optimal policy can be given in terms of a path integral. Path Integral (PI) based control methods have recently been shown to provide elegant solutions to a broad class of stochastic optimal control problems. One of the implementation challenges with this formalism is the computation of the expectation of a cost functional over the trajectories of the unforced dynamics. Computing such expectation over trajectories that are sampled uniformly may induce numerical instabilities due to the exponentiation of the cost. Therefore, sampling of low-cost trajectories is essential for the practical implementation of PI-based methods. In this paper, we use incremental sampling-based algorithms to sample useful trajectories from the unforced system dynamics, and make a novel connection between Rapidly-exploring Random Trees (RRTs) and information-theoretic stochastic optimal control. We show the results from the numerical implementation of the proposed approach to several examples.

cs.RO↗