Robust policy updates for stochastic optimal control

For controlling high-dimensional robots, most stochastic optimal control algorithms use approximations of the system dynamics and of the cost function (e.g., using linearizations and Taylor expansions). These approximations are typically only locally correct, which might cause instabilities in the greedy policy updates, lead to oscillations or the algorithms diverge. To overcome these drawbacks, we add a regularization term to the cost function that punishes large policy update steps in the trajectory optimization procedure. We applied this concept to the Approximate Inference Control method (AICO), where the resulting algorithm guarantees convergence for uninformative initial solutions without complex hand-tuning of learning rates. We evaluated our new algorithm on two simulated robotic platforms. A robot arm with five joints was used for reaching multiple targets while keeping the roll angle constant. On the humanoid robot Nao, we show how complex skills like reaching and balancing can be inferred from desired center of gravity or end effector coordinates

Generalizing movements with information-theoretic stochastic optimal control

Stochastic optimal control is typically used to plan a movement for a specific situation. Although most stochastic optimal control methods fail to generalize this movement plan to a new situation without replanning, a stochastic optimal control method is presented that allows reuse of the obtained policy in a new situation, as the policy is more robust to slight deviations from the initial movement plan. To improve the robustness of the policy, we employ information-theoretic policy updates that explicitly operate on trajectory distributions instead of single trajectories. To ensure a stable and smooth policy update, the ”distance” is limited between the trajectory distributions of the old and the new control policies. The introduced bound offers a closed-form solution for the resulting policy and extends results from recent developments in stochastic optimal control. In contrast to many standard stochastic optimal control algorithms, the current approach can directly infer the system dynamics from data points, and hence can also be used for model-based reinforcement learning. This paper represents an extension of the paper by Lioutikov et al. (“Sample-Based Information-Theoretic Stochastic Optimal Control,” Proceedings of 2014 IEEE International Conference on Robotics and Automation (ICRA), IEEE, Piscataway, NJ, 2014, pp. 3896–3902). In addition to revisiting the content, an extensive theoretical comparison is presented of the approach with related work, additional aspects of the implementation are discussed, and further evaluations are introduced

Decentralized Delay Optimal Control for Interference Networks with Limited Renewable Energy Storage

In this paper, we consider delay minimization for interference networks with renewable energy source, where the transmission power of a node comes from both the conventional utility power (AC power) and the renewable energy source. We assume the transmission power of each node is a function of the local channel state, local data queue state and local energy queue state only. In turn, we consider two delay optimization formulations, namely the decentralized partially observable Markov decision process (DEC-POMDP) and Non-cooperative partially observable stochastic game (POSG). In DEC-POMDP formulation, we derive a decentralized online learning algorithm to determine the control actions and Lagrangian multipliers (LMs) simultaneously, based on the policy gradient approach. Under some mild technical conditions, the proposed decentralized policy gradient algorithm converges almost surely to a local optimal solution. On the other hand, in the non-cooperative POSG formulation, the transmitter nodes are non-cooperative. We extend the decentralized policy gradient solution and establish the technical proof for almost-sure convergence of the learning algorithms. In both cases, the solutions are very robust to model variations. Finally, the delay performance of the proposed solutions are compared with conventional baseline schemes for interference networks and it is illustrated that substantial delay performance gain and energy savings can be achieved

Data-driven Economic NMPC using Reinforcement Learning

Reinforcement Learning (RL) is a powerful tool to perform data-driven optimal control without relying on a model of the system. However, RL struggles to provide hard guarantees on the behavior of the resulting control scheme. In contrast, Nonlinear Model Predictive Control (NMPC) and Economic NMPC (ENMPC) are standard tools for the closed-loop optimal control of complex systems with constraints and limitations, and benefit from a rich theory to assess their closed-loop behavior. Unfortunately, the performance of (E)NMPC hinges on the quality of the model underlying the control scheme. In this paper, we show that an (E)NMPC scheme can be tuned to deliver the optimal policy of the real system even when using a wrong model. This result also holds for real systems having stochastic dynamics. This entails that ENMPC can be used as a new type of function approximator within RL. Furthermore, we investigate our results in the context of ENMPC and formally connect them to the concept of dissipativity, which is central for the ENMPC stability. Finally, we detail how these results can be used to deploy classic RL tools for tuning (E)NMPC schemes. We apply these tools on both a classical linear MPC setting and a standard nonlinear example from the ENMPC literature

Anytime Point-Based Approximations for Large POMDPs

The Partially Observable Markov Decision Process has long been recognized as a rich framework for real-world planning and control problems, especially in robotics. However exact solutions in this framework are typically computationally intractable for all but the smallest problems. A well-known technique for speeding up POMDP solving involves performing value backups at specific belief points, rather than over the entire belief simplex. The efficiency of this approach, however, depends greatly on the selection of points. This paper presents a set of novel techniques for selecting informative belief points which work well in practice. The point selection procedure is combined with point-based value backups to form an effective anytime POMDP algorithm called Point-Based Value Iteration (PBVI). The first aim of this paper is to introduce this algorithm and present a theoretical analysis justifying the choice of belief selection technique. The second aim of this paper is to provide a thorough empirical comparison between PBVI and other state-of-the-art POMDP methods, in particular the Perseus algorithm, in an effort to highlight their similarities and differences. Evaluation is performed using both standard POMDP domains and realistic robotic tasks