Karthikeya S. Parunandi

Karthikeya S Parunandi, Suman Chakravorty

Traditional stochastic optimal control methods that attempt to obtain an optimal feedback policy for nonlinear systems are computationally intractable. In this paper, we derive a decoupling principle between the open loop plan, and the closed loop feedback gains, that leads to a perturbation feedback control based solution to optimal control problems under action uncertainty, that is near-optimal to the third order. Extensive numerical simulations validate the theory, revealing a wide range of applicability, coping with medium levels of noise. The performance is compared with Nonlinear Model Predictive Control in several difficult robotic planning and control examples that show near identical performance to NMPC while requiring much lesser computational effort. It also leads us to raise the bigger question as to why NMPC should be used in robotic control as opposed to perturbation feedback approaches.

Ran Wang, Karthikeya S. Parunandi, Aayushman Sharma et al.

The problem of Reinforcement Learning (RL) in an unknown nonlinear dynamical system is equivalent to the search for an optimal feedback law utilizing the simulations/ rollouts of the dynamical system. Most RL techniques search over a complex global nonlinear feedback parametrization making them suffer from high training times as well as variance. Instead, we advocate searching over a local feedback representation consisting of an open-loop sequence, and an associated optimal linear feedback law completely determined by the open-loop. We show that this alternate approach results in highly efficient training, the answers obtained are repeatable and hence reliable, and the resulting closed performance is superior to global state-of-the-art RL techniques. Finally, if we replan, whenever required, which is feasible due to the fast and reliable local solution, it allows us to recover global optimality of the resulting feedback law.

Karthikeya S Parunandi, Aayushman Sharma, Suman Chakravorty et al.

In this paper, we propose a structured linear parameterization of a feedback policy to solve the model-free stochastic optimal control problem. This parametrization is corroborated by a decoupling principle that is shown to be near-optimal under a small noise assumption, both in theory and by empirical analyses. Further, we incorporate a model-free version of the Iterative Linear Quadratic Regulator (ILQR) in a sample-efficient manner into our framework. Simulations on systems over a range of complexities reveal that the resulting algorithm is able to harness the superior second-order convergence properties of ILQR. As a result, it is fast and is scalable to a wide variety of higher dimensional systems. Comparisons are made with a state-of-the-art reinforcement learning algorithm, the Deep Deterministic Policy Gradient (DDPG) technique, in order to demonstrate the significant merits of our approach in terms of training-efficiency.

Ran Wang, Karthikeya Parunandi, Dan Yu et al.

This paper addresses the problem of learning the optimal control policy for a nonlinear stochastic dynamical system with continuous state space, continuous action space and unknown dynamics. This class of problems are typically addressed in stochastic adaptive control and reinforcement learning literature using model-based and model-free approaches respectively. Both methods rely on solving a dynamic programming problem, either directly or indirectly, for finding the optimal closed loop control policy. The inherent `curse of dimensionality' associated with dynamic programming method makes these approaches also computationally difficult. This paper proposes a novel decoupled data-based control (D2C) algorithm that addresses this problem using a decoupled, `open loop - closed loop', approach. First, an open-loop deterministic trajectory optimization problem is solved using a black-box simulation model of the dynamical system. Then, a closed loop control is developed around this open loop trajectory by linearization of the dynamics about this nominal trajectory. By virtue of linearization, a linear quadratic regulator based algorithm can be used for this closed loop control. We show that the performance of D2C algorithm is approximately optimal. Moreover, simulation performance suggests significant reduction in training time compared to other state of the art algorithms.