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Register a new userGeneralized Policy Iteration for Optimal Control in Continuous Time
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This paper proposes the Deep Generalized Policy Iteration (DGPI) algorithm to find the infinite horizon optimal control policy for general nonlinear continuous-time systems with known dynamics. Unlike existing adaptive dynamic programming algorithms for continuous time systems, DGPI does not require the admissibility of initialized policy, and input-affine nature of controlled systems for convergence. Our algorithm employs the actor-critic architecture to approximate both policy and value functions with the purpose of iteratively solving the Hamilton-Jacobi-Bellman equation. Both the policy and value functions are approximated by deep neural networks. Given any arbitrary initial policy, the proposed DGPI algorithm can eventually converge to an admissible, and subsequently an optimal policy for an arbitrary nonlinear system. We also relax the update termination conditions of both the policy evaluation and improvement processes, which leads to a faster convergence speed than conventional Policy Iteration (PI) methods, for the same architecture of function approximators. We further prove the convergence and optimality of the algorithm with thorough Lyapunov analysis, and demonstrate its generality and efficacy using two detailed numerical examples.
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We present an algorithm for local, regularized, policy improvement in reinforcement learning (RL) that allows us to formulate model-based and model-free variants in a single framework. Our algorithm can be interpreted as a natural extension of work on KL-regularized RL and introduces a form of tree search for continuous action spaces. We demonstrate that additional computation spent on model-based policy improvement during learning can improve data efficiency, and confirm that model-based policy improvement during action selection can also be beneficial. Quantitatively, our algorithm improves data efficiency on several continuous control benchmarks (when a model is learned in parallel), and it provides significant improvements in wall-clock time in high-dimensional domains (when a ground truth model is available). The unified framework also helps us to better understand the space of model-based and model-free algorithms. In particular, we demonstrate that some benefits attributed to model-based RL can be obtained without a model, simply by utilizing more computation.
When transferring a control policy from simulation to a physical system, the policy needs to be robust to variations in the dynamics to perform well. Commonly, the optimal policy overfits to the approximate model and the corresponding state-distribution, often resulting in failure to trasnfer underlying distributional shifts. In this paper, we present Robust Fitted Value Iteration, which uses dynamic programming to compute the optimal value function on the compact state domain and incorporates adversarial perturbations of the system dynamics. The adversarial perturbations encourage a optimal policy that is robust to changes in the dynamics. Utilizing the continuous-time perspective of reinforcement learning, we derive the optimal perturbations for the states, actions, observations and model parameters in closed-form. Notably, the resulting algorithm does not require discretization of states or actions. Therefore, the optimal adversarial perturbations can be efficiently incorporated in the min-max value function update. We apply the resulting algorithm to the physical Furuta pendulum and cartpole. By changing the masses of the systems we evaluate the quantitative and qualitative performance across different model parameters. We show that robust value iteration is more robust compared to deep reinforcement learning algorithm and the non-robust version of the algorithm. Videos of the experiments are shown at https://sites.google.com/view/rfvi
This paper considers a distributed reinforcement learning problem for decentralized linear quadratic control with partial state observations and local costs. We propose a Zero-Order Distributed Policy Optimization algorithm (ZODPO) that learns linear local controllers in a distributed fashion, leveraging the ideas of policy gradient, zero-order optimization and consensus algorithms. In ZODPO, each agent estimates the global cost by consensus, and then conducts local policy gradient in parallel based on zero-order gradient estimation. ZODPO only requires limited communication and storage even in large-scale systems. Further, we investigate the nonasymptotic performance of ZODPO and show that the sample complexity to approach a stationary point is polynomial with the error tolerances inverse and the problem dimensions, demonstrating the scalability of ZODPO. We also show that the controllers generated throughout ZODPO are stabilizing controllers with high probability. Lastly, we numerically test ZODPO on multi-zone HVAC systems.
State estimation is critical to control systems, especially when the states cannot be directly measured. This paper presents an approximate optimal filter, which enables to use policy iteration technique to obtain the steady-state gain in linear Gaussian time-invariant systems. This design transforms the optimal filtering problem with minimum mean square error into an optimal control problem, called Approximate Optimal Filtering (AOF) problem. The equivalence holds given certain conditions about initial state distributions and policy formats, in which the system state is the estimation error, control input is the filter gain, and control objective function is the accumulated estimation error. We present a policy iteration algorithm to solve the AOF problem in steady-state. A classic vehicle state estimation problem finally evaluates the approximate filter. The results show that the policy converges to the steady-state Kalman gain, and its accuracy is within 2 %.
This paper presents a constrained deep adaptive dynamic programming (CDADP) algorithm to solve general nonlinear optimal control problems with known dynamics. Unlike previous ADP algorithms, it can directly deal with problems with state constraints. Both the policy and value function are approximated by deep neural networks (NNs), which directly map the system state to action and value function respectively without needing to use hand-crafted basis function. The proposed algorithm considers the state constraints by transforming the policy improvement process to a constrained optimization problem. Meanwhile, a trust region constraint is added to prevent excessive policy update. We first linearize this constrained optimization problem locally into a quadratically-constrained quadratic programming problem, and then obtain the optimal update of policy network parameters by solving its dual problem. We also propose a series of recovery rules to update the policy in case the primal problem is infeasible. In addition, parallel learners are employed to explore different state spaces and then stabilize and accelerate the learning speed. The vehicle control problem in path-tracking task is used to demonstrate the effectiveness of this proposed method.
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