Tag Archives: Continuous Mdps

Hybridizing model-free and model-based in continuous RL, and a nice review of current research and benchmarks in robotics

Pinosky A, Abraham I, Broad A, Argall B, Murphey TD. Hybrid control for combining model-based and model-free reinforcement learning The International Journal of Robotics Research. 2023;42(6):337-355 DOI: 10.1177/02783649221083331.

We develop an approach to improve the learning capabilities of robotic systems by combining learned predictive models with experience-based state-action policy mappings. Predictive models provide an understanding of the task and the dynamics, while experience-based (model-free) policy mappings encode favorable actions that override planned actions. We refer to our approach of systematically combining model-based and model-free learning methods as hybrid learning. Our approach efficiently learns motor skills and improves the performance of predictive models and experience-based policies. Moreover, our approach enables policies (both model-based and model-free) to be updated using any off-policy reinforcement learning method. We derive a deterministic method of hybrid learning by optimally switching between learning modalities. We adapt our method to a stochastic variation that relaxes some of the key assumptions in the original derivation. Our deterministic and stochastic variations are tested on a variety of robot control benchmark tasks in simulation as well as a hardware manipulation task. We extend our approach for use with imitation learning methods, where experience is provided through demonstrations, and we test the expanded capability with a real-world pick-and-place task. The results show that our method is capable of improving the performance and sample efficiency of learning motor skills in a variety of experimental domains.

Dealing with continuous spaces in Q-learning by maintaining several spaces, each one corresponding to a particular time-step

Joao Pedro Araujo, Mario A.T. Figueiredo, Miguel Ayala Botto, Control with adaptive Q-learning: A comparison for two classical control problems, Engineering Applications of Artificial Intelligence, Volume 112, 2022 DOI: 10.1016/j.engappai.2022.104797.

This paper evaluates adaptive Q-learning (AQL) and single-partition adaptive Q-learning (SPAQL), two algorithms for efficient model-free episodic reinforcement learning (RL), in two classical control problems (Pendulum and CartPole). AQL adaptively partitions the state\u2013action space of a Markov decision process (MDP), while learning the control policy, i.e., the mapping from states to actions. The main difference between AQL and SPAQL is that the latter learns time-invariant policies, where the mapping from states to actions does not depend explicitly on the time step. This paper also proposes the SPAQL with terminal state (SPAQL-TS), an improved version of SPAQL tailored for the design of regulators for control problems. The time-invariant policies are shown to result in a better performance than the time-variant ones in both problems studied. These algorithms are particularly fitted to RL problems where the action space is finite, as is the case with the CartPole problem. SPAQL-TS solves the OpenAI GymCartPole problem, while also displaying a higher sample efficiency than trust region policy optimization (TRPO), a standard RL algorithm for solving control tasks. Moreover, the policies learned by SPAQL are interpretable, while TRPO policies are typically encoded as neural networks, and therefore hard to interpret. Yielding interpretable policies while being sample-efficient are the major advantages of SPAQL. The code for the experiments is available at https://github.com/jaraujo98/SinglePartitionAdaptiveQLearning.

Adaptation of model-free RL to variations in the task under continuous state and action spaces applied to robot grasping

Shahid, A.A., Piga, D., Braghin, F. et al. Continuous control actions learning and adaptation for robotic manipulation through reinforcement learning, Auton Robot 46, 483\u2013498 (2022) DOI: 10.1007/s10514-022-10034-z.

This paper presents a learning-based method that uses simulation data to learn an object manipulation task using two model-free reinforcement learning (RL) algorithms. The learning performance is compared across on-policy and off-policy algorithms: Proximal Policy Optimization (PPO) and Soft Actor-Critic (SAC). In order to accelerate the learning process, the fine-tuning procedure is proposed that demonstrates the continuous adaptation of on-policy RL to new environments, allowing the learned policy to adapt and execute the (partially) modified task. A dense reward function is designed for the task to enable an efficient learning of the agent. A grasping task involving a Franka Emika Panda manipulator is considered as the reference task to be learned. The learned control policy is demonstrated to be generalizable across multiple object geometries and initial robot/parts configurations. The approach is finally tested on a real Franka Emika Panda robot, showing the possibility to transfer the learned behavior from simulation. Experimental results show 100% of successful grasping tasks, making the proposed approach applicable to real applications.

Quantizing a continuous POMDP into a finite MDP to preserve optimality

Naci Saldi; Serdar Yüksel; Tamás Linder, Asymptotic Optimality of Finite Model Approximations for Partially Observed Markov Decision Processes With Discounted Cost, IEEE Transactions on Automatic Control ( Volume: 65, Issue: 1, Jan. 2020), DOI: 10.1109/TAC.2019.2907172.

We consider finite model approximations of discrete-time partially observed Markov decision processes (POMDPs) under the discounted cost criterion. After converting the original partially observed stochastic control problem to a fully observed one on the belief space, the finite models are obtained through the uniform quantization of the state and action spaces of the belief space Markov decision process (MDP). Under mild assumptions on the components of the original model, it is established that the policies obtained from these finite models are nearly optimal for the belief space MDP, and so, for the original partially observed problem. The assumptions essentially require that the belief space MDP satisfies a mild weak continuity condition. We provide an example and introduce explicit approximation procedures for the quantization of the set of probability measures on the state space of POMDP (i.e., belief space).

A universal approximator for the value function in continuous-state VI

William B. Haskell; Rahul Jain; Hiteshi Sharma; Pengqian Yu, TA Universal Empirical Dynamic Programming Algorithm for Continuous State MDPs, IEEE Transactions on Automatic Control ( Volume: 65, Issue: 1, Jan. 2020), DOI: 10.1109/TAC.2019.2907414.

We propose universal randomized function approximation-based empirical value learning (EVL) algorithms for Markov decision processes. The “empirical” nature comes from each iteration being done empirically from samples available from simulations of the next state. This makes the Bellman operator a random operator. A parametric and a nonparametric method for function approximation using a parametric function space and a reproducing kernel Hilbert space respectively are then combined with EVL. Both function spaces have the universal function approximation property. Basis functions are picked randomly. Convergence analysis is performed using a random operator framework with techniques from the theory of stochastic dominance. Finite time sample complexity bounds are derived for both universal approximate dynamic programming algorithms. Numerical experiments support the versatility and computational tractability of this approach.

Incremental (hierarchical) search for the optimal policy on markov decision processes

Vu Anh Huynh, Sertac Karaman, and Emilio Frazzoli, An incremental sampling-based algorithm for stochastic optimal control, The International Journal of Robotics Research April 2016 35: 305-333, DOI: 10.1177/0278364915616866.

In this paper, we consider a class of continuous-time, continuous-space stochastic optimal control problems. Using the Markov chain approximation method and recent advances in sampling-based algorithms for deterministic path planning, we propose a novel algorithm called the incremental Markov Decision Process to incrementally compute control policies that approximate arbitrarily well an optimal policy in terms of the expected cost. The main idea behind the algorithm is to generate a sequence of finite discretizations of the original problem through random sampling of the state space. At each iteration, the discretized problem is a Markov Decision Process that serves as an incrementally refined model of the original problem. We show that with probability one, (i) the sequence of the optimal value functions for each of the discretized problems converges uniformly to the optimal value function of the original stochastic optimal control problem, and (ii) the original optimal value function can be computed efficiently in an incremental manner using asynchronous value iterations. Thus, the proposed algorithm provides an anytime approach to the computation of optimal control policies of the continuous problem. The effectiveness of the proposed approach is demonstrated on motion planning and control problems in cluttered environments in the presence of process noise.