Robust Reinforcement Learning

2005 ◽  
Vol 17 (2) ◽  
pp. 335-359 ◽  
Author(s):  
Jun Morimoto ◽  
Kenji Doya
Keyword(s):  
Reinforcement Learning ◽  
Value Function ◽  
Learning Algorithm ◽  
Action Planning ◽  
Control Agent ◽  
Control Input ◽  
Environmental Models ◽  
Online Learning Algorithms ◽  
The Difference ◽  
The Value Function

This letter proposes a new reinforcement learning (RL) paradigm that explicitly takes into account input disturbance as well as modeling errors. The use of environmental models in RL is quite popular for both off-line learning using simulations and for online action planning. However, the difference between the model and the real environment can lead to unpredictable, and often unwanted, results. Based on the theory of H∞ control, we consider a differential game in which a “disturbing” agent tries to make the worst possible disturbance while a “control” agent tries to make the best control input. The problem is formulated as finding a min-max solution of a value function that takes into account the amount of the reward and the norm of the disturbance. We derive online learning algorithms for estimating the value function and for calculating the worst disturbance and the best control in reference to the value function. We tested the paradigm, which we call robust reinforcement learning (RRL), on the control task of an inverted pendulum. In the linear domain, the policy and the value function learned by online algorithms coincided with those derived analytically by the linear H∞ control theory. For a fully nonlinear swing-up task, RRL achieved robust performance with changes in the pendulum weight and friction, while a standard reinforcement learning algorithm could not deal with these changes. We also applied RRL to the cart-pole swing-up task, and a robust swing-up policy was acquired.

scholarly journals Risk-Sensitive Reinforcement Learning Applied to Control under Constraints

2005 ◽  
Vol 24 ◽  
pp. 81-108 ◽  
Author(s):  
P. Geibel ◽  
F. Wysotzki
Keyword(s):  
Reinforcement Learning ◽  
Value Function ◽  
Learning Algorithm ◽  
Optimal Solution ◽  
Feed Tank ◽  
Model Free ◽  
Constrained Problem ◽  
Risk Sensitive ◽  
Markov Decision ◽  
The Value Function

In this paper, we consider Markov Decision Processes (MDPs) with error states. Error states are those states entering which is undesirable or dangerous. We define the risk with respect to a policy as the probability of entering such a state when the policy is pursued. We consider the problem of finding good policies whose risk is smaller than some user-specified threshold, and formalize it as a constrained MDP with two criteria. The first criterion corresponds to the value function originally given. We will show that the risk can be formulated as a second criterion function based on a cumulative return, whose definition is independent of the original value function. We present a model free, heuristic reinforcement learning algorithm that aims at finding good deterministic policies. It is based on weighting the original value function and the risk. The weight parameter is adapted in order to find a feasible solution for the constrained problem that has a good performance with respect to the value function. The algorithm was successfully applied to the control of a feed tank with stochastic inflows that lies upstream of a distillation column. This control task was originally formulated as an optimal control problem with chance constraints, and it was solved under certain assumptions on the model to obtain an optimal solution. The power of our learning algorithm is that it can be used even when some of these restrictive assumptions are relaxed.

scholarly journals Hierarchical Reinforcement Learning with the MAXQ Value Function Decomposition

2000 ◽  
Vol 13 ◽  
pp. 227-303 ◽  
Author(s):  
T. G. Dietterich
Keyword(s):  
Reinforcement Learning ◽  
Optimal Policy ◽  
Value Function ◽  
Learning Algorithm ◽  
Value Functions ◽  
Procedural Semantics ◽  
Hierarchical Reinforcement Learning ◽  
Model Free ◽  
Function Decomposition ◽  
The Value Function

This paper presents a new approach to hierarchical reinforcement learning based on decomposing the target Markov decision process (MDP) into a hierarchy of smaller MDPs and decomposing the value function of the target MDP into an additive combination of the value functions of the smaller MDPs. The decomposition, known as the MAXQ decomposition, has both a procedural semantics---as a subroutine hierarchy---and a declarative semantics---as a representation of the value function of a hierarchical policy. MAXQ unifies and extends previous work on hierarchical reinforcement learning by Singh, Kaelbling, and Dayan and Hinton. It is based on the assumption that the programmer can identify useful subgoals and define subtasks that achieve these subgoals. By defining such subgoals, the programmer constrains the set of policies that need to be considered during reinforcement learning. The MAXQ value function decomposition can represent the value function of any policy that is consistent with the given hierarchy. The decomposition also creates opportunities to exploit state abstractions, so that individual MDPs within the hierarchy can ignore large parts of the state space. This is important for the practical application of the method. This paper defines the MAXQ hierarchy, proves formal results on its representational power, and establishes five conditions for the safe use of state abstractions. The paper presents an online model-free learning algorithm, MAXQ-Q, and proves that it converges with probability 1 to a kind of locally-optimal policy known as a recursively optimal policy, even in the presence of the five kinds of state abstraction. The paper evaluates the MAXQ representation and MAXQ-Q through a series of experiments in three domains and shows experimentally that MAXQ-Q (with state abstractions) converges to a recursively optimal policy much faster than flat Q learning. The fact that MAXQ learns a representation of the value function has an important benefit: it makes it possible to compute and execute an improved, non-hierarchical policy via a procedure similar to the policy improvement step of policy iteration. The paper demonstrates the effectiveness of this non-hierarchical execution experimentally. Finally, the paper concludes with a comparison to related work and a discussion of the design tradeoffs in hierarchical reinforcement learning.

scholarly journals Stochastic Brownian Game of Absolute Dominance

2014 ◽  
Vol 51 (2) ◽  
pp. 436-452
Author(s):  
Shangzhen Luo
Keyword(s):  
Nash Equilibrium ◽  
Value Function ◽  
The Other ◽  
Equilibrium Strategy ◽  
Minimax Criterion ◽  
Nash Equilibrium Strategy ◽  
Suitable Parameter ◽  
The Difference ◽  
The Value Function ◽  
Absolute Dominance

In this paper we study a reinsurance game between two insurers whose surplus processes are modeled by arithmetic Brownian motions. We assume a minimax criterion in the game. One insurer tries to maximize the probability of absolute dominance while the other tries to minimize it through reinsurance control. Here absolute dominance is defined as the event that liminf of the difference of the surplus levels tends to -∞. Under suitable parameter conditions, the game is solved with the value function and the Nash equilibrium strategy given in explicit form.

Stochastic Brownian Game of Absolute Dominance

2014 ◽  
Vol 51 (02) ◽  
pp. 436-452 ◽  
Author(s):  
Shangzhen Luo
Keyword(s):  
Nash Equilibrium ◽  
Value Function ◽  
The Other ◽  
Equilibrium Strategy ◽  
Minimax Criterion ◽  
Nash Equilibrium Strategy ◽  
Suitable Parameter ◽  
The Difference ◽  
The Value Function ◽  
Absolute Dominance

In this paper we study a reinsurance game between two insurers whose surplus processes are modeled by arithmetic Brownian motions. We assume a minimax criterion in the game. One insurer tries to maximize the probability of absolute dominance while the other tries to minimize it through reinsurance control. Here absolute dominance is defined as the event that liminf of the difference of the surplus levels tends to -∞. Under suitable parameter conditions, the game is solved with the value function and the Nash equilibrium strategy given in explicit form.

A Unified Analysis of Value-Function-Based Reinforcement-Learning Algorithms

1999 ◽  
Vol 11 (8) ◽  
pp. 2017-2060 ◽  
Author(s):  
Csaba Szepesvári ◽  
Michael L. Littman
Keyword(s):  
Reinforcement Learning ◽  
Value Function ◽  
Learning Algorithm ◽  
Learning Algorithms ◽  
Sequential Decision ◽  
Q Learning ◽  
Markov Games ◽  
Optimal Behavior ◽  
Risk Sensitive ◽  
Optimal Value

Reinforcement learning is the problem of generating optimal behavior in a sequential decision-making environment given the opportunity of interacting with it. Many algorithms for solving reinforcement-learning problems work by computing improved estimates of the optimal value function. We extend prior analyses of reinforcement-learning algorithms and present a powerful new theorem that can provide a unified analysis of such value-function-based reinforcement-learning algorithms. The usefulness of the theorem lies in how it allows the convergence of a complex asynchronous reinforcement-learning algorithm to be proved by verifying that a simpler synchronous algorithm converges. We illustrate the application of the theorem by analyzing the convergence of Q-learning, model-based reinforcement learning, Q-learning with multistate updates, Q-learning for Markov games, and risk-sensitive reinforcement learning.

Autonomous underwater vehicle path planning based on actor-multi-critic reinforcement learning

2020 ◽  
pp. 095965182093708
Author(s):  
Zhuo Wang ◽  
Shiwei Zhang ◽  
Xiaoning Feng ◽  
Yancheng Sui
Keyword(s):  
Reinforcement Learning ◽  
Path Planning ◽  
Value Function ◽  
Autonomous Underwater Vehicle ◽  
Autonomous Underwater Vehicles ◽  
Underwater Vehicle ◽  
Learning Efficiency ◽  
Environmental Adaptability ◽  
Vehicle Path ◽  
The Value Function

The environmental adaptability of autonomous underwater vehicles is always a problem for its path planning. Although reinforcement learning can improve the environmental adaptability, the slow convergence of reinforcement learning is caused by multi-behavior coupling, so it is difficult for autonomous underwater vehicle to avoid moving obstacles. This article proposes a multi-behavior critic reinforcement learning algorithm applied to autonomous underwater vehicle path planning to overcome problems associated with oscillating amplitudes and low learning efficiency in the early stages of training which are common in traditional actor–critic algorithms. Behavior critic reinforcement learning assesses the actions of the actor from perspectives such as energy saving and security, combining these aspects into a whole evaluation of the actor. In this article, the policy gradient method is selected as the actor part, and the value function method is selected as the critic part. The strategy gradient and the value function methods for actor and critic, respectively, are approximated by a backpropagation neural network, the parameters of which are updated using the gradient descent method. The simulation results show that the method has the ability of optimizing learning in the environment and can improve learning efficiency, which meets the needs of real time and adaptability for autonomous underwater vehicle dynamic obstacle avoidance.

Variational Bayesian Exploration-Based Active Sarsa Algorithm

2019 ◽  
Vol 33 (10) ◽  
pp. 1951005 ◽  
Author(s):  
Qiming Fu ◽  
Zhengxia Yang ◽  
You Lu ◽  
Hongjie Wu ◽  
Fuyuan Hu ◽  
...  
Keyword(s):  
Learning Process ◽  
Bayesian Method ◽  
Value Function ◽  
Information Gain ◽  
Learning Algorithm ◽  
Exploration And Exploitation ◽  
Variational Bayesian ◽  
Q Learning ◽  
Reward Function ◽  
The Value Function

We proposed an improved variational Bayesian exploration-based active Sarsa (VBE-ASAR) algorithm, which tries to balance the exploration and exploitation dilemma, and speeds up the convergence rate. First, in the learning process, variational Bayesian method is adopted to measure the information gain, which is used as an exploration factor to construct an internal reward function for heuristic exploration. In addition, before the learning process, in order to improve the exploration performance, transfer learning is used to initialize the value function, where Bisimulation metric is introduced to measure the distance between two states from the source MDP and the target MDP, respectively. Finally, we apply the proposed algorithm to the cliff walking problem, and compare with the Sarsa algorithm, the Q-Learning algorithm, the VFT-Sarsa algorithm and the Bayesian Sarsa (BS) algorithm. Experimental results show that the VBE-ASAR algorithm has a faster learning rate.

scholarly journals How Active is Active Learning: Value Function Method Versus an Approximation Method

2020 ◽  
Vol 56 (3) ◽  
pp. 675-693
Author(s):  
Hans M. Amman ◽  
Marco P. Tucci
Keyword(s):  
Active Learning ◽  
Approximation Method ◽  
Function Method ◽  
Value Function ◽  
Stationary Process ◽  
Nonstationary Process ◽  
Function Approach ◽  
The Difference ◽  
The Value Function

AbstractIn a previous paper Amman et al. (Macroecon Dyn, 2018) compare the two dominant approaches for solving models with optimal experimentation (also called active learning), i.e. the value function and the approximation method. By using the same model and dataset as in Beck and Wieland (J Econ Dyn Control 26:1359–1377, 2002), they find that the approximation method produces solutions close to those generated by the value function approach and identify some elements of the model specifications which affect the difference between the two solutions. They conclude that differences are small when the effects of learning are limited. However the dataset used in the experiment describes a situation where the controller is dealing with a nonstationary process and there is no penalty on the control. The goal of this paper is to see if their conclusions hold in the more commonly studied case of a controller facing a stationary process and a positive penalty on the control.

scholarly journals Generation of Policy-Level Explanations for Reinforcement Learning

2019 ◽  
Vol 33 ◽  
pp. 2514-2521
Author(s):  
Nicholay Topin ◽  
Manuela Veloso
Keyword(s):  
Neural Networks ◽  
Deep Learning ◽  
Reinforcement Learning ◽  
Markov Chains ◽  
Time Complexity ◽  
Value Function ◽  
Worst Case ◽  
Policy Level ◽  
Individual Decisions ◽  
The Value Function

Though reinforcement learning has greatly benefited from the incorporation of neural networks, the inability to verify the correctness of such systems limits their use. Current work in explainable deep learning focuses on explaining only a single decision in terms of input features, making it unsuitable for explaining a sequence of decisions. To address this need, we introduce Abstracted Policy Graphs, which are Markov chains of abstract states. This representation concisely summarizes a policy so that individual decisions can be explained in the context of expected future transitions. Additionally, we propose a method to generate these Abstracted Policy Graphs for deterministic policies given a learned value function and a set of observed transitions, potentially off-policy transitions used during training. Since no restrictions are placed on how the value function is generated, our method is compatible with many existing reinforcement learning methods. We prove that the worst-case time complexity of our method is quadratic in the number of features and linear in the number of provided transitions, O(|F|2|tr samples|). By applying our method to a family of domains, we show that our method scales well in practice and produces Abstracted Policy Graphs which reliably capture relationships within these domains.

Sign in / Sign up

Export Citation Format

Share Document