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 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.

An Actor-critic Algorithm Using Cross Evaluation of Value Functions

2018 ◽  
Vol 7 (1) ◽  
pp. 39
Author(s):  
Hui Wang ◽  
Peng Zhang ◽  
Quan Liu
Keyword(s):  
Optimal Policy ◽  
Value Function ◽  
Learning Algorithm ◽  
Optimization Methods ◽  
Value Functions ◽  
Continuous Space ◽  
Real Value ◽  
Global Optimal ◽  
The Stability ◽  
Greedy Optimization

In order to overcome the difficulty of learning a global optimal policy caused by maximization bias in a continuous space, an actor-critic algorithm for cross evaluation of double value function is proposed. Two independent value functions make the critique closer to the real value function. And the actor is guided by a crossover function to choose its optimal actions. Cross evaluation of value functions avoids the policy jitter phenomenon behaved by greedy optimization methods in continuous spaces. The algorithm is more robust than CACLA learning algorithm, and the experimental results show that our algorithm is smoother and the stability of policy is improved obviously under the condition that the computation remains almost unchanged.

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 Fixed-Horizon Temporal Difference Methods for Stable Reinforcement Learning

2020 ◽  
Vol 34 (04) ◽  
pp. 3741-3748
Author(s):  
Kristopher De Asis ◽  
Alan Chan ◽  
Silviu Pitis ◽  
Richard Sutton ◽  
Daniel Graves
Keyword(s):  
Reinforcement Learning ◽  
Function Approximation ◽  
Value Function ◽  
Temporal Difference ◽  
Value Functions ◽  
Difference Methods ◽  
Td Methods ◽  
The Stability ◽  
The Value Function ◽  
Temporal Difference Methods

We explore fixed-horizon temporal difference (TD) methods, reinforcement learning algorithms for a new kind of value function that predicts the sum of rewards over a fixed number of future time steps. To learn the value function for horizon h, these algorithms bootstrap from the value function for horizon h−1, or some shorter horizon. Because no value function bootstraps from itself, fixed-horizon methods are immune to the stability problems that plague other off-policy TD methods using function approximation (also known as “the deadly triad”). Although fixed-horizon methods require the storage of additional value functions, this gives the agent additional predictive power, while the added complexity can be substantially reduced via parallel updates, shared weights, and n-step bootstrapping. We show how to use fixed-horizon value functions to solve reinforcement learning problems competitively with methods such as Q-learning that learn conventional value functions. We also prove convergence of fixed-horizon temporal difference methods with linear and general function approximation. Taken together, our results establish fixed-horizon TD methods as a viable new way of avoiding the stability problems of the deadly triad.

scholarly journals Improved Q-Learning Algorithm Based on Approximate State Matching in Agricultural Plant Protection Environment

Entropy ◽  
2021 ◽  
Vol 23 (6) ◽  
pp. 737
Author(s):  
Fengjie Sun ◽  
Xianchang Wang ◽  
Rui Zhang
Keyword(s):  
Decision Making ◽  
Reinforcement Learning ◽  
Optimal Policy ◽  
Feasible Solution ◽  
Learning Algorithm ◽  
Plant Protection ◽  
Agricultural Plant ◽  
Q Learning ◽  
Aerial Vehicle ◽  
Optimal Action

An Unmanned Aerial Vehicle (UAV) can greatly reduce manpower in the agricultural plant protection such as watering, sowing, and pesticide spraying. It is essential to develop a Decision-making Support System (DSS) for UAVs to help them choose the correct action in states according to the policy. In an unknown environment, the method of formulating rules for UAVs to help them choose actions is not applicable, and it is a feasible solution to obtain the optimal policy through reinforcement learning. However, experiments show that the existing reinforcement learning algorithms cannot get the optimal policy for a UAV in the agricultural plant protection environment. In this work we propose an improved Q-learning algorithm based on similar state matching, and we prove theoretically that there has a greater probability for UAV choosing the optimal action according to the policy learned by the algorithm we proposed than the classic Q-learning algorithm in the agricultural plant protection environment. This proposed algorithm is implemented and tested on datasets that are evenly distributed based on real UAV parameters and real farm information. The performance evaluation of the algorithm is discussed in detail. Experimental results show that the algorithm we proposed can efficiently learn the optimal policy for UAVs in the agricultural plant protection environment.

scholarly journals Solving Channel Allocation by Reinforcement Learning in Cognitive Enabled Vehicular Ad Hoc Networks

2021 ◽  
Author(s):  
Yunfan Su
Keyword(s):  
Dynamic Programming ◽  
Reinforcement Learning ◽  
Optimal Policy ◽  
Ad Hoc ◽  
Transition Probabilities ◽  
Channel Allocation ◽  
Dynamic Programming Method ◽  
Learning Method ◽  
Time Intervals ◽  
Model Free

Vehicular ad hoc network (VANET) is a promising technique that improves traffic safety and transportation efficiency and provides a comfortable driving experience. However, due to the rapid growth of applications that demand channel resources, efficient channel allocation schemes are required to utilize the performance of the vehicular networks. In this thesis, two Reinforcement learning (RL)-based channel allocation methods are proposed for a cognitive enabled VANET environment to maximize a long-term average system reward. First, we present a model-based dynamic programming method, which requires the calculations of the transition probabilities and time intervals between decision epochs. After obtaining the transition probabilities and time intervals, a relative value iteration (RVI) algorithm is used to find the asymptotically optimal policy. Then, we propose a model-free reinforcement learning method, in which we employ an agent to interact with the environment iteratively and learn from the feedback to approximate the optimal policy. Simulation results show that our reinforcement learning method can acquire a similar performance to that of the dynamic programming while both outperform the greedy method.

scholarly journals Hill Climbing on Value Estimates for Search-control in Dyna

2019 ◽  
Author(s):  
Yangchen Pan ◽  
Hengshuai Yao ◽  
Amir-massoud Farahmand ◽  
Martha White
Keyword(s):  
Value Function ◽  
Gradient Algorithm ◽  
Hill Climbing ◽  
Value Functions ◽  
Current Estimate ◽  
Sampling Distributions ◽  
Current Value ◽  
Empirical Demonstration ◽  
Search Control ◽  
The Value Function

Dyna is an architecture for model based reinforcement learning (RL), where simulated experience from a model is used to update policies or value functions. A key component of Dyna is search control, the mechanism to generate the state and action from which the agent queries the model, which remains largely unexplored. In this work, we propose to generate such states by using the trajectory obtained from Hill Climbing (HC) the current estimate of the value function. This has the effect of propagating value from high value regions and of preemptively updating value estimates of the regions that the agent is likely to visit next. We derive a noisy projected natural gradient algorithm for hill climbing, and highlight a connection to Langevin dynamics. We provide an empirical demonstration on four classical domains that our algorithm, HC Dyna, can obtain significant sample efficiency improvements. We study the properties of different sampling distributions for search control, and find that there appears to be a benefit specifically from using the samples generated by climbing on current value estimates from low value to high value region.

scholarly journals Solving Channel Allocation by Reinforcement Learning in Cognitive Enabled Vehicular Ad Hoc Networks

2021 ◽  
Author(s):  
Yunfan Su
Keyword(s):  
Dynamic Programming ◽  
Reinforcement Learning ◽  
Optimal Policy ◽  
Ad Hoc ◽  
Transition Probabilities ◽  
Channel Allocation ◽  
Dynamic Programming Method ◽  
Learning Method ◽  
Time Intervals ◽  
Model Free

Vehicular ad hoc network (VANET) is a promising technique that improves traffic safety and transportation efficiency and provides a comfortable driving experience. However, due to the rapid growth of applications that demand channel resources, efficient channel allocation schemes are required to utilize the performance of the vehicular networks. In this thesis, two Reinforcement learning (RL)-based channel allocation methods are proposed for a cognitive enabled VANET environment to maximize a long-term average system reward. First, we present a model-based dynamic programming method, which requires the calculations of the transition probabilities and time intervals between decision epochs. After obtaining the transition probabilities and time intervals, a relative value iteration (RVI) algorithm is used to find the asymptotically optimal policy. Then, we propose a model-free reinforcement learning method, in which we employ an agent to interact with the environment iteratively and learn from the feedback to approximate the optimal policy. Simulation results show that our reinforcement learning method can acquire a similar performance to that of the dynamic programming while both outperform the greedy method.

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