662 research outputs found
State Abstraction in MAXQ Hierarchical Reinforcement Learning
Many researchers have explored methods for hierarchical reinforcement
learning (RL) with temporal abstractions, in which abstract actions are defined
that can perform many primitive actions before terminating. However, little is
known about learning with state abstractions, in which aspects of the state
space are ignored. In previous work, we developed the MAXQ method for
hierarchical RL. In this paper, we define five conditions under which state
abstraction can be combined with the MAXQ value function decomposition. We
prove that the MAXQ-Q learning algorithm converges under these conditions and
show experimentally that state abstraction is important for the successful
application of MAXQ-Q learning.Comment: 7 pages, 2 figure
Scaling Ant Colony Optimization with Hierarchical Reinforcement Learning Partitioning
This paper merges hierarchical reinforcement learning (HRL) with ant colony optimization (ACO) to produce a HRL ACO algorithm capable of generating solutions for large domains. This paper describes two specific implementations of the new algorithm: the first a modification to Dietterich’s MAXQ-Q HRL algorithm, the second a hierarchical ant colony system algorithm. These implementations generate faster results, with little to no significant change in the quality of solutions for the tested problem domains. The application of ACO to the MAXQ-Q algorithm replaces the reinforcement learning, Q-learning, with the modified ant colony optimization method, Ant-Q. This algorithm, MAXQ-AntQ, converges to solutions not significantly different from MAXQ-Q in 88% of the time. This paper then transfers HRL techniques to the ACO domain and traveling salesman problem (TSP). To apply HRL to ACO, a hierarchy must be created for the TSP. A data clustering algorithm creates these subtasks, with an ACO algorithm to solve the individual and complete problems. This paper tests two clustering algorithms, k-means and G-means. The results demonstrate the algorithm with data clustering produces solutions 20 times faster with 5-10% decrease in solution quality due to the effects of clustering
Scaling Ant Colony Optimization with Hierarchical Reinforcement Learning Partitioning
This research merges the hierarchical reinforcement learning (HRL) domain and the ant colony optimization (ACO) domain. The merger produces a HRL ACO algorithm capable of generating solutions for both domains. This research also provides two specific implementations of the new algorithm: the first a modification to Dietterich\u27s MAXQ-Q HRL algorithm, the second a hierarchical ACO algorithm. These implementations generate faster results, with little to no significant change in the quality of solutions for the tested problem domains. The application of ACO to the MAXQ-Q algorithm replaces the reinforcement learning, Q-learning and SARSA, with the modified ant colony optimization method, Ant-Q. This algorithm, MAXQ-AntQ, converges to solutions not significantly different from MAXQ-Q in 88% of the time. This research then transfers HRL techniques to the ACO domain and traveling salesman problem (TSP). To apply HRL to ACO, a hierarchy must be created for the TSP. A data clustering algorithm creates these subtasks, with an ACO algorithm to solve the individual and complete problems. This research tests two clustering algorithms, k-means and G-means. The results demonstrate the algorithm with data clustering produces solutions 85-95% faster but with 5-10% decrease in solution quality
Hierarchical Reinforcement Learning with the MAXQ Value Function Decomposition
This paper presents the MAXQ 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 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 wih 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.Comment: 63 pages, 15 figure
Hierarchical Linearly-Solvable Markov Decision Problems
We present a hierarchical reinforcement learning framework that formulates
each task in the hierarchy as a special type of Markov decision process for
which the Bellman equation is linear and has analytical solution. Problems of
this type, called linearly-solvable MDPs (LMDPs) have interesting properties
that can be exploited in a hierarchical setting, such as efficient learning of
the optimal value function or task compositionality. The proposed hierarchical
approach can also be seen as a novel alternative to solving LMDPs with large
state spaces. We derive a hierarchical version of the so-called Z-learning
algorithm that learns different tasks simultaneously and show empirically that
it significantly outperforms the state-of-the-art learning methods in two
classical hierarchical reinforcement learning domains: the taxi domain and an
autonomous guided vehicle task.Comment: 11 pages, 6 figures, 26th International Conference on Automated
Planning and Schedulin
A Tutorial on Bayesian Optimization of Expensive Cost Functions, with Application to Active User Modeling and Hierarchical Reinforcement Learning
We present a tutorial on Bayesian optimization, a method of finding the
maximum of expensive cost functions. Bayesian optimization employs the Bayesian
technique of setting a prior over the objective function and combining it with
evidence to get a posterior function. This permits a utility-based selection of
the next observation to make on the objective function, which must take into
account both exploration (sampling from areas of high uncertainty) and
exploitation (sampling areas likely to offer improvement over the current best
observation). We also present two detailed extensions of Bayesian optimization,
with experiments---active user modelling with preferences, and hierarchical
reinforcement learning---and a discussion of the pros and cons of Bayesian
optimization based on our experiences
Decentralized Cooperative Planning for Automated Vehicles with Hierarchical Monte Carlo Tree Search
Today's automated vehicles lack the ability to cooperate implicitly with
others. This work presents a Monte Carlo Tree Search (MCTS) based approach for
decentralized cooperative planning using macro-actions for automated vehicles
in heterogeneous environments. Based on cooperative modeling of other agents
and Decoupled-UCT (a variant of MCTS), the algorithm evaluates the
state-action-values of each agent in a cooperative and decentralized manner,
explicitly modeling the interdependence of actions between traffic
participants. Macro-actions allow for temporal extension over multiple time
steps and increase the effective search depth requiring fewer iterations to
plan over longer horizons. Without predefined policies for macro-actions, the
algorithm simultaneously learns policies over and within macro-actions. The
proposed method is evaluated under several conflict scenarios, showing that the
algorithm can achieve effective cooperative planning with learned macro-actions
in heterogeneous environments
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