Online Planning for Large Markov Decision Processes with Hierarchical Decomposition

2015 ◽  
Vol 6 (4) ◽  
pp. 1-28 ◽  
Author(s):  
Aijun Bai ◽  
Feng Wu ◽  
Xiaoping Chen
Keyword(s):  
Markov Decision Processes ◽  
Decision Processes ◽  
Hierarchical Decomposition ◽  
Online Planning ◽  
Markov Decision

scholarly journals Simple Regret Optimization in Online Planning for Markov Decision Processes

2014 ◽  
Vol 51 ◽  
pp. 165-205 ◽  
Author(s):  
Z. Feldman ◽  
C. Domshlak
Keyword(s):  
Markov Decision Processes ◽  
State Of The Art ◽  
Search Algorithm ◽  
Empirical Evaluation ◽  
Decision Processes ◽  
Monte Carlo Tree Search ◽  
Performance Loss ◽  
Online Planning ◽  
Markov Decision ◽  
High Level

We consider online planning in Markov decision processes (MDPs). In online planning, the agent focuses on its current state only, deliberates about the set of possible policies from that state onwards and, when interrupted, uses the outcome of that exploratory deliberation to choose what action to perform next. Formally, the performance of algorithms for online planning is assessed in terms of simple regret, the agent's expected performance loss when the chosen action, rather than an optimal one, is followed. To date, state-of-the-art algorithms for online planning in general MDPs are either best effort, or guarantee only polynomial-rate reduction of simple regret over time. Here we introduce a new Monte-Carlo tree search algorithm, BRUE, that guarantees exponential-rate and smooth reduction of simple regret. At a high level, BRUE is based on a simple yet non-standard state-space sampling scheme, MCTS2e, in which different parts of each sample are dedicated to different exploratory objectives. We further extend BRUE with a variant of ``learning by forgetting.'' The resulting parametrized algorithm, BRUE(alpha), exhibits even more attractive formal guarantees than BRUE. Our empirical evaluation shows that both BRUE and its generalization, BRUE(alpha), are also very effective in practice and compare favorably to the state-of-the-art.

Extreme-point solutions in Markov decision processes

1983 ◽  
Vol 20 (04) ◽  
pp. 835-842
Author(s):  
David Assaf
Keyword(s):  
Convex Function ◽  
Extreme Point ◽  
Markov Decision Processes ◽  
Convex Functions ◽  
Sufficient Conditions ◽  
Decision Processes ◽  
Markov Decision ◽  
Full Solution

The paper presents sufficient conditions for certain functions to be convex. Functions of this type often appear in Markov decision processes, where their maximum is the solution of the problem. Since a convex function takes its maximum at an extreme point, the conditions may greatly simplify a problem. In some cases a full solution may be obtained after the reduction is made. Some illustrative examples are discussed.

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