scholarly journals Kalman Temporal Differences

2010 ◽  
Vol 39 ◽  
pp. 483-532 ◽  
Author(s):  
M. Geist ◽  
O. Pietquin
Keyword(s):  
Markov Decision Processes ◽  
Function Approximation ◽  
Approximation Scheme ◽  
State Of The Art ◽  
Decision Processes ◽  
Temporal Differences ◽  
Special Cases ◽  
Markov Decision ◽  
Biased Estimates ◽  
Q Function

Because reinforcement learning suffers from a lack of scalability, online value (and Q-) function approximation has received increasing interest this last decade. This contribution introduces a novel approximation scheme, namely the Kalman Temporal Differences (KTD) framework, that exhibits the following features: sample-efficiency, non-linear approximation, non-stationarity handling and uncertainty management. A first KTD-based algorithm is provided for deterministic Markov Decision Processes (MDP) which produces biased estimates in the case of stochastic transitions. Than the eXtended KTD framework (XKTD), solving stochastic MDP, is described. Convergence is analyzed for special cases for both deterministic and stochastic transitions. Related algorithms are experimented on classical benchmarks. They compare favorably to the state of the art while exhibiting the announced features.

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.

Risk-sensitive semi-Markov decision processes with general utilities and multiple criteria

2018 ◽  
Vol 50 (3) ◽  
pp. 783-804
Author(s):  
Yonghui Huang ◽  
Zhaotong Lian ◽  
Xianping Guo
Keyword(s):  
Markov Decision Processes ◽  
Decision Processes ◽  
Finite Horizon ◽  
Performance Criteria ◽  
Occupation Measure ◽  
Constrained Problems ◽  
Constrained Problem ◽  
Risk Sensitive ◽  
Special Cases ◽  
Markov Decision

Abstract In this paper we investigate risk-sensitive semi-Markov decision processes with a Borel state space, unbounded cost rates, and general utility functions. The performance criteria are several expected utilities of the total cost in a finite horizon. Our analysis is based on a type of finite-horizon occupation measure. We express the distribution of the finite-horizon cost in terms of the occupation measure for each policy, wherein the discount is not needed. For unconstrained and constrained problems, we establish the existence and computation of optimal policies. In particular, we develop a linear program and its dual program for the constrained problem and, moreover, establish the strong duality between the two programs. Finally, we provide two special cases of our results, one of which concerns the discrete-time model, and the other the chance-constrained problem.

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