PASCAL - Pattern Analysis, Statistical Modelling and Computational Learning

Efficient Solutions to Factored MDPs with Imprecise Transition Probabilities
Karina Valdivia Delgado, Scott Sanner, Leliane Nunes de Barros and Fabio G. Cozman
In: ICAPS 2009, 19-23 Sept 2009, Thessaloniki, Greece.

Abstract

When modeling real-world decision-theoretic planning problems in the Markov decision process (MDP) framework, it is often impossible to obtain a completely accurate estimate of transition probabilities. For example, natural uncertainty arises in the transition specification due to elicitation of MDP transition models from an expert or data, or non-stationary transition distributions arising from insufficient state knowledge. In the interest of obtaining the most robust policy under transition uncertainty, the Markov Decision Process with Imprecise Transition Probabilities (MDP-IPs) has been introduced to model such scenarios. Unfortunately, while solutions to the MDP-IP are well-known, they require nonlinear optimization and are extremely time-consuming in practice. To address this deficiency, we propose efficient dynamic programming methods to exploit the structure of factored MDP-IPs. Noting that the key computational bottleneck in the solution of MDP-IPs is the need to repeatedly solve nonlinear constrained optimization problems, we show how to target approximation techniques to drastically reduce the computational overhead of the nonlinear solver while producing bounded, approximately optimal solutions. Our results show up to two orders of magnitude speedup in comparison to traditional ``flat'' dynamic programming approaches and up to an order of magnitude speedup over the extension of factored MDP approximate value iteration techniques to MDP-IPs.

EPrint Type:Conference or Workshop Item (Oral)
Project Keyword:Project Keyword UNSPECIFIED
Subjects:Learning/Statistics & Optimisation
Theory & Algorithms
ID Code:5561
Deposited By:Scott Sanner
Deposited On:01 March 2010