PASCAL - Pattern Analysis, Statistical Modelling and Computational Learning

Open loop optimistic planning
Sébastien Bubeck and Rémi Munos
In: COLT 2010, Israel(2010).

Abstract

We consider the problem of planning in a stochastic and discounted environment with a limited numerical budget. More precisely, we investigate strategies exploring the set of possible sequences of actions, so that, once all available numerical resources (e.g. CPU time, number of calls to a generative model) have been used, one returns a recommendation on the best possible immediate action to follow based on this exploration. The performance of a strategy is assessed in terms of its simple regret, that is the loss in performance resulting from choosing the recommended action instead of an optimal one. We first provide a minimax lower bound for this problem, and show that a uniform planning strategy matches this minimax rate (up to a logarithmic factor). Then we propose a UCB (Upper Confidence Bounds)-based planning algorithm, called OLOP (Open-Loop Optimistic Planning), which is also minimax optimal, and prove that it enjoys much faster rates when there is a small proportion of near-optimal sequences of actions. Finally, we compare our results with the regret bounds one can derive for our setting with bandits algorithms designed for an infinite number of arms.

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EPrint Type:Conference or Workshop Item (Paper)
Project Keyword:Project Keyword UNSPECIFIED
Subjects:Learning/Statistics & Optimisation
Theory & Algorithms
ID Code:7408
Deposited By:Rémi Munos
Deposited On:17 March 2011