“How hard is my MDP?” Distribution-norm to the rescue.

2014, Discussing articles

Odalric-Ambrym Maillard, Timothy A. Mann, Shie Mannor.
In advances in Neural Information Processing Systems, 2014.

[Download]

Abstract:
In Reinforcement Learning (RL), state-of-the-art algorithms require a large number of samples per state-action pair to estimate the transition kernel p. In many problems, a good approximation of p is not needed. For instance, if from one state-action pair (s,a), one can only transit to states with the same value, learning p(|s,a) accurately is irrelevant (only its support matters). This paper aims at capturing such behavior by defining a novel hardness measure for Markov Decision Processes (MDPs) we call the distribution-norm. The distribution-norm w.r.t. a measure ν is defined on zero ν-mean functions f by the standard variation of f with respect to ν. We first provide a concentration inequality for the dual of the distribution-norm. This allows us to replace the generic but loose ||||1 concentration inequalities used in most previous analysis of RL algorithms, to benefit from this new hardness measure. We then show that several common RL benchmarks have low hardness when measured using the new norm. The distribution-norm captures finer properties than the number of states or the diameter and can be used to assess the difficulty of MDPs.

You can dowload the paper from the NIPS website (here) or from the HAL online open depository* (soon).

Bibtex:
@incollection{MaiManMan14,
title = {How hard is my MDP?” The distribution-norm to the rescue”},
author = {Maillard, Odalric-Ambrym and Mann, Timothy A and Mannor, Shie},
booktitle = {Advances in Neural Information Processing Systems 27},
editor = {Z. Ghahramani and M. Welling and C. Cortes and N.D. Lawrence and K.Q. Weinberger},
pages = {1835–1843},
year = {2014},
publisher = {Curran Associates, Inc.},
url = {http://papers.nips.cc/paper/5441-how-hard-is-my-mdp-the-distribution-norm-to-the-rescue.pdf}
}
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