Here we provide the value of an optimal solution for some of above problems for several horizons, which can for instance be used to benchmark approximate solutions. The table also notes in which papers the problem had been first solved optimally for a given horizon. Note that values reported are for the undiscounted setting, i.e., the discount factor (often denoted by gamma) was set to 1.0, overriding sometimes the discount factor specified in the .dpomdp files. This explains discrepancies with some of the cited papers. In most cases the reported values have been computed using GMAA*-Cluster (OWS2009), otherwise they have been copied from the referred paper.

To report errors, mistakes, additions, omissions, “prior art” with respect to the “first solved by” column, please send an email to Matthijs Spaan.

1) In (NTYPM2003) an incorrect optimal value for DecTiger h=3 was presented.
2) The (ADZ2009) paper included new results obtained using the algorithm presented in (OWS2009).
3) In these cases the results reported in the referred paper concern a different discount factor (usually as stated in the problem definition).
4) In (OWS2009) a typo in the third decimal was published for Fire Fighting h=2 (-4.3825 instead of the correct -4.3835).
5) In (DABC2013) epsilon-optimal solutions were found with an epsilon of 0.01.

NTYPM2003 (Nair, Tambe, Yokoo, Pynadath & Marsella, IJCAI 2003)
HBZ2004 (Hansen, Bernstein & Zilberstein, AAAI 2004)
SCZ2005 (Szer, Charpillet & Zilberstein, UAI 2005)
SC2006 (Szer & Charpillet, AAAI 2006)
OSV2008 (Oliehoek, Spaan & Vlassis, JAIR 2008)
OWS2009 (Oliehoek, Whiteson & Spaan, AAMAS 2009)
ADZ2009 (Amato, Dibangoye & Zilberstein, ICAPS 2009)
SOA2011 (Spaan, Oliehoek & Amato, IJCAI 2011)
DABC2013 (Dibangoye, Amato, Buffet & Charpillet, IJCAI 2013)

The table below provides the highest known values for a range of benchmark problems with the common discount factor of 0.9 (except Wireless network which used 0.99). We also list the paper that each result first appeared. Note that the results are often an average over a number of runs, so single runs may have higher values than those listed here.

To report errors, mistakes, additions, or omissions, please send an email to Chris Amato.

4) In (PP2011), the value produced from (KZ2010) is reported.

ABZ2007 (Amato, Bernstein & Zilberstein, UAI 2007)
AZ2009 (Amato & Zilberstein, AAMAS 2009)
KZ2010 (Kumar & Zilberstein, UAI 2010)
PP2011 (Pajarinen & Peltonen, NIPS 2011)