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MATHEMATICS OF OPERATIONS RESEARCH
Vol. 38, No. 2, May 2013, pp. 209–227
ISSN 0364-765X (print) ISSN 1526-5471 (online)
/10.1287/moor.1120.0562
© 2013 INFORMS
On Boundedness of Q-Learning Iterates for
Stochastic Shortest Path Problems
. . Huizhen Yu
) /
s g Laboratory for Information and Decision Systems, Massachusetts Institute of Technology,
( r
r o. Cambridge, Massachusetts 02139, janey_yu@
o
h s
t m
u Dimitri P. Bertsekas
a r
o
f Laboratory for Information and Decision Systems and Department of EECS, Massachusetts Institute of Technology,
e n
h i. Cambridge, Massachusetts 02139, dimitrib@
t s
l
o a We consider a totally asynchronous stochastic approximation algorithm, Q-learning, for solving finite space stochastic shortest
t n
r
y u path (SSP) problems, which are undiscounted, total cost Markov decision processes with an absorbing and cost-free state. For
s o
j the most commonly used SSP models, existing convergence proofs assume that the sequence of Q-learning iterates is bounded
e /
t /
r : with probability one, or some other condition that guarantees boundedness. We prove that the sequence of iterates is naturally
u p
t
o t bounded with probability one, thus furnishing the boundedness condition in the convergence
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