  Partially-observable Markov decision processes (POMDPs) with discounted-sum
payoff are a standard framework to model a wide range of problems related to
decision making under uncertainty. Traditionally, the goal has been to obtain
policies that optimize the expectation of the discounted-sum payoff. A key
drawback of the expectation measure is that even low probability events with
extreme payoff can significantly affect the expectation, and thus the obtained
policies are not necessarily risk-averse. An alternate approach is to optimize
the probability that the payoff is above a certain threshold, which allows
obtaining risk-averse policies, but ignores optimization of the expectation. We
consider the expectation optimization with probabilistic guarantee (EOPG)
problem, where the goal is to optimize the expectation ensuring that the payoff
is above a given threshold with at least a specified probability. We present
several results on the EOPG problem, including the first algorithm to solve it.
