  It is commonly recognized that a major issue of robust optimization is the
tendency to produce overly conservative solutions. To address this issue, a new
regret-based criterion with a single control parameter is proposed and
axiomatized to offer smooth control of conservatism in a wide range without
tampering with the uncertainty set. This criterion has many appealing
analytical properties, such as decreasing conservatism with regard to the
control parameter, which makes it a unique choice for fine control of
conservatism. Tractability for robust linear programs with this criterion is
established by reformulating them into those with the maximin criterion, for
which tractable solution schemes and theoretical results are actively developed
in the literature. Closed-form solutions are obtained for the robust one-way
trading problem with this criterion, leading to a greatly simplified
competitive ratio analysis. Numerical experiments are conducted to demonstrate
smooth control of conservatism and the effects on revenue and risk.
