1 research outputs found
Efficient Algorithms for Minimizing Compositions of Convex Functions and Random Functions and Its Applications in Network Revenue Management
In this paper, we study a class of nonconvex stochastic optimization in the
form of , where
the objective function is a composition of a convex function and a
random function . Leveraging an (implicit) convex reformulation via a
variable transformation , we develop stochastic
gradient-based algorithms and establish their sample and gradient complexities
for achieving an -global optimal solution. Interestingly, our
proposed Mirror Stochastic Gradient (MSG) method operates only in the original
-space using gradient estimators of the original nonconvex objective and
achieves sample and gradient complexities,
which matches the lower bounds for solving stochastic convex optimization
problems. Under booking limits control, we formulate the air-cargo network
revenue management (NRM) problem with random two-dimensional capacity, random
consumption, and routing flexibility as a special case of the stochastic
nonconvex optimization, where the random function ,
i.e., the random demand truncates the booking limit decision .
Extensive numerical experiments demonstrate the superior performance of our
proposed MSG algorithm for booking limit control with higher revenue and lower
computation cost than state-of-the-art bid-price-based control policies,
especially when the variance of random capacity is large.
KEYWORDS: stochastic nonconvex optimization, hidden convexity, air-cargo
network revenue management, gradient-based algorithm