# Efficient Algorithms for A Class of Stochastic Hidden Convex Optimization and Its Applications in Network Revenue Management

arXiv: https://arxiv.org/abs/2205.01774 · HTML: https://mlsanity.com/paper/2205.01774/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 May 2022.

## Built on by (most cited first, 5 of 5)

- [Momentum Provably Improves Error Feedback!](https://mlsanity.com/paper/2305.15155/) (2023)
- [Contextual Stochastic Bilevel Optimization](https://mlsanity.com/paper/2310.18535/) (2023)
- [Non-convex Stochastic Composite Optimization with Polyak Momentum](https://mlsanity.com/paper/2403.02967/) (2024)
- [Causal Invariance Learning via Efficient Nonconvex Optimization](https://mlsanity.com/paper/2412.11850/) (2024)
- [Online Learning on Hidden-Convex Losses via Algorithmic Equivalence: Optimal Regret, Geometric Barrier, and Bandit Feedback](https://mlsanity.com/paper/2605.26373/) (2026)

## Abstract (arXiv)

We study a class of stochastic nonconvex optimization in the form of minx∈X F(x):=mathbbE_xi [f(φ(x,xi))], i.e., F is a composition of a convex function f and a random function φ. Leveraging an (implicit) convex reformulation via a variable transformation u=mathbbE[φ(x,xi)], we develop stochastic gradient-based algorithms and establish their sample and gradient complexities for achieving an ε-global optimal solution. Interestingly, our proposed Mirror Stochastic Gradient (MSG) method operates only in the original x-space using gradient estimators of the original nonconvex objective F and achieves tildeO(ε-2) 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 φ(x,xi)=xwedgexi, i.e., the random demand xi truncates the booking limit decision x. 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, gradient methods, passenger network revenue management, air-cargo network revenue management