# Stochastic Optimization under Hidden Convexity

arXiv: https://arxiv.org/abs/2401.00108 · HTML: https://mlsanity.com/paper/2401.00108/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Dec 2023.

## Built on by (most cited first, 12 of 12)

- [Taming Nonconvex Stochastic Mirror Descent with General Bregman Divergence](https://mlsanity.com/paper/2402.17722/) (2024)
- [On the Global Optimality of Policy Gradient Methods in General Utility Reinforcement Learning](https://mlsanity.com/paper/2410.04108/) (2024)
- [Learning Equilibria in Adversarial Team Markov Games: A Nonconvex-Hidden-Concave Min-Max Optimization Problem](https://mlsanity.com/paper/2410.05673/) (2024)
- [Natural Gradient VI: Guarantees for Non-Conjugate Models](https://mlsanity.com/paper/2510.19163/) (2025)
- [Causal Invariance Learning via Efficient Nonconvex Optimization](https://mlsanity.com/paper/2412.11850/) (2024)
- [Solving Hidden Monotone Variational Inequalities with Surrogate Losses](https://mlsanity.com/paper/2411.05228/) (2024)
- [Convex Markov Games and Beyond: New Proof of Existence, Characterization and Learning Algorithms for Nash Equilibria](https://mlsanity.com/paper/2602.12181/) (2026)
- [Gradient Dominance in the Linear Quadratic Regulator: A Unified Analysis for Continuous-Time and Discrete-Time Systems](https://mlsanity.com/paper/2602.22577/) (2026)
- [Global Optimality for Constrained Exploration via Penalty Regularization](https://mlsanity.com/paper/2604.28144/) (2026)
- [Online Learning on Hidden-Convex Losses via Algorithmic Equivalence: Optimal Regret, Geometric Barrier, and Bandit Feedback](https://mlsanity.com/paper/2605.26373/) (2026)
- [A proximal subgradient method for nonconvex stochastic optimization under the Kurdyka-Lojasiewicz condition](https://mlsanity.com/paper/2608.05460/) (2026)
- [Benign Nonconvex Landscape for Policy Optimization: Infinite-Horizon Discounted MDPs with General State and Action Spaces](https://mlsanity.com/paper/2609.21433/) (2026)

## Abstract (arXiv)

In this work, we consider constrained stochastic optimization problems under hidden convexity, i.e., those that admit a convex reformulation via non-linear (but invertible) map c(·). A number of non-convex problems ranging from optimal control, revenue and inventory management, to convex reinforcement learning all admit such a hidden convex structure. Unfortunately, in the majority of applications considered, the map c(·) is unavailable or implicit; therefore, directly solving the convex reformulation is not possible. On the other hand, the stochastic gradients with respect to the original variable are often easy to obtain. Motivated by these observations, we examine the basic projected stochastic (sub-) gradient methods for solving such problems under hidden convexity. We provide the first sample complexity guarantees for global convergence in smooth and non-smooth settings. Additionally, in the smooth setting, we improve our results to the last iterate convergence in terms of function value gap using the momentum variant of projected stochastic gradient descent.