Engineering design under uncertainty requires methodologies that can balance performance, safety, and cost. In reliability-based design optimization (RBDO), this balance is achieved by enforcing probabilistic safety constraints while minimizing a design objective. A major practical limitation of RBDO is its computational cost, since reliability assessments must be repeated for every design explored during the optimization process. Although surrogate modeling is commonly employed to alleviate this burden, classical deterministic surrogates often become ineffective as the dimensionality of the uncertainty space increases. This work presents an alternative RBDO strategy based on stochastic emulators, which are surrogate models developed to approximate the response distributions of stochastic simulators. Unlike deterministic models, stochastic simulators exhibit intrinsic variability and produce different outputs when evaluated multiple times at the same design point, reflecting latent sources of randomness that are not explicitly represented through model parameters. The proposed framework reformulates the RBDO problem by distinguishing between deterministic design variables and uncertain inputs. The latter are aggregated into a set of latent variables and integrated out, yielding a stochastic response associated with each design point. This response is efficiently approximated using stochastic emulators, such as stochastic polynomial chaos expansions (SPCE) [1] or surrogate-based empirical distributions, including generalized lambda models [2]. This formulation implicitly reduces dimensionality by capturing the influence of high-dimensional uncertainty through a latent representation, while simultaneously providing direct access to conditional response distributions and enabling semi-analytical evaluation of reliability measures such as quantiles or exceedance probabilities. The proposed approach is validated on a set of numerical examples of increasing complexity and dimensionality. The results demonstrate its scalability and show that stochastic emulators provide an efficient tool for reliability-based design optimization in high-dimensional settings. REFERENCES [1] Zhu, X. and B. Sudret (2023). Stochastic polynomial chaos expansions to emulate stochastic simulators. Int. J. Uncer. Quantif., 13(2), 31–52 [2] Zhu, X. and B. Sudret (2021). Emulation of stochastic simulators using generalized lambda models. SIAM/ASA J. Uncertain. Quantification, 9(4), 1345-80