将学习与优化统一建模，解决参数未知时的协同求解问题。

We study a class of misspecified saddle point (SP) problems, where the optimization objective depends on an unknown parameter that must be learned concurrently from data. Unlike existing studies that assume parameters are fully known or pre-estimated, our framework integrates optimization and learning into a unified formulation, enabling a more flexible problem class. To address this setting, we propose two algorithms based on the accelerated primal-dual (APD) by Hamedani & Aybat 2021. In particular, we first analyze the naive extension of the APD method by directly substituting the evolving parameter estimates into the primal-dual updates; then, we design a new learning-aware variant of the APD method that explicitly accounts for parameter dynamics by adjusting the momentum updates. Both methods achieve a provable convergence rate of $\mathcal{O}(\log K / K)$, while the learning-aware approach attains a tighter $\mathcal{O}(1)$ constant and further benefits from an adaptive step-size selection enabled by a backtracking strategy. Furthermore, we extend the framework to problems where the learning problem admits multiple optimal solutions, showing that our modified algorithm for a structured setting achieves an $\mathcal{O}(1/\sqrt{K})$ rate. To demonstrate practical impact, we evaluate our methods on a misspecified portfolio optimization problem and show superior empirical performance compared to state-of-the-art algorithms.