I am trying to compute the value of the following function $R:\mathbb{R}^m\mapsto\mathbb{R}$

$$R_n(\theta)=\sup_{\lambda\in\mathbb{R}^m}\left\{-\frac{1}{n}\sum_{i=1}^{n}\sup_{x\in\mathbb{R}^m}\lbrace \lambda^{\mathsf{T}}(Y_i-x^{\mathsf{T}}\theta)x-||x-X_i||^2\rbrace\right\}$$

where $Y_i\in\mathbb{R}$ and $X_i\in\mathbb{R}^m$ for all $i=1,\ldots,n$

My question is how to simplify this expression or in any case how to approximate it or at least sketch an algorithm to do so.


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