# Oracle in optimization

I have encountered the word oracle in the following context:

Given an $$\alpha$$-approximate oracle for stochastic optimization we show how to implement an $$\alpha$$-approximate solution for robust optimization under a necessary extension, and illustrate its effectiveness in applications.

I saw this question, but it doesn't seem to have the same meaning. I was wondering what does oracle mean in this context.

Edits:

I found the following definition in this paper:

A $$\rho$$-approximate Bayesian optimization oracle is a function $$\mathcal{O}_{\rho}:(\Theta \rightarrow \mathbb{R}) \rightarrow > \Theta$$ for which: $$f\left(\mathcal{O}_{\rho}(f)\right) \leq \inf _{\theta^{*} \in \Theta} f\left(\theta^{*}\right)+\rho$$ for any $$f: \Theta \rightarrow \mathbb{R}$$ that can be written as a nonnegative linear combination of the objective and constraint functions $$g_0, g_1, \dots, g_m$$.

I would appreciate if someone can shed some light on it.

The definition of $$\alpha$$-Approximate Stochastic oracle has been given in the paper that you provide on Page $$3$$.
Given a distribution $$D$$ over $$\mathcal{L}$$, an $$\alpha$$-approximate stochastic oracle $$M(D)$$ computes $$x^*$$ such that such that $$\mathbb{E}_{L \sim D}[L(x^*)] \le \alpha \min_{x \in \mathcal{X}} \mathbb{E}_{L \sim D}[L(x)]$$
You need not know the details of $$M$$, but if you provide it with a distribution $$D$$, then it returns you an $$x^*$$ such that if you evaluate the expected loss it is an most $$\alpha$$ times the objective value of the minimum of the expected loss.