1.完全正确。

2.翻译为…所面临的…

3.本身就是很常见的表达，在外刊和词典中都广为出现，你问出这个问题已经默认他是错误的表达了。

4.你会产生这种问题是因为你用中文去看待这个句子，face你翻译为面临当然认为只能sb face sth，但是在英文中sb face sth=sth face sb=sb have to deal with sth.你可以把这里的face看作正对着…，也就是这个问题正对着某人，也就是某人面临着…的意思，这里facing…为现在分词作后置定语。

The details of this formalization must wait until Chapter 3, but the basic idea is simply to capture the most important aspects of the real problem facing a learning agent interacting over time with its environment to achieve a goal

【并列句1】// The details of this formalization【主语】//  must wait 【谓语动词】// until Chapter 3【时间状语】//  

【并列句2】but【连词】//  the basic idea【主语】//  is 【系动词】// simply to capture the most important aspects of the real problem facing a learning agent interacting over time with its environment to achieve a goal【表语】// 

【不定式】to capture【不定式】//  the most important aspects 【宾语】// of the real problem【后置定语(1)】//  facing a learning agent interacting over time with its environment to achieve a goal【后置定语(2)】//  interacting over time with....是现在分词作后置定语修饰名词a learning agent

备注:face  vt. 面对/面向/面临/面朝 通常有以下几种结构

【1】A face B(主动);  B be faced by A(被动)

They stood facing each other.他们面对面站着。【现在分词作方式状语】

The garden faces south.  花园朝南。

She stood up from the table and faced him.她从桌前站起来，面对着他。

These are the problems faced by one-parent families.

这些是单亲家庭面对的问题。【过去分词作后置定语】

The company is facing a financial crisis.公司正面临财政危机。

The immense difficulties facing European businessmen in Russia were only too evident.

在俄罗斯的欧洲商人所面临的巨大困难是显而易见的。【现在分词作后置定语】

【2】A be faced with B

She is faced with a difficult decision.她眼前有一项难作的决定。