Fact 1:
The US Immigration and Nationality Act places an automatic lifetime ban upon anyone who has ever committed an act of 'moral turpitude' (unless they were a minor at the time and it was a single act). It's irrelevant as to whether the person was actually convicted before a court.
Fact 2:
The definition of 'moral turpitude' (which is referred to elsewhere in US law) varies between US states but the one used by immigration officials is that given in Volume 9 of the US Department of State Foreign Affairs Manual, which includes all offences of theft.
Fact 3:
Accepting a caution is an admission of having carried out the act to which it relates.
Fact 4:
Anyone who has committed a criminal offence (even if they weren't convicted in court) is, according to the rules on the US Embassy website, ineligible to enter the USA under the Visa Waiver Program; they must apply for a visa. (It's a long-winded process, including getting hold of a copy of their 'police record' and attending an interview in London)
Fact 5:
Due to Fact 1, the US Embassy staff MUST (in the first instance) REFUSE to issue a visa.
Fact 6:
Anyone refused a visa on the grounds of Fact 1 has the right to ask that their request is then forwarded to Washington as an 'application for a waiver of permanent ineligibility'.
Fact 7:
IF that application is granted, the US Embassy staff can then reconsider the application and may grant a visa.
Fact 8:
The processes above take a VERY long time. The US Embassy website indicates that it takes at least 6 months for the 'administrative processing'. (The longest wait I've seen reported on this forum was one of 15 months. The application was then refused due to the applicant having committed 2 offences of driving without insurance).