We had the same problem when making our API as well. We were looking for an HTTP status code equivalent to an InvalidArgumentException. After reading the source article below, we ended up using 422 Unprocessable Entity which states:
The 422 (Unprocessable Entity) status code means the server understands the content type of the request entity (hence a 415 (Unsupported Media Type) status code is inappropriate), and the syntax of the request entity is correct (thus a 400 (Bad Request) status code is inappropriate) but was unable to process the contained instructions. For example, this error condition may occur if an XML request body contains well-formed (i.e., syntactically correct), but semantically erroneous, XML instructions.
source: https://www.bennadel.com/blog/2434-http-status-codes-for-invalid-data-400-vs-422.htm