An unconventional administrative law judge who recently sparked an investigation into possible corruption among federal mine inspectors in eastern Kentucky has run afoul of Reagan administration officials.

They claim that he has improperly swapped his judicial robe for a detective's trench coat; he insists that the administration does not want to admit that it has a problem.

The government has refused to reimburse Joseph B. Kennedy, a judge at the Federal Mine Safety and Health Review Commission, $479 for a trip to meet, he said, with "confidential informants" to discuss "shakedowns and payoffs" involving federal inspectors.

Kennedy contends that his May trip to Paintsville, Ky., had the Justice Department's blessing and that his meeting turned up 36 leads for federal investigators.

But a department official said yesterday that Justice never approved the trip, and Kennedy's boss has said the trip was not made on commission business. The independent commission resolves disputes involving miners, mine operators and the Labor Department's Mine Safety and Health Administration, mostly over fines levied by federal mine inspectors.

Kennedy first raised corruption charges in a strongly worded opinion issued in March as part of a settlement of safety citations against the Pontiki Coal Corp. Kennedy criticized MSHA inspectors for lax enforcement and suggested that they ignored "conditions of wanton, if not criminal, endangerment."

Kennedy's ruling prompted an investigation by Justice and the Labor Department's inspector general. It also angered Labor Department officials, who asked the commission to review the Pontiki case.

Labor officials contended that Kennedy could not support his charges and "abused his authority" by issuing an opinion that "deals with matters far beyond the scope of the proceeding."

In May, Kennedy was contacted by a "confidential informant" with information about the Pontiki case, Kennedy's attorney, Philip G. Sunderland, said yesterday. Kennedy in turn contacted Susan Kuzma, an attorney in Justice's Public Integrity Section, who agreed to travel with him, Sunderland said.

Rosemary Collyer, then the chairman of the commission, verbally approved the trip, Sunderland said. Collyer, who was appointed general counsel of the National Labor Relations Board this week, could not be reached for comment.

Sunderland said Kuzma backed out of the trip the night before, but did not object to Kennedy's going on his own. Kennedy met with an informant, briefed Kuzma, and filed his expense voucher, Sunderland said.

William Hendricks, deputy chief of the public integrity section, denied yesterday that Kuzma ever agreed to accompany Kennedy to Paintsville. Speaking for the department, he said, "On a couple of occasions, Judge Kennedy sought to have her travel with him to meet informants . . . . The matter was considered, but at no time did we agree to any such travel."

Kennedy responded that the administration "doesn't want to get involved before an election."