The Food and Drug Administration, overriding the advice of an expert panel, said Monday that it would not require doctors to have special training before they could prescribe long-acting narcotic painkillers that can lead to addiction. The F.D.A. announcement came after several years of deliberations by the agency into the growing problem of prescription painkiller abuse and misuse. In 2010, a panel of outside experts assembled by the F.D.A. overwhelmingly rejected the agency’s proposal that physician training be voluntary.