What do you do with 2 million square feet of vacant Washington-area office space worth $18 million a year in rent?

The General Services Administration decided to try to sublease as much of it as it could, but so far its attempts have not been a wild success.

Empty federal office space in the Washington area has more than doubled since the arrival of the Reagan administration because of cuts in federal programs and staff levels. After the GSA was unable to renegotiate its leases or move other agencies into the space, it decided to turn for the first time to subleasing.

But the agency failed to receive a single bid by the deadline yesterday for the more than 38,000 square feet of space it offered at 711 14th St. NW. A previous offering, 4,000 square feet in a Chevy Chase building, drew one bid, which the agency hasn't decided whether to accept.

Kenneth L. Perrin, acting chief of the GSA's regional utilization branch, said he was surprised that there was only a single bid on the first offering, but "this is a new program."

The GSA had expected to recoup about $1.4 million from those two sites and six more that it plans to offer later this month. Space in another two dozen buildings is expected to be offered later in the year.

In the past, the GSA has leased space only in buildings that the federal government owns. Currently in the Washington area, it leases 11,978 square feet of space in nine federal buildings, earning an annual rental of $141,265 a year. Four of the tenants are banks, and the rest are small businesses.