MIKHAIL GORBACHEV threw Ronald Reagan a bold challenge in his Time interview.

He offered to make deep cuts in existing offensive weapons if the United States would limit to research its work on the prospective Reagan Strategic Defense Initiative, the apple of the president's eye and the ace -- the American technological advantage -- in his bargaining hand. Mr. Reagan fired back at his news conference on Tuesday, in effect daring Mr. Gorbachev to engage him on the terrain of American public opinion and declaring that he would carry his no-compromise position on SDI right up to the summit in November.

And then? Any attempt to guess what will happen in Geneva comes down to expressing not much more than the degree of confidence one has in Mr. Reagan. What has happened this week, however, is quite clear. Mr. Gorbachev made the familiar initiative open to a totalitarian leader negotiating with a democratic adversary. Secure in the knowledge that there is no Soviet opinion that an American president can turn against him, he attempted to enlist a part of American opinion against the U.S. president before meeting him at Geneva.

And he did it well. To an audience, considerable parts of which were bound to be sympathetic, Mr. Gorbachev said that he sees SDI not in the Reagan image of an ultimate shield protecting everyone equally and allowing nuclear disarmament, but as a weapon enabling and encouraging the United States alone to plan a first strike. The arms control package that he hinted at -- in terms not yet presented concretely at the bargaining table -- had more or less appeal not just to broad sectors of the American public but also to some officials within the administration.

President Reagan was under considerable pressure to vie with Mr. Gorbachev on the field of American and Western opinion for the title of presummit moderate. Instead he chose to make a display of his capacity to sustain the bargaining position of his choice. In the teeth of threats from Moscow and warnings from many Americans that he was putting an arms control agreement out of reach, he insisted he would not make the SDI negotiable at any of the early-middle, research-testing-development stages of which the would-be compromisers speak.

Within this administration there are differences on whether any agreement that may be available is in the American interest. The evidence is, however, that the administration understands trade- offs are going to be needed for an agreement. Just what these trade-offs should be is a matter still and necessarily under review. What Mr. Reagan should be judged on is not how he looks in the run up to the summit but what discipline and responsibility he brings to the process of hammering out a position there. In any event, wherever the process fetches, Mr. Reagan is plainly determined that he, and not Mikhail Gorbachev, be the master of it.