The house is surrounded by a moat. A small one, filled with vinegar. Humans just step over. But an real-life ant could not traverse it. Some ants can swim or float in water. The purpose of the vinegar is to make it too noxious to try. Or use water with some oil on top. This reduces the surface tension of the water so that the ant can not float.
Ant Man is an ant-sized human, not an actual ant, but he'd still need to either float or swim across the moat. Make the sides too slippery to climb up and the liquid impossible to survive.
So maybe Ant Man shrinks to exit the house then grows to step over the moat then shrinks again to sneak away. To prevent that, make sure the moat has a fence on both sides. No human can get in or out of it and it's too small to transform to human-sized while inside. The fence can be electrified so the small version of Ant Man can not climb it.
Honestly, room arrest (in a lovely glass or plexiglass cage with mini-moats at the threshold of the door and any other openings) makes much more sense. Combine it with great security cameras to know when or if he shrinks. Not fun for privacy, but necessary due to his superpowers.
If he can stay shrunk down for the duration of his confinement, then your job is easy. Constructing a box with tiny doll furniture and no escape is quite simple. The boxes probably already exist retail.
If you can't shrink him or confine him to a room or set of rooms, your best hope might be psychological. Make the penalty for violating the house arrest too great to transgress. Like custody of his kids, if he has any. Losing his job. Etc. Fines wouldn't do it as whoever breaks him out would just pay them.
House arrest in real life is only sometimes literal. In the United States, prisoners are allowed to leave their homes for work, school, medical and other appointments, even to run errands. It's restricted and they have to inform the police where they are going and when. Their ankle monitors are to find them if they flee.