LightInTheBox offers the Xiaomi Mi Robot Vacuum Cleaner for $368.99. Coupon code "XIAOMIBT25" cuts it to $289.99. With $45.47 for shipping, that's $309 off and the lowest price we could find. It can be controlled via smartphone app and can clean for up to two and a half hours per charge.
Note: This item ships from China and may take two to five weeks to arrive. Uncheck "Add Shipping Insurance to your order" during checkout to remove the $7.99 fee.