This circuit only steps the voltage down. If your LED voltage drop at 18mA is 1.8V then the circuit will go into regulation at 1.9V. The efficiency is somwhere around 76% because of the 1K resistor, but you can half the losses by going to a 2.2K resistor. The penalty is that you then you need more battery voltage to go into regulation; 2.0V in the example above. Use of a FET and a 4584 hex inverter really helps the efficiency but then you are looking at higher voltage operation around 6Volts, though that would be needed anyhow if white LED used.