Is this considered acceleration or deceleration

If you increase your speed at a decreasing rate. Is that even possible?

It is definitely possible. Imagine you pull onto a freeway and realize a truck is coming behind you faster than expected. Naturally, you gun the engine and begin accelerating at an extremely fast rate. However, you soon realize that you are fast approaching the speed limit, and the truck is no longer an issue. To avoid shooting over the speed limit, you lighten up on the pedal. You are still accelerating, in that you are getting faster, but you are not getting faster quite as fast, if that makes sense.

To explain the other comment about "negative acceleration," it is true that in a purely physics-oriented discussion there is no such thing as "deceleration." Because velocity is defined as "speed with direction," deceleration is really just acceleration in the other direction, or negative acceleration. However, in normal conversation and for the purpose of this question, "deceleration" is perfectly acceptable to mean the same general principle. Regardless, though, this is still acceleration, not deceleration.

It would be considered acceleration. Although it's a decreasing rate, you're saying that you're speeding up, but in smaller amounts for every interval of time that passes. You could start off increasing your speed by 10mph and in the end you could be increasing it by 1/10mph.

In layman's terms this simply means that you are speeding up(accelerating) by less and less.
Imagine a car accelerating up a hill, it will (natuarally, besauce of gravity) slow down how fast it is speeding up, but it is still none the less getting faster, just not as fast as before.

Any change in speed, or more correctly velocity, is called acceleration in physics. Reducing speed involves negative acceleration. What you describe is accelerating at a decreasing rate.

you are still accelerating, just at a decreasing rate.