At what rate could AI theoretically self-improve? Due to recursive self-improvement, AI could lead to an intelligence explosion improving on itself year over year exponentially.

Assuming the proper environment was created to allow an AI to self-improve, how fast would this occur?

With human intervention we might say AI could improve similar to GDP or science growth say 3% per year. But this intervention would be additive to the self-recurring improvements made by the AI.

What is a reasonable annual rate of self-growth and what would the processing power of the AI be after 10 years given an initial value of say 1PFLOP?

Example:

human rate = 3% annually

AI rate = 1% of current processing power annually

Year 1. 1 PFLOP

Year 2. 1 PFLOP + (1 PFLOP * 3%) + (1 PFLOP * 1%) = 1.04 PFLOP

Year 3. 1.04 PFLOP + (1.04 PFLOP * 3%) + (1.04 PFLOP * 1.04%) = 1.082 PFLOP

Year 4. 1.082 PFLOP + (1.082 PFLOP * 3%) + (1.082 PFLOP * 1.082%) = 1.126 PFLOP

Year 5. 1.126 PFLOP + (1.126 PFLOP * 3%) + (1.126 PFLOP * 1.126%) = 1.172 PFLOP
The processing power might still follow the Moore's law, but it is basically an economical law, although it has worked surprisingly well considering the physical limitations of technology. An Artificially Intelligent agent could focus on manipulating the market, research possible hardware improvements, allocate human resources more effectively to the problem, etc.

I would expect some improvement in the AI algorithm design itself, which will not influence the number of operations available, but the number of operations required to complete a task. By using a better heuristics, the AI algorithm will consume less brute force to complete the task, thus being able to complete more tasks given the same number of operations. Sorry if I misunderstood the question. Thanks for the improvement.