Diamonds are much harder to find and worth a lot more.

I once read a post by someone who was unimpressed with the paper that introduced Generative Adversarial Networks (GANs). They pointed out some sloppy math and other such problems and were confused why such a paper had garnered so much praise.

Someone replied that, in her decades of reading research papers, she learned that finding flaws is easy and uninteresting. The real trick is being able to find the rare glint of insight that a paper brings to the table. Understanding how even a subtle idea can move a whole field forward. I kinda sympathize as a software developer.

I remember when I first tried to slog through Marcus Hutter’s book on AIXI, I found the idea absurd. I have no formal background in mathematics, so I chalked some of that up to me not fully understanding what I was reading. I kept coming back to the question (among many others): “If AIXI is incomputable, how can Hutter supposedly prove that it performs ‘optimally’? What does ‘optimal’ even mean? Surely it should include the computational complexity of the agent itself!”

I tried to modify AIXI to include some notion of computational resource utilization until I realized that any attempt to do so would be arbitrary. Some problems are much more sensitive to computational resource utilization than others. If I’m designing a computer chip, I can afford to have the algorithm run an extra month if it means my chip will be 10% faster. The algorithm that produces a sub-optimal solution in milliseconds using less than 20 MB of RAM doesn’t help me. At the same time, if a saber-toothed tiger jumps out of a bush next to me. I don’t have months to figure out a 10% faster route to get away.

I believe there are problems with AIXI, but lots of digital ink has been spilled on that subject. I plan on contributing a little to that in the near future, but I also wanted to point out that, it’s easy to look at an idea like AIXI from the wrong perspective and miss a lot of what it truly has to say.

Rough is easy to find and not worth much.

Diamonds are much harder to find and worth a lot more.

I once read a post by someone who was unimpressed with the paper that introduced Generative Adversarial Networks (GANs). They pointed out some sloppy math and other such problems and were confused why such a paper had garnered so much praise.

Someone replied that, in her decades of reading research papers, she learned that finding flaws is easy and uninteresting. The real trick is being able to find the rare glint of insight that a paper brings to the table. Understanding how even a subtle idea can move a whole field forward. I kinda sympathize as a software developer.

I remember when I first tried to slog through Marcus Hutter’s book on AIXI, I found the idea absurd. I have no formal background in mathematics, so I chalked some of that up to me not fully understanding what I was reading. I kept coming back to the question (among many others): “If AIXI is incomputable, how can Hutter supposedly prove that it performs ‘optimally’? What does ‘optimal’ even mean? Surely it should include the computational complexity of the agent itself!”

I tried to modify AIXI to include some notion of computational resource utilization until I realized that any attempt to do so would be arbitrary. Some problems are much more sensitive to computational resource utilization than others. If I’m designing a computer chip, I can afford to have the algorithm run an extra month if it means my chip will be 10% faster. The algorithm that produces a sub-optimal solution in milliseconds using less than 20 MB of RAM doesn’t help me. At the same time, if a saber-toothed tiger jumps out of a bush next to me. I don’t have months to figure out a 10% faster route to get away.

I believe there are problems with AIXI, but lots of digital ink has been spilled on that subject. I plan on contributing a little to that in the near future, but I also wanted to point out that, it’s easy to look at an idea like AIXI from the wrong perspective and miss a lot of what it truly has to say.