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Showing posts with the label Galerkin's method

Constrained MDPs and the reward hypothesis

It's been a looong ago that I posted on this blog. But this should not mean the blog is dead. Slow and steady wins the race, right? Anyhow, I am back and today I want to write about constrained Markovian Decision Process (CMDPs). The post is prompted by a recent visit of Eugene Feinberg , a pioneer of CMDPs, of our department, and also by a growing interest in CMPDs in the RL community (see this , this , or this paper). For impatient readers, a CMDP is like an MDP except that there are multiple reward functions, one of which is used to set the optimization objective, while the others are used to restrict what policies can do. Now, it seems to me that more often than not the problems we want to solve are easiest to specify using multiple objectives (in fact, this is a borderline tautology!). An example, which given our current sad situation is hard to escape, is deciding what interventions a government should apply to limit the spread of a virus while maintaining economic ...

Numerical Errors, Perturbation Analysis and Machine Learning

Everyone hates numerical errors. We love to think that computers are machines with infinite precision. When I was a student, I really hated error analysis. It sounded like a subject that is set out to study an annoying side-effect of our imperfect computers, a boring detail that is miles away from anything that anyone would ever consider a nice part of mathematics. I will not try to convince you today that the opposite is true. However, even in error analysis there are some nice ideas and lessons to be learned. This post asks the question whether, if you are doing machine learning, you should care about numerical errors. This issue should be well understood. However, I don't think that it is as well appreciated as it should be, or that it received the attention it should. In fact, I doubt that the issue is discussed in any of the recent machine learning textbooks beyond the usual caveat "beware the numerical errors" (scary!). In this blog, I will illustrate the questi...