![]() You work as a consultant for an oil company, and you want to maximize a probability density function \(f()\).Instead, you need to begin with a few random drug concentrations, test them, and then use the experimental outcomes to predict the most promising drug combination to use next. Therefore, considering all possible concentration combinations is not a realistic approach. Evaluating the objective function \(f(c_1,c_2,c_3)\) in this context entails conducting actual experiments in the lab requiring personnel, consumables, and waiting for hours or days for the cell cultures to grow. You have narrowed it down to three candidate molecules, and you need to find the best combination of concentrations \(c_1, c_2, c_3\) of the three drugs. You are a researcher investigating mixtures of chemotherapeutic drugs for their ability to kill cancer cells.Mind that the evaluation of the objective function is not necessarily computational! Let me give you a couple of examples, where \(f(x)\) is not something you can calculate with a computer: And for this kind of problem, Bayesian Optimization (BO) is a universal and robust method. To summarize, we want to optimize an expensive, black-box, derivative-free, possibly non-convex function. So, we can’t just go ahead and massively evaluate \(f(x)\) in, say, 100 billion random points and keep the one \(x\) that optimizes \(f(x)\)’s value. However, as if the situation was not bad enough, the function we want to optimize is very costly. The only thing we can do is to evaluate \(f(x)\) at some \(x\)’s. Therefore, methods from the convex optimization field are also not available to us. Also, we don’t have any convexity guarantees about \(f(x)\). It follows that we don’t have access to the first or second derivatives, hence using gradient descent or Newton’s method is a no-go. We are asked to optimize a function we don’t have an analytic expression for. So, what does it mean to be in an optimization hell? Plot: We died and ended up in Dante’s inferno – the optimization version. Brute-force evaluation of objective function.The ingredients of Bayesian Optimization. ![]()
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |