Missing utility function in equation (4) in the Botorch paper #1147
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Hi, I have a question regarding an equation in BOTROCH paper, BOTORCH: A Framework for Efficient Monte-Carlo Bayesian Optimization, and I was wondering if someone could help me with it. In equation (1) I can see utility function, a, while in equation (4), there seems to be a missing utility function. Why is it missing? Is it a typo or a reason behind not involving utility function in equaion (4). Thank you in advance for your help. equation (1) equation (4) |
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Hi, (1) is a general form of MC acquisition functions, whereas (4) is specific to KG. It so happens that in KG we maximize the posterior mean, so the utility function “a” here is just the identity. You could use a different utility function in a lookahead strategy as well, but then that wouldn’t be the classic Knowledge Gradient. |
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Thank you Balandat for your help. |
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Hi, (1) is a general form of MC acquisition functions, whereas (4) is specific to KG. It so happens that in KG we maximize the posterior mean, so the utility function “a” here is just the identity. You could use a different utility function in a lookahead strategy as well, but then that wouldn’t be the classic Knowledge Gradient.