Justification for Simplification in Policy Optimization
A colleague is working on an optimization problem with the objective function arg min_θ Eₓ[ f(θ, x) + C(x) ], where θ are the parameters to be optimized. They simplify the objective to arg min_θ Eₓ[ f(θ, x) ] and justify it by stating, 'The term C(x) is a constant, so it can be ignored.' Evaluate this justification. Is it entirely correct? If not, refine the statement to be more precise.
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Ch.4 Alignment - Foundations of Large Language Models
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Solution to KL Divergence Minimization for Policy Optimization
When optimizing a policy π_θ to match an optimal policy π*, the objective function is often simplified from Objective A to Objective B:
Objective A:
arg min_θ Eₓ[KL(π_θ(·|x) || π*(·|x)) - log Z(x)]Objective B:arg min_θ Eₓ[KL(π_θ(·|x) || π*(·|x))]What is the fundamental mathematical reason this simplification is valid?
Efficiency in Policy Optimization Implementation
Justification for Simplification in Policy Optimization