We’ll say that a consequentialist optimiser ψ=λu:Γ→R.{γ∈Γ|u(γ)∈q(u)} is context-independent if Image(u)=Image(u′)⟹ψ(u)=ψ(u′).
Context-independence is a stronger condition than consequentialism — this condition says that, once we know which payoffs are achievable in the agent’s task, then the only thing relevant to the optimality of a particular option is its payoff. For example, argmaxX is context-independent, but better-than-averageπ is not.
argmaxX is not context-independent according to the given definition.
Consider tasks u,u′:{0,1}→{0,1}, with u(x)=x and u′(x)=1−x. Then argmaxu={1}≠argmaxu′={0}, despite Imageu=Imageu′.
I guess the correct definition says q(u)=q(u′) instead of ψ(u)=ψ(u′).
argmaxX is not context-independent according to the given definition.
Consider tasks u,u′:{0,1}→{0,1}, with u(x)=x and u′(x)=1−x. Then argmaxu={1}≠argmaxu′={0}, despite Imageu=Imageu′.
I guess the correct definition says q(u)=q(u′) instead of ψ(u)=ψ(u′).
Thanks v much! Can’t believe this sneaked through.