ON FR ´ ECHET SUBDIFFERENTIALS

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Toward Off-Policy Learning Control with Function Approximation (2010, background): “(1) Due to the chain-rule of subdifferentials (e.g., Kruger, 2003), it follows that if ϕ̂t+1(θ) is an unbiased estimate of the subgradient of V t+1(θ) (given St+1), then bt+1(θ) = γϕ̂t+1(θ)− ϕt is a subdifferential to δt+1(θ) and thus E[ bt+1(θ)ϕ>t ]E [ ϕtϕ > t ]−1 E[ δt+1(θ)ϕt ] = = −E[ δt+1(θ)ϕt…”
About Regularity of Collections of Sets (2006, background): “Taking into account the extremal characterizations of Asplund spaces in [24] one can conclude that asplundity of the space is not only sufficient but also necessary for the Extended extremal principle to be valid (see [17]).”