Original: Thus
Revised: Thus

Original: [Equation]
Revised: [Equation]

Original: we have
Revised: we have

Original: [Equation]
Revised: [Equation]

Original: where we use the fact that
Revised: where we use the fact that

Original: [Equation]
Revised: [Equation]

Original: Thus
Revised: Thus

Original: [Equation]
Revised: [Equation]

Original: it remains to upper bound the right-hand side of (H.26).
Revised: it remains to upper bound the right-hand side of (H.26).

Original: We have 
Revised: We have (cid:104)

Original: [Equation]
Revised: [Equation]

Original: Taking expectation with respect to s ∼ ν ∗ on the both sides of (H.27) and using the Cauchy-Schwarz inequality, we obatin

Original: [Equation] [Table] [Equation] [Table]
Revised: [Table]

Original: [Equation]

Original: [Table]

Original: [Equation]

Original: [Table]

Original: [Equation]

Original: [Table]

Original: [Equation]
Revised: [Equation]

Original: where in the last inequality we use the error bound in (E [Equation] 20) and the deﬁnition of φ ∗ k and ψ ∗ k in
Revised: where in the last inequality we use the error bound in (E.20) and the deﬁnition of φ ∗ k and ψ ∗ k in

Original: Assumption C
Revised: Assumption C.1.

Original: [Equation]

Original: This ﬁnishes the proof of the ﬁrst inequality
Revised: This ﬁnishes the proof of the ﬁrst inequality.

Original: [Equation]

Original: Part 2.
Revised: Part 2.

Original: The proof of the second inequality follows from a similar argument as above.
Revised: The proof of the second inequality follows from a similar argument as above.

Original: We have
Revised: We have

Original: [Equation]
Revised: [Equation]

Original: 28) where we use the fact that
Revised: where we use the fact that

Original: [Equation]
Revised: [Equation]

Original: Thus [Equation] it remains to upper bound the right-hand side of (H.28).
Revised: Thus, it remains to upper bound the right-hand side of (H.28).

Original: We have
Revised: We have

Original: [Equation]
Revised: [Equation]

Original: [Table]
Revised: Taking expectation with respect to s ∼ ν ∗ on the both sides of (H.29) and using the Cauchy-Schwarz inequality, we obatin

Original: [Equation]
Revised: [Equation]

Original: [Table]

Original: where in the last inequality we use the error bound in (E.20) and the deﬁnition of ψ ∗ k in Assumption
Revised: where in the last inequality we use the error bound in (E.20) and the deﬁnition of ψ ∗ k in Assumption

Original: C.1.
Revised: C [Equation]

Original: This ﬁnishes the proof of the second inequality.
Revised: This ﬁnishes the proof of the second inequality.