Help solve the following question:

Let K ⊂ R^d be a closed convex set with diameter D. Consider

W_{t+1} = Π_K [ W_t − (η/n) Σ_{i=1}^n Π_{B_K}[ ∇ℓ_i(W_t) ] + G_t ],
G_t ~ N(0, σ² I),

for t = 0,...,T−1, where Π_{B_K} denotes projection onto the ℓ2-ball of radius K.

Let W'_t be the corresponding process when exactly one loss term ℓ_i is replaced
by ℓ'_i, with W_0 = W'_0. Assume that for every loss function involved,

‖∇ℓ_i(x) − ∇ℓ_i(y)‖ ≤ L‖x − y‖^λ,   0 < λ ≤ 1,

for all x, y ∈ K. Only the final iterate W_T is released.

For any α > 1, derive the tightest upper bound you can on

D_α( L(W_T) ‖ L(W'_T) ).

Your final result should be explicit enough to evaluate numerically for arbitrary
(T, n, η, K, L, λ, σ, D, α).