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Statements
‖ g σ ^ c ( 𝝅 ( c ) , 𝜸 ( c ) ) − g σ ^ c ′ ( 𝝅 ( c ′ ) , 𝜸 ( c ′ ) ) ‖ 2 = ‖ g τ ∘ σ ^ c ( 𝝅 ( c ) , 𝜸 ( c ) ) − g τ ∘ σ ^ c ′ ( 𝝅 ( c ′ ) , 𝜸 ( c ′ ) ) ‖ 2 subscript norm subscript 𝑔 subscript ^ 𝜎 𝑐 superscript 𝝅 𝑐 superscript 𝜸 𝑐 subscript 𝑔 subscript ^ 𝜎 superscript 𝑐 ′ superscript 𝝅 superscript 𝑐 ′ superscript 𝜸 superscript 𝑐 ′ 2 subscript norm subscript 𝑔 𝜏 subscript ^ 𝜎 𝑐 superscript 𝝅 𝑐 superscript 𝜸 𝑐 subscript 𝑔 𝜏 subscript ^ 𝜎 superscript 𝑐 ′ superscript 𝝅 superscript 𝑐 ′ superscript 𝜸 superscript 𝑐 ′ 2 \|g_{\hat{\sigma}_{c}(\boldsymbol{\pi}^{(c)},\boldsymbol{\gamma}^{(c)})}-g_{\hat{\sigma}_{c^{\prime}}(\boldsymbol{\pi}^{(c^{\prime})},\boldsymbol{\gamma}^{(c^{\prime})})}\|_{2}=\|g_{\tau\circ\hat{\sigma}_{c}(\boldsymbol{\pi}^{(c)},\boldsymbol{\gamma}^{(c)})}-g_{\tau\circ\hat{\sigma}_{c^{\prime}}(\boldsymbol{\pi}^{(c^{\prime})},\boldsymbol{\gamma}^{(c^{\prime})})}\|_{2} ∥ italic_g start_POSTSUBSCRIPT over^ start_ARG italic_σ end_ARG start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT ( bold_italic_π start_POSTSUPERSCRIPT ( italic_c ) end_POSTSUPERSCRIPT , bold_italic_γ start_POSTSUPERSCRIPT ( italic_c ) end_POSTSUPERSCRIPT ) end_POSTSUBSCRIPT - italic_g start_POSTSUBSCRIPT over^ start_ARG italic_σ end_ARG start_POSTSUBSCRIPT italic_c start_POSTSUPERSCRIPT ′ end_POSTSUPERSCRIPT end_POSTSUBSCRIPT ( bold_italic_π start_POSTSUPERSCRIPT ( italic_c start_POSTSUPERSCRIPT ′ end_POSTSUPERSCRIPT ) end_POSTSUPERSCRIPT , bold_italic_γ start_POSTSUPERSCRIPT ( italic_c start_POSTSUPERSCRIPT ′ end_POSTSUPERSCRIPT ) end_POSTSUPERSCRIPT ) end_POSTSUBSCRIPT ∥ start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT = ∥ italic_g start_POSTSUBSCRIPT italic_τ ∘ over^ start_ARG italic_σ end_ARG start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT ( bold_italic_π start_POSTSUPERSCRIPT ( italic_c ) end_POSTSUPERSCRIPT , bold_italic_γ start_POSTSUPERSCRIPT ( italic_c ) end_POSTSUPERSCRIPT ) end_POSTSUBSCRIPT - italic_g start_POSTSUBSCRIPT italic_τ ∘ over^ start_ARG italic_σ end_ARG start_POSTSUBSCRIPT italic_c start_POSTSUPERSCRIPT ′ end_POSTSUPERSCRIPT end_POSTSUBSCRIPT ( bold_italic_π start_POSTSUPERSCRIPT ( italic_c start_POSTSUPERSCRIPT ′ end_POSTSUPERSCRIPT ) end_POSTSUPERSCRIPT , bold_italic_γ start_POSTSUPERSCRIPT ( italic_c start_POSTSUPERSCRIPT ′ end_POSTSUPERSCRIPT ) end_POSTSUPERSCRIPT ) end_POSTSUBSCRIPT ∥ start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT
