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A.1 Adv Setup
For Adv, we use 3 sub-discriminators as Han et al. (2021c), where each sub-discriminator consists of two MLP layers with a hidden size of 256, followed by a classifier layer to predict the protected attribute. Sub-discriminators are optimised for at most 100 epochs after each epoch of main model training, leading to extra training time.
A.2 Hyperparameter Settings for Twitter Sentiment Analysis
For all models except for Adv, the learning rate is  $3e - 3$ , and the batch size is 2,048. For INLP, following Ravfogel et al. (2020), we use 300 linear SVM classifiers. For Adv, the learning rate is  $1e - 3$ , and the batch size is 2,048, the number of discriminators is 3,  $\lambda_{\mathrm{adv}}$  is 0.5, and  $\lambda_{\mathrm{diff}}$  is  $1e - 3$ . For FairBatch,  $\alpha$  is set as 0.1. For both EOCLA and EOGLB,  $\lambda$  is set as 0.5. All hyperparameters are finetuned on the Moji dev set.
A.3 Hyperparameter Settings for Profession Classification
For all models except for Adv, the learning rate is  $3e - 3$ , and the batch size is 2,048. For INLP, following Ravfogel et al. (2020), we use 300 linear SVM classifiers. For Adv, the learning rate is  $1e - 2$ , and the batch size is 1,024, the number of discriminators is 3,  $\lambda_{\mathrm{adv}}$  is  $1e - 2$ , and  $\lambda_{\mathrm{diff}}$  is  $1e4$ . For FairBatch,  $\alpha$  is set as  $5e - 2$ . For EOCLA,  $\lambda$  is set as  $1e - 2$ , and for EOGLB,  $\lambda$  is set as  $5e - 3$ . All hyperparameters are finetuned on the Bios dev set.
B.1 Ablation Study hyperparameter Settings
For all models, we have tuned the hyperparameter  $\lambda$  and selected model based on performance on the dev set. On the Moji dataset, for EO $_{\mathrm{CLA}}^{\mathrm{max}}$ ,  $\lambda = 2$ , for EO $_{\mathrm{CLA}}^{\mathrm{min}}$ ,  $\lambda = 0.4$ , for EO $_{\mathrm{GLB}}^{\mathrm{max}}$ ,  $\lambda = 2$ , for EO $_{\mathrm{GLB}}^{\mathrm{min}}$ ,  $\lambda = 0.2$ . On the Bios dataset, for EO $_{\mathrm{CLA}}^{\mathrm{max}}$ ,  $\lambda = 0.05$ , for EO $_{\mathrm{CLA}}^{\mathrm{min}}$ ,  $\lambda = 0.005$ , for EO $_{\mathrm{GLB}}^{\mathrm{max}}$ ,  $\lambda = 0.005$ , for EO $_{\mathrm{GLB}}^{\mathrm{min}}$ ,  $\lambda = 1e - 4$ .