Android Back Button and Progress Dialog

First, you should show your dialog from OnPreExecute, hide it in OnPostExecute, and – if necessary – modify it by publishing progress. (see here)

Now to your question: ProgressDialog.show() can take a OnCancelListener as an argument. You should provide one that calls cancel() on the progress dialog instance.

example:

    @Override
    protected void onPreExecute(){
        _progressDialog = ProgressDialog.show(
                YourActivity.this,
                "Title",
                "Message",
                true,
                true,
                new DialogInterface.OnCancelListener(){
                    @Override
                    public void onCancel(DialogInterface dialog) {
                        YourTask.this.cancel(true);
                        finish();
                    }
                }
        );
    }

where _progressDialog is a ProgressDialog member of YourTask.

This class was deprecated in API level 26. ProgressDialog is a modal
dialog, which prevents the user from interacting with the app. Instead
of using this class, you should use a progress indicator like
ProgressBar, which can be embedded in your app’s UI. Alternatively,
you can use a notification to inform the user of the task’s progress. LINK