How do you define an xgboost model where the predicted value is based on previous iterations?

I've built the following model, but can't work out how to implement it in xgboost.

I'm trying to approximate probabilities within a given portfolio using an existing spreadsheet as the basis (initial y_test values).

Assuming I have split my dataset into data tables train_db and test_db:

oos_error <- Inf

repeat {
    rf <- 
        train(
            train_dt[, .(<x values>)],
            train_dt[, y / y_test],
            weights = train_dt$WEIGHTS,
            preProcess = c("center", "scale"),
            method = "rpart2",
            tuneGrid = expand.grid(maxdepth = 2)
        )
    
    train_dt[, y_test := 0.99 * y_test + 0.01 * y_test * predict(rf, newdata = train_dt)]
    test_dt[, y_test := 0.99 * y_test + 0.01 * y_test * predict(rf, newdata = test_dt)]
    
    oos_error_prev <- oos_error
    oos_error <- test_dt[, LOSS_FUNCTION(.)] ## Residual squared error
    
    if (oos_error > oos_error_prev) {
        break()
    }
}

When trying to construct my train_dt xgb.DMatrix input, I'm not sure what to put as the input, since what is trying to be predicted is based on the previous input.