  We propose a novel multi-task method for quantile forecasting with shared
Linear layers. Our method is based on the Implicit quantile learning approach,
where samples from the Uniform distribution $\mathcal{U}(0, 1)$ are
reparameterized to quantile values of the target distribution. We combine the
implicit quantile and input time series representations to directly forecast
multiple quantile estimations for multiple horizons jointly. Prior works have
adopted a Linear layer for the direct estimation of all forecasting horizons in
a multi-task learning setup. We show that following similar intuition from
multi-task learning to exploit correlations among forecast horizons, we can
model multiple quantile estimates as auxiliary tasks for each of the forecast
horizon to improve forecast accuracy across the quantile estimates compared to
modeling only a single quantile estimate. We show learning auxiliary quantile
tasks leads to state-of-the-art performance on deterministic forecasting
benchmarks concerning the main-task of forecasting the 50$^{th}$ percentile
estimate.
