Forking Uncertainties: Reliable Prediction and Model Predictive Control
  with Sequence Models via Conformal Risk Control
Matteo Zecchin Sangwoo Park Osvaldo Simeone
In many real-world problems, predictions are leveraged to monitor and control
cyber-physical systems, demanding guarantees on the satisfaction of reliability
and safety requirements. However, predictions are inherently uncertain, and
managing prediction uncertainty presents significant challenges in environments
characterized by complex dynamics and forking trajectories. In this work, we
assume access to a pre-designed probabilistic implicit or explicit sequence
model, which may have been obtained using model-based or model-free methods. We
introduce probabilistic time series-conformal risk prediction (PTS-CRC), a
novel post-hoc calibration procedure that operates on the predictions produced
by any pre-designed probabilistic forecaster to yield reliable error bars. In
contrast to existing art, PTS-CRC produces predictive sets based on an ensemble
of multiple prototype trajectories sampled from the sequence model, supporting
the efficient representation of forking uncertainties. Furthermore, unlike the
state of the art, PTS-CRC can satisfy reliability definitions beyond coverage.
This property is leveraged to devise a novel model predictive control (MPC)
framework that addresses open-loop and closed-loop control problems under
general average constraints on the quality or safety of the control policy. We
experimentally validate the performance of PTS-CRC prediction and control by
studying a number of use cases in the context of wireless networking. Across
all the considered tasks, PTS-CRC predictors are shown to provide more
informative predictive sets, as well as safe control policies with larger
returns.