When Does Risk-Controlled Throughput Forecasting Actually Control Risk? A Reproduction Study on LEO Satellite Link

Many applications of black-box predictive models require controlling task-relevant error rates, such as missed lesion pixels in segmentation or missed labels in multilabel classification. Conformal risk control (CRC; Angelopoulos et al., arXiv:2208.02814) gives distribution-free guarantees for such losses, but it calibrates a single threshold shared by all inputs. Because conditional risk varies with the input, this marginal guarantee often overprotects easy cases and underprotects hard ones. We propose ReCIRC (Rectified Conformal Risk Control), which inverts each input's estimated local risk curve to reparameterize the calibrated threshold as a risk budget $a$ representing a common target conditional risk, and then applies CRC unchanged to the resulting family. ReCIRC retains CRC's finite-sample marginal guarantee regardless of the accuracy of the estimated curves, while accurate curves yield approximate conditional risk control and, under additional conditions, asymptotically exact conditional risk control; they also support a risk-calibration diagnostic. Across three synthetic and five real-data settings spanning segmentation, multilabel and multiclass classification, and regression, ReCIRC attained the lowest average worst-group risk and mean positive group excess in every setting, while maintaining marginal risk close to the target, whereas changes in prediction size were application-dependent.

Low Earth Orbit (LEO) satellite mega-constellations such as Starlink require frequent handovers due to high orbital velocities, resulting in substantial Round-Trip Time (RTT) fluctuations. Accurate RTT prediction can mitigate these fluctuations, yet it fundamentally relies on continuously updated serving- satellite information. Existing serving-satellite identification methods typically complete identification only at the end of each scheduling cycle, creating an identification blind zone that limits real-time prediction. To overcome this limitation, we develop StarRTT, an end-to-end real-time framework that eliminates the blind zone by integrating per-second serving-satellite identification with RTT prediction. Within this framework, we propose Real-Time Long Short-Term Memory (RT-LSTM), an LSTM-based RTT prediction model designed to capture both non-stationary RTT evolution and time-varying geometric relationships among the serving satellite, user terminal, and gateways. Specifically, a historical LSTM encodes historical RTT observations and real-time serving-satellite and gateway-relative features, while a future LSTM processes Two-Line Element (TLE)-propagated future features of the identified serving satellite up to the next scheduling instant. Under strict real-time back-testing, RT-LSTM achieves a Mean Absolute Error (MAE) of 1.405 ms averaged over all 15 prediction horizons and 15 reference time-slot indices, reducing the error by 4.3 %, 11.6 %, and 22.1 % compared with the existing baseline models, LSTM, StarNet, and Attention-based Spatiotemporal Model (ASTM), respectively. Notably, the reduction over LSTM reaches 12.5 % at the scheduling instant, highlighting the benefit of real-time serving-satellite information when recent RTT observations are limited.

Conformal risk control (CRC) provides distribution-free guarantees for controlling the expected loss at a user-specified level. Existing theory typically assumes that the loss decreases monotonically with a tuning parameter that governs the size of the prediction set. However, this assumption is often violated in practice, where losses may behave non-monotonically due to competing objectives such as coverage and efficiency. In this paper, we study CRC under non-monotone loss functions when the tuning parameter is selected from a finite grid, a setting commonly arising in thresholding and discretized decision rules. Revisiting a known counterexample, we show that the validity of CRC without monotonicity depends critically on the relationship between the calibration sample size and the grid resolution. In particular, reliable risk control can still be achieved when the calibration sample is sufficiently large relative to the grid size. We establish a finite-sample guarantee for bounded losses over a grid of size $m$, showing that the excess risk above the target level $α$ scales on the order of $\sqrt{\log(m)/n}$, where $n$ is the calibration sample size. A matching lower bound demonstrates that this rate is minimax optimal. We also derive refined guarantees under additional structural conditions, including Lipschitz continuity and monotonicity, and extend the analysis to settings with distribution shift via importance weighting. Numerical experiments on synthetic multilabel classification and real object detection data illustrate the practical implications of non-monotonicity. Methods that explicitly account for finite-sample uncertainty achieve more stable risk control than approaches based on monotonicity transformations, while maintaining competitive prediction set sizes.