#01Nov 9, 2026
stat.ME
Conformal Prediction for Multi-Step Forecasting: Conditional Coverage and Sharp Score Calibration Rates
Siyuan He, Yuhong Yang
Uncertainty quantification in prediction is a central problem in statistics and machine learning. Conformal prediction provides a flexible approach to constructing prediction sets with valid marginal coverage under exchangeability. In this paper, we investigate conformal prediction for both one-step and multi-step forecasting from a single stationary time series, addressing temporal dependence and the additional challenges of joint prediction across multiple horizons. We propose a kernel-based framework, called Time series Residual Analysis for Calibration with Kernels (TRACK), for estimating conditional quantiles of residual scores and constructing prediction sets from rolling-window forecasters. The framework accommodates heterogeneous uncertainty across horizons and accounts for dependence induced by rolling estimation, while allowing predictor memory and forecast horizons to grow with the sample size. Our finite-sample bounds quantify how temporal dependence and overlapping score windows affect calibration and coverage. We further derive bounds for conditional quantile estimation and pointwise conditional coverage discrepancy. The guarantees extend to more general predictors that admit an accurate rolling-window approximation. We also derive matching minimax bounds over classes of known score maps, clarifying how overlapping score windows affect calibration accuracy. Experimental results from simulations and applications to wind energy generation and bike sharing demand show that our methods improve regional conditional coverage while maintaining competitive interval widths.
#02Nov 9, 2026
cs.RO
The Relative Value of Demonstration Data: Execution Time Limits and Operator Mixtures in Behavior Cloning
Jiaxuan Guo, Xingyu Ren, Youran Sun and 3 more
Robot demonstration datasets combine demonstrations from teleoperators of uneven experience, so collection teams need to know how many demonstrations from one group match those from another. We measure this with a data multiple: the ratio of the numbers of demonstrations two groups need for their policies to reach the same success rate. On robomimic's simulated Square and Can tasks, we train behavior-cloning policies on demonstrations from the two teleoperators robomimic labels Better and the two it labels Worse, varying dataset size and the share of Worse demonstrations. On Square, within robomimic's 25-second time limit, an all-Worse training set needs 1.55 times as many demonstrations as an all-Better set. Most of this difference is late completion: policies trained on Worse demonstrations finish later, as the Worse teleoperators do, and with a 100-second limit the multiple falls to 1.11. On Can, most of the difference remains at 100 seconds. If each Worse demonstration were worth 1/1.55 of a Better one, as in an all-Worse set, a half-Better, half-Worse set on Square would need 1.22 times as many demonstrations as an all-Better set. In fact, it needs 13% more than that, and this excess persists at every time limit from 20 to 200 seconds. The excess remains when training draws demonstrations uniformly instead of in proportion to their length. On Square, within the 25-second limit, switching to these Worse teleoperators is cheaper at equal success only if they earn less than a third of the Better teleoperators' hourly pay, because Worse demonstrations also take longer to record.
#03Nov 9, 2026
stat.ML
Beyond Prediction Residuals: Conformal Regret Calibration for Robust Contextual Linear Optimization
Lingjie Zhao, Hansheng Jiang, Wei Qi
Predict-then-optimize systems convert contextual forecasts into decisions, yet conformal robust optimization typically calibrates prediction residuals rather than downstream loss. For linear optimization, this parameter-space geometry can be badly misaligned with decision risk: large objective perturbations may preserve the optimizer, while small boundary-crossing perturbations may cause substantial regret. We introduce Conformal Regret Sets, a post-hoc, model-agnostic framework that conformalizes an optimization-derived regret surrogate and uses its calibrated level set for minimax-regret refinement. We first show that directly conformalizing exact regret, although sufficient to certify the nominal predict-then-optimize decision, yields a degenerate robust problem: absent an exogenous bounded support, every alternative decision has unbounded worst-case regret. We therefore use SPO+, a pointwise upper bound on exact regret, as the conformal score, obtaining distribution-free finite-sample marginal regret guarantees under exchangeability. For contextual linear programs, the resulting set decomposes into polyhedral pieces aligned with the normal fan of the feasible polytope. A vertex is active if and only if its predicted suboptimality gap is at most half the calibrated threshold $η$, enabling local, output-sensitive generation of all relevant pieces. Moreover, if $Γ$ is the predicted gap to the closest competing vertex, the nominal and refined decisions admit the sharper worst-case-regret certificate $(η-2Γ)_+$, with an exact early exit when $η\leq 2Γ$. Experiments on contextual fractional knapsack validate the geometry and certificates: continuous refinement reduces the $0.95$-quantile and $\operatorname{CVaR}_{0.95}$ of regret by $9.1\%$ and $13.1\%$ relative to nominal PTO, while vertex-restricted refinement changes only $10.0\%$ of nominal decisions.
#04Nov 9, 2026
cs.LG
Reward-Estimated Hypergradient for Bilevel Reinforcement Learning with Black-Box Follower
Shigeki Kusaka, Mikoto Kudo, Takumi Tanabe and 2 more
Hypergradient (HG) methods for bilevel reinforcement learning (RL) typically assume a white-box follower whose reward is known. In practice, however, the leader rarely knows the follower's reward function and can only observe its trajectories. We address this black-box setting and propose Reward-Estimated Hypergradients (RE-HG), which recovers the follower's reward from these trajectories via inverse RL (IRL). Yet IRL identifies the reward only up to potential-based shaping, a transformation that leaves the follower's behavior unchanged but biases the HG. We prove that, for linear rewards, this bias cancels when IRL estimates are aggregated across sufficiently diverse dynamics, which the leader's own updates naturally supply. To handle finite samples, RE-HG truncates small eigenvalues of the aggregated feature covariance, restoring the identifiable subspace and stabilizing the estimation. Experiments show that RE-HG estimates gradients aligned with a white-box Oracle and achieves comparable performance; empirically, the truncation also suppresses HG explosions, letting RE-HG avoid local optima that trap the Oracle in sharp reward landscapes.
#05Nov 9, 2026
cs.LG
Scale-Invariant Empirical-Bayes Laplace Approximation for ReLU Networks
Shivam Pal, Piyush Rai
ReLU networks are well-known to have continuous scale symmetries; infinitely many reparameterized weight vectors that represent the same function. Dinh et al. (2017) have shown that, by reparameterizing, the geometry of the loss landscape (e.g., curvature) of these networks can be changed arbitrarily without affecting the underlying function. Thus, any quantity that depends on the network's geometry should be defined with care. In this paper, we show that the Empirical Bayes (EB) Laplace's approximation is not well-defined for ReLU networks, mainly due to Hessian dependence in computing the marginal likelihood, which is not invariant under ReLU scale symmetries. Thus, we can get different prior precisions, posterior covariances, and predictive uncertainties for a network having identical predictions under ReLU scaling. We define family of prior precision fields indexed by $γ$ and introduce $γ$-canonicalization, which first converts the network to its canonical representation by balancing the ratio of incoming to outgoing weights, and then fits the Empirical Bayes (EB) Laplace to the canonical representation. This procedure is equivalent to transporting the isotropic Gaussian prior from the canonical representation to the original coordinates, by producing a ReLU-scale-compatible precision field. This makes the marginal likelihood invariant under ReLU scaling, while allowing $γ$ to be selected by maximizing the marginal likelihood. The resulting EB Laplace approximation is well-defined on ReLU scale-equivalence classes and yields consistent prior precision selection and predictive uncertainties across functionally identical parameterizations.