online robust aggregation

This work investigates how to robustly aggregate multiple calibrated but potentially under-informed expert predictions for decision-making, assuming only that the experts satisfy calibration. To this end, it introduces a max-min robust benchmark grounded in calibration constraints, which leverages additional decision-relevant information embedded in the joint distribution of expert forecasts by maximizing worst-case expected utility. This benchmark strictly dominates the classical ex-post optimal benchmark—particularly when accounting for calibration errors—and can be computed efficiently via linear programming. Furthermore, the paper designs an online learning algorithm that asymptotically achieves this robust performance bound using only predictions or state feedback, thereby revealing the added value inherent in the information structure of calibrated expert advice.

This work addresses the problem of aggregating multiple calibrated Bayesian expert forecasts to construct a new predictor that remains calibrated and is Blackwell-dominated by the target expert, rather than merely minimizing a specific loss function. Under the setting where only the experts’ prior distributions are observed—without access to the true state—the authors formally define the aggregation objective as simultaneously achieving calibration and Blackwell refinability. By modeling calibrated experts through reduced-form information structures, they characterize the set of feasible predictions using the row space of a linear system intersected with a non-negative cone, and analyze it via Blackwell dominance theory. Their main contributions include efficient solvability of both randomized aggregation problems, while showing that determining the existence of a deterministic aggregator is NP-hard and admits no multiplicative PTAS unless P = NP, thereby revealing a fundamental computational distinction between randomized and deterministic aggregation.

This paper studies online expert aggregation under unbounded quadratic loss—a setting where conventional methods require prior knowledge of the loss upper bound, while our work proposes the first adaptive algorithm that operates without such a bound. Methodologically, we design an exponential-weighting-based dynamic weight update scheme, integrating online learning with adaptive truncation to ensure robustness against highly volatile losses. We theoretically establish that the algorithm achieves the optimal sublinear regret bound $O(sqrt{T log N})$. Empirically, it significantly outperforms classical weighted averaging and existing adaptive approaches on benchmark tasks featuring unbounded and rapidly varying losses. The key contribution is the elimination of dependence on a known loss bound, thereby enabling a more general and robust aggregation framework for online prediction in real-world dynamic environments.

This paper addresses the challenge that incomplete and fragmented expert forecasts often yield aggregated predictions no better than random selection. To tackle this, we propose a novel robust prediction aggregation framework based on structured auxiliary queries. Methodologically, we design a game-theoretic incentive mechanism to elicit truthful belief reports from experts and systematically characterize the theoretical trade-off among query complexity, reasoning order, and aggregation error under an independent yet overlapping signals model. Our key contributions are: (i) the first precise characterization of the query–error trade-off—showing that, in the worst case, only *O*(*n*) queries suffice for optimal aggregation, with error decaying linearly in the number of queries; and (ii) establishing that when the effective number of experts exceeds √*n*, the aggregation error converges to zero—thereby breaking a fundamental performance bottleneck inherent in conventional aggregation methods.

This paper addresses the degradation of probabilistic forecast calibration in dynamic data streams caused by distributional shift, feedback loops, and adversarial perturbations. We propose the first general online calibration framework grounded in Blackwell approachability—a theoretically rigorous foundation for sequential decision-making under uncertainty. Our method provides strong calibration guarantees in compact output spaces (e.g., classification and bounded regression) and enables lossless post-hoc recalibration of arbitrary pre-trained predictors. Technically, it unifies insights from Blackwell approachability theory, online optimization, and gradient-based updates, and introduces task-specific efficient algorithms for both classification and regression. Empirical evaluation demonstrates substantial improvements in calibration quality for energy system forecasting, with marked gains in robustness and practical utility for downstream decision-making tasks.

This work proposes the first closed-form robust prediction aggregator applicable to any binary state space over [0,1], operating without knowledge of either the state space structure or the experts’ information structures. The method aggregates expert forecasts via linear pooling in logit space, requiring no prior distributional assumptions. Under conditionally independent signals, it achieves a minimax regret upper bound of 0.0255. In the classical {0,1} setting, the regret is below 0.0226, and it reaches 0.0228 in extended scenarios—approaching the theoretical lower bound of 0.0225. These results substantially advance the theoretical limits of robust prediction aggregation.

This work addresses the problem of feedback-free online conformal prediction for black-box classifiers operating on non-i.i.d. data streams in safety-critical settings where predictive feedback is unavailable. At each round, the learner must choose between outputting a prediction set or querying the true label, but not both. The authors innovatively frame this setting as a partial monitoring game and integrate online learning with conformal prediction theory to develop a label-efficient algorithm. Their method achieves an expected coverage no less than $\beta - O(T^{-1/3})$ while querying labels at a rate of only $O(T^{-1/3})$, and attains a regret bound of $O(T^{2/3})$. Empirical evaluations demonstrate the approach’s effectiveness across arbitrary black-box models and non-stationary data streams.

This work addresses the degradation of coverage guarantees in online conformal prediction when feedback is corrupted by noise, communication failures, or adversarial attacks. It presents the first systematic modeling of arbitrary binary feedback corruption and provides explicit miscoverage bounds under two distinct error models: independent random flips and memory-bounded adversarial errors. To mitigate the impact of corrupted feedback, the paper introduces two robust mechanisms—a threshold-based feedback filtering scheme and an active compensation strategy—effectively preserving predictive reliability. The proposed approach integrates online conformal prediction with robust statistical learning, making it suitable for non-stationary sequential environments. Empirical evaluations on real-world datasets demonstrate substantial improvements over existing baselines, achieving better calibration and significantly smaller prediction sets.

This work addresses the limitations of traditional Bayesian online learning, which relies on pre-specified inference components—such as priors, variational families, and learning rates—and struggles to adapt to dynamic data streams, thereby constraining predictive performance. The paper proposes the first adaptive Bayesian online learning framework based on expert aggregation, treating distinct Bayesian update rules as experts and dynamically combining them via weights determined by sequential prediction loss. The approach enables adaptation to unknown smoothness in Gaussian process regression and yields an oracle inequality for cumulative KL risk. By integrating online conformal inference, it also ensures valid stochastic coverage. Theoretically, the aggregated predictor is shown to compete with the best expert in hindsight, and experiments demonstrate that, without requiring prior knowledge, it effectively tracks strong experts and significantly enhances both predictive accuracy and robustness.