Ma Tc

Tianyi Ma, Hanzhang Qin, Ruihao Zhu et al.

Best-arm identification is a canonical model for data-driven decision-making, but in many applications each reward observation is costly. Motivated by the growing availability of cheap predictions from machine learning and large language models, we study fixed-confidence best-arm identification in which each costly reward pull is paired with a cheap but correlated proxy score. The marginal mean of the proxy can be estimated offline and is treated as known, whereas its correlation $ρ$ with the reward, which governs how much the proxy helps, is unknown and must be learned online in pair with real rewards. We show that a control-variate adjustment turns this model into a heteroscedastic identification problem whose oracle sample complexity improves by residual variance $1-ρ^2$. The central difficulty is that the correlation must be learned from the same costly samples that identification consumes online, and that a plug-in estimate of the residual variance is anti-conservative and can compromise correctness. We propose PROBE (PRoxy OLS for Best-arm Exploration), a phase-elimination algorithm that directly maintains an upper certificate on the residual variance with an ordinary least squares fit, whose exact chi-square law keeps the certificate valid regardless of the unknown correlation. We prove that PROBE is $δ$-PAC and attains the known-correlation oracle sample complexity up to a constant multiplicative factor and a constant additive calibration cost. The guarantee extends to the $(ε,δ)$-PAC setting under minimal changes to the algorithm. Numerical experiments on synthetic instances and on an auto-loan pricing replay with large language model and tabular proxies confirm that the sample savings of PROBE scale with the strength of the reward-proxy correlation, exactly as the theory predicts.

Xin Wang, Yunshi Wen, Yanan He et al.

The operational integrity of complex industrial systems relies on precise anomaly detection and diagnosis. The vast majority of existing methods narrowly focus on capturing temporal similarities of representations, often overlooking the disruption of internal causal relationships, which characterizes system failures and latent anomalies. In this paper, we propose a novel framework (CAAD) that reframes anomaly detection as the continuous verification of Granger causality consistency through exogenous variables. Specifically, the CAAD framework models exogenous time-series variables as residuals, identifying anomalies as significant deviations caused by external interventions. The proposed framework leverages multi-scale alignment to internalize system dynamics and utilizes a gradient-based matrix to monitor internal causal relationship breakdowns. By quantifying causal deviations of both dynamic evolution and relational topology, the CAAD is able to capture subtle causal shifts to achieve precise anomaly detection. Extensive experiments on real-world industrial datasets demonstrate that the CAAD achieves high-precision anomaly detection, outperforming most state-of-the-art baselines.