Finite-sample analyses of deep Q-learning typically treat replayed data as independent, even though it is sampled from temporally dependent state-action trajectories. We study the Deep Q-networks (DQN) algorithm under explicit dependence by modelling the minibatches used for updating the network as $τ$-mixing. We show that this assumption holds under certain dependence conditions on the underlying trajectories and the mechanism used to sample minibatches. Building on this observation, we extend statistical analyses of DQN with fully connected ReLU architectures to dependent data. We formulate each update as a nonparametric regression problem with $τ$-mixing observations and derive finite-sample risk bounds under this dependence structure. Our results show that temporal dependence leads to a degradation in the statistical rate by inducing an additional dimensionality penalty in the rate exponent, reflecting the reduced effective sample size of $τ$-mixing data. Moreover, we derive the sample complexity of DQN under $tau$-mixing from these risk bounds. Finally, we empirically demonstrate on standard Gymnasium environments that the independence assumption is systematically violated and that replay sampling yields approximately exponentially decaying correlations, supporting our theoretical framework.

Traditional multi-population models, such as the Li-Lee framework, rely on the assumption of mean-reverting country-specific deviations. However, recent data from high-longevity clusters suggest a systemic break in this paradigm. We identify a stationarity paradox where mortality residuals in countries like Sweden and West Germany exhibit persistent unit roots, leading to a systematic mispricing of longevity risk in linear models. To address these non-linearities, we propose Hybrid-Lift, a neural-actuarial framework that combines Hierarchical LSTM networks with a Mean-Bias Correction (MBC) anchoring mechanism. Positioned as a governance-friendly model challenger rather than a replacement of classical approaches, the framework exhibits selective superiority on out-of-sample validation (2012-2020): it outperforms Li-Lee by 17.40% in Sweden and 12.57% in West Germany, while remaining comparable for near-linear regimes such as Switzerland and Japan. We complement the predictive model with an integrated governance suite comprising SHAP-based cross-country influence mapping, a dual uncertainty framework for regulatory capital calibration (Swiss ES 99.0% of +1.153 years), and a reverse stress test identifying the critical shock threshold for solvency buffer exhaustion. This research provides evidence that neural networks, when properly anchored by actuarial principles, can serve as effective model challengers for longevity risk management under the SST and Solvency II standards.

Predictive models are often deployed through existing decision policies that stakeholders are reluctant to change unless a risk constraint requires intervention. We study risk-controlled post-processing: given a deterministic baseline policy, choose a new policy that maximizes agreement with the baseline subject to a chance constraint on a user-specified loss. At the population level, we show that the optimal policy has a threshold structure: it follows the baseline except on contexts where switching to the oracle fallback policy yields a large reduction in conditional violation risk. At the finite-sample level, given a fitted fallback policy and score, we develop a post-processing algorithm that uses calibration data to select a threshold. Leveraging tools from algorithmic stability and stochastic processes, we show that under regularity conditions, in the i.i.d. setting, the expected excess risk of the post-processed policy is $O(\log n/n)$. In the special case when an exact-safe fallback policy is available, the algorithm achieves precise expected risk control under exchangeability. In this setting, we also give high-probability near-optimality guarantees on the post-processed policy. Experiments on a COVID-19 radiograph diagnosis task, an LLM routing problem, and a synthetic multiclass decision task show that targeted post-processing can meet or nearly meet risk budgets while preserving substantially more agreement with the baseline than score-blind random mixing.

In many scientific domains, including experimentation, researchers rely on measurements of proxy outcomes to achieve faster and more frequent reads, especially when the primary outcome of interest is challenging to measure directly. While proxies offer a more readily accessible observation for inference, the ultimate goal is to draw statistical inferences about the primary outcome parameter and proxy data are typically imperfect in some ways. To correct for these imperfections, current statistical inference methods often depend on strict identifying assumptions (such as surrogacy, covariate/label shift, or missingness assumptions). These assumptions can be difficult to validate and may be violated by various additional sources of distribution shift, potentially leading to biased parameter estimates and miscalibrated uncertainty quantification. We introduce an estimate-level framework, inspired by domain adaptation techniques, to empirically calibrate proxy-based inference. This framework models the proxy-primary metric discrepancy as a random effect at the parameter level, estimating its distribution from aggregated historical observations across past domains (e.g., experiments, time periods, or distinct segments). This method avoids the requirement for retaining individual-level response data. Additionally, this adjustment can be layered on top of existing proxy-correction methods (such as prediction-powered inference or importance weighting) to account for additional biases not addressed by those corrections. To manage uncertainty when the number of historical domains is limited, we provide both a method-of-moments estimator and a domain bootstrap procedure. We further validate this approach using publicly available datasets and real-world experiments.

We study online prediction under distribution shift, where inputs arrive chronologically and outcomes are revealed only after prediction. In this setting, predictors must remain stable in quiet regimes yet adapt when regimes shift, and the right adaptation memory is unknown in advance. We propose MELO (Memory-hedged Exponentially Weighted Least-Squares Online aggregation), a model-agnostic method that hedges across adaptation scales: it wraps any non-anticipating base-predictor pool with exponentially weighted least-squares (EWLS) adaptation experts at multiple forgetting factors, and aggregates raw and EWLS-adapted forecasts with MLpol which is a parameter-free online aggregation rule. Under boundedness conditions, we establish deterministic oracle inequalities showing that it competes with both the best raw predictor and the best bounded, time-varying affine combinations of the base predictions, up to a path-length-dependent tracking cost and a sublinear aggregation overhead. We evaluate MELO on French national electricity-load forecasting through the COVID-19 lockdown using no regime indicators, lockdown dates, or policy covariates. MELO reduces overall RMSE by 34.7%relative to base-only MLpol and achieves lower overall RMSE than a TabICL reference supplied with an external COVID policy-response covariate. MELO requires only lightweight per-step recursive updates without model retraining.

In networks, effective dynamic treatment allocation requires deciding both whom to treat and also when, so as to amplify policy impact through spillovers. An early intervention at a well-connected node can trigger cascades that change which nodes are worth targeting in the next period. Existing treatment strategies under network interference are largely static while dynamic treatment frameworks typically ignore network structure altogether. We integrate these perspectives and propose Q-Ising, a three-stage pipeline that (i) estimates network adoption dynamics via a Bayesian dynamic Ising model from a single observed panel, (ii) augments treatment adoption histories with continuous posterior latent states, and (iii) learns a dynamic policy via offline reinforcement learning. The Bayesian mechanism enables uncertainty quantification over dynamic decisions, yielding posterior ensemble policies with interpretable spillover estimates. We provide a finite-sample regret upper bound that decomposes into standard offline-RL uncertainty, network abstraction error, and first stage error in Ising state estimation. We apply our method to data from Indian village microfinance networks and synthetic stochastic block models under simulated heterogeneous susceptible-infected-susceptible (SIS) dynamics and demonstrate that adaptive targeting outperforms static centrality benchmarks.

This paper proposes a hybrid methodology to improve the approximation of SABR (Stochastic Alpha Beta Rho) implied volatility by combining analytical structure with machine learning. The approach augments the neural-network input representation with geometric features derived from the stochastic differential equations of the SABR model. Unlike approaches that fully replace analytical formulas with black-box models, the proposed framework preserves the analytical backbone of the model. The hybridization operates along two complementary dimensions. First, geometry-aware variables reflecting intrinsic properties of the SABR dynamics are used as structured inputs to the network. Second, the neural network is trained to learn the residual error relative to Hagan's closed-form approximation rather than implied volatility directly. The resulting model acts as a structured residual correction to the analytical formula, retaining interpretability while capturing higher-order effects that are not included in the asymptotic expansion. Numerical experiments conducted over realistic parameter domains, as well as stressed environments, show that the method improves accuracy and robustness compared with both analytical approximations and standard neural-network approaches. Because the correction remains lightweight and structurally consistent with the underlying model, the framework is well suited for real-time pricing and calibration in practical trading environments.

Megan Rapinoe, in a shock to no one, backs Angel Reese skipping interviews as'taking power back' Here's why the coaches association's 24-team College Football Playoff could ruin the sport Boston Celtics star Jaylen Brown tells ESPN's Stephen A Smith to'be quiet and retire' President Trump on $1,000 World Cup ticket prices: 'I wouldn't pay it either, to be honest' Pirates vs. Diamondbacks betting preview targets the under as both offenses go cold in series Former LSU coach Brian Kelly uses AI to prepare for job interviews, proving he's just like the rest of us Newsom office source responds to planned protest against trans athlete at state playoff girls' track meet US waits for Iran's response on peace proposal Authorities try to'connect the dots' on hantavirus infections Jesse Watters: Spencer Pratt is a'charismatic, common-sense populist' Greg Gutfeld: Dana White laughs off the'toxic masculinity thing' Iranians are fearful of facing the regime's frustration and anger after the war, activist says OutKick White House calls out Newsom as California girls' track and field controversy reignites Spokeswoman called Newsom'a truly sick individual who has no regard for fairness, dignity, and respect' Jurupa Valley High School graduate Hadeel Hazameh responded to the news that the Trump administration has launched a Title IX investigation into her district over an incident involving trans volleyball teammate, which has resulted in her graduating early and leaving her sports career behind. President Donald Trump's White House has officially put California Gov. Gavin Newsom on notice as a controversial girls' track and field postseason is set to begin this weekend. A White House spokesperson called out Newsom in a statement to Fox News Digital as his state continues to allow biological male trans athletes to compete in girls' high school sports. Gavin Newscum is a truly sick individual who has no regard for fairness, dignity, and respect. If he did, he wouldn't allow men to compete in women's sports, limiting women's opportunities and jeopardizing their health and safety.

A man has been charged after allegedly threatening Andrew Mountbatten-Windsor during an incident near his home on the Sandringham Estate in Norfolk. Norfolk Police earlier said a man was arrested shortly after 19:30 BST on Wednesday after officers received a report of a man a behaving in an intimidating manner in Wolferton. The Daily Telegraph reported Mountbatten-Windsor was threatened by a balaclava-clad man while out walking his dogs and fled to his car along with his security. Alex Jenkinson, 39, of Stowmarket, Suffolk, has been remanded in custody and is due to appear at Norwich Magistrates' Court on Friday. Police said he has been charged with two counts of using threatening, abusive or insulting words or behaviour to harass someone or cause alarm or distress and failing to provide a specimen of blood in custody.

Here's why the coaches association's 24-team College Football Playoff could ruin the sport Boston Celtics star Jaylen Brown tells ESPN's Stephen A Smith to'be quiet and retire' President Trump on $1,000 World Cup ticket prices: 'I wouldn't pay it either, to be honest' Pirates vs. Diamondbacks betting preview targets the under as both offenses go cold in series Former LSU coach Brian Kelly uses AI to prepare for job interviews, proving he's just like the rest of us Newsom office source responds to planned protest against trans athlete at state playoff girls' track meet'This can touch anyone': Gorman family speaks following loss of Sheridan'Project Freedom' could soon resume: Report Iranian people are not citizens, but'subjects' of the regime: Middle East expert Vice Admiral Robert Harward weighs in on restarting'Project Freedom' in Strait of Hormuz Largest teachers' union accused of antisemitism in federal civil rights complaint McEnany's URGENT plea: 'Be Spencer Pratt!' WHO doesn't expect large Hantavirus outbreak US blockade keeps stranglehold on Iran's economy What And Who Is Next In The Russini Saga? | OutKick Hot Mic TMZ Sports obtained documents this week showing that New England Patriots coach Mike Vrabel and former NFL reporter Dianna Russini signed a waiver for a private boating trip during her pregnancy in 2021. The report adds that Vrabel and Russini were the only two people on board for the two-to-three-hour excursion. On Thursday, the outlet obtained video and photos of the two on a dock in Putnam County, TN. See TMZ Sports' video below: ARE WE SURE MIKE VRABEL WILL SURVIVE RUSSINI SCANDAL AND COACH PATRIOTS THIS SEASON? According to the report, Russini gave birth to her first child with her husband, Kevin, later that summer. She was about six to seven months pregnant during the boating trip with Vrabel.