We study policy optimization for online episodic tabular Markov decision processes with unknown transition kernels, aiming for best-of-both-worlds guarantees together with data-dependent regret bounds. Recent work (Dann et al., 2023; Li et al., 2026) has shown that policy optimization can adapt to both adversarial and stochastic losses with first-order, second-order, and path-length bounds, but only under known transitions, leaving open whether such data-dependent guarantees are achievable by policy optimization when the transition kernel is unknown. We resolve this by developing a new algorithm based on optimistic follow-the-regularized-leader that attains these guarantees under unknown transitions. The key ingredient is a new design of optimistic $Q$-function estimators together with a data-dependent transition bonus that controls estimator bias through the loss-prediction error. Our analysis further identifies an unavoidable transition-dependent complexity term that captures the intrinsic cost of estimating the transition kernel. As a result, we obtain first-order, second-order, and path-length bounds with the transition-dependent complexity term while simultaneously achieving gap-dependent $\mathrm{polylog}(T)$ regret in the stochastic regime.

Stochastic Gradient Descent ($\textsf{SGD}$) is one of the most classical optimization algorithms with favorable theoretical guarantees, yet the practical implementation of $\textsf{SGD}$ differs subtly from its well-known form and is often referred to as Shuffling Stochastic Gradient Descent ($\textsf{Shuffling SGD}$). A particularly popular strategy in $\textsf{Shuffling SGD}$ is Random Reshuffling ($\textsf{RR}$), which has achieved great empirical success across numerous experiments. Despite its strong performance, $\textsf{RR}$ has long been considered a heuristic due to a lack of theoretical support. Over the last decade, people have finally established provable convergence rates for $\textsf{RR}$, thus justifying its observed superiority. However, for smooth convex optimization, two clouds over the convergence theory of $\textsf{RR}$ remain to this day. More precisely, according to the current theory, $\textsf{Shuffling SGD}$ under $\textsf{RR}$ converges only when the stepsize is smaller than a threshold proportional to $1/n$, where $n$ is the number of summands in the objective (or the number of data points). Consequently, the optimally tuned theoretical rate of $\textsf{Shuffling SGD}$ under $\textsf{RR}$ is strictly worse than that of $\textsf{SGD}$ when the number of epochs is smaller than another threshold proportional to $n$. These two restrictions heavily limit the applicability of existing theories and leave a critical mismatch with practice. In this work, for the first time, we prove that $\textsf{RR}$ dominates $\textsf{SGD}$ in smooth convex optimization under any reasonable stepsize after any finite number of epochs, thereby addressing a longstanding open question.

Market microstructure has long classified trading activity by its informational role: an informed trader demands liquidity by trading in the direction of private information, while a market maker supplies liquidity by absorbing that order flow and earning the spread in compensation Kyle (1985); Glosten and Milgrom (1985). This classification is typically recovered from the data the classifier requires: signed order flow, quote revisions, or the sequential-trade structure of the market. The classification is harder to apply to an algorithmic strategy whose internal logic is unobservable. However, the signals or optimization problems generating the decisions of a typical quantitative fund are not visible, even though the trades and reported positions may be available. This paper shows that the liquidity role of such a strategy (consumer or provider) can be recovered from realized portfolio costs and trade decisions alone, without observing quotes, order flow, or any other microstructure-specific signal.

A central challenge in statistical modeling is identifying the subset of features that belong in the true regression model. The classical best subset selection problem, recently made tractable via mixed-integer optimization (MIO), finds the globally optimal sparse solution. It does not, however, make use of any information beyond the observed data. In many applied settings, domain experts can meaningfully rank or score the relevance of candidate predictors, yet no existing framework integrates such probabilistic expert assessments directly into the best-subsets objective. This paper presents Expert-Implied Bayesian Best Subsets (EBBS), a method that incorporates domain-expert probability estimates of feature relevance into the MIO best-subsets problem through a maximum a posteriori (MAP) framework. Expert views from multiple respondents are aggregated into a single prior probability per feature using the Poisson binomial distribution for marginal probability estimates, the pairwise win rate for pairwise comparisons, or the normalized mean rank for ordinal rankings. This probability enters the objective function as a log-odds penalty term that smoothly encourages or discourages the selection of each feature consistent with the expert consensus. This paper provides analytic derivations of the MAP formulation and characterizes its theoretical properties. The proposed model reduces to Best Subsets when experts all have no views. Empirical results on synthetic and real datasets are forthcoming.

Deep learning problems rarely involve objectives that are equal in importance. A primary objective defines the goal, whilst secondary objectives, such as sparsity, compression, or robustness constrain the solution. While existing multi-objective methods have proven effective in practice, they have a clear symmetry problem and neglect the inherent objective hierarchy built into these objective spaces. We introduce Priority-Constrained Descent (PCD), a gradient-based optimization framework designed to explicitly exploit hierarchical objective structures. PCD preserves the direction of primary descent whilst allowing for the minimal distortion necessary to guarantee progress on secondary objectives, controlled by a single $τ\in [0, 1]$ that dictates the strength of the distortion. The resulting formulation is invariant to objective scaling and admits exact closed-form solutions for problems with two and three objectives. We evaluate PCD within structured network compression settings, unstructured sparsity and low-rankness, and across a variety of synthetic experiments, showing Pareto dominance and better per-objective performance with secondary progress guarantees over existing methods, further exhibiting the interpretable trade-off that $τ$ provides.

Adaptive gradient methods are among the standard tools for training machine learning models. Their appeal is that they reduce the need to tune a fixed learning rate by adjusting the effective stepsize using information observed along the optimization trajectory. AdaGrad, introduced by Duchi et al. [2011], is a prototypical example: it rescales the update by the square root of the cumulative sum of past squared subgradients, coordinate by coordinate. The method was originally proposed for nonsmooth Lipschitz-continuous composite convex optimization, achieving the optimal rate O(1/ n) in the objective gap. Later works considered the smooth setting and asked whether AdaGrad can adapt to the unknown smoothness level of the objective, while attaining the corresponding standard rate.

In recent years, fueled by the rapid advancement of diffusion models, text-to-video (T2V) generation models have achieved remarkable progress, with notable examples including Pika, Luma, Kling, and Open-Sora. Although these models exhibit impressive generative capabilities, they also expose significant security risks due to their vulnerability to jailbreak attacks, where the models are manipulated to produce unsafe content such as pornography, violence, or discrimination. Existing works such as T2VSafetyBench provide preliminary benchmarks for safety evaluation, but lack systematic methods for thoroughly exploring model vulnerabilities. To address this gap, we are the first to formalize the T2V jailbreak attack as a discrete optimization problem and propose a joint objective-based optimization framework, called \emph{T2V-OptJail}. This framework consists of two key optimization goals: bypassing the built-in safety filtering mechanisms to increase the attack success rate, preserving semantic consistency between the adversarial prompt and the unsafe input prompt, as well as between the generated video and the unsafe input prompt, to enhance content controllability. In addition, we introduce an iterative optimization strategy guided by prompt variants, where multiple semantically equivalent candidates are generated in each round, and their scores are aggregated to robustly guide the search toward optimal adversarial prompts. We conduct large-scale experiments on several T2V models, covering both open-source models (\textit{e.g.}, Open-Sora) and real commercial closed-source models (\textit{e.g.}, Pika, Luma, Kling). The experimental results show that the proposed method improves 11.4\% and 10.0\% over the existing state-of-the-art method (SoTA) in terms of attack success rate assessed by GPT-4, attack success rate assessed by human accessors, respectively, verifying the significant advantages of the method in terms of attack effectiveness and content control. This study reveals the potential abuse risk of the semantic alignment mechanism in the current T2V model and provides a basis for the design of subsequent jailbreak defense methods.

Modern machine learning systems have outgrown their origins as isolated predictive constructs, evolving into complex socio-technical architectures that actively mediate human opportunity. As algorithms increasingly determine access to economic and social opportunities, it has become widely recognized that these systems are deeply embedded with the structural inequalities and prejudices of their environments. The field of algorithmic fairness emerged in response to the growing recognition that models optimized for predictive accuracy can systematically disadvantage marginalized groups. Early mitigation strategies, however, rested on fragile simplifications that limited their effectiveness in complex sociotechnical environments. This thesis identifies and addresses two fundamental limitations of contemporary fairness paradigms: the reliance on deterministic point estimates for auditing and the treatment of individuals as isolated entities devoid of structural context. First, the diagnosis of algorithmic unfairness has traditionally depended on scalar metrics that fail to capture the nuances of real-world deployment. This deterministic approach ignores the high statistical variance inherent in small, intersectional groups, often leading to false alarms or missed detections of bias. Furthermore, standard auditing struggles with the opacity of black-box models, frequently conflating unjustifiable bias with the influence of legitimate features.

Causal discovery in the form of a directed acyclic graph (DAG) for dynamic time series data has been widely studied in various applications. In this work, we propose a dynamic DAG discovery algorithm, Meta-D2AG, based on online metalearning. Meta-D2AG is designed to learn dynamic DAG structures from potentially nonlinear and non-stationary time series datasets, accounting for changes in both parameters and graph structures. Unlike most of the existing work focusing on observational, offline, and/or stationary settings, Meta-D2AG explicitly treats data collected at different time points with distribution shifts as distinct domains, which is assumed to occur as a result of external interventions. Moreover, MetaD2AG involves a new online meta-learning framework to take advantage of the temporal transition among existing domains such that it can quickly adapt to new domains with few measurements. A first-order optimization approach is utilized to efficiently solve the meta-learning framework, and theoretical analysis establishes the identifiability conditions and the convergence of the learning process. We demonstrate the promising performance of the proposed meta learning framework through better accuracy on benchmark datasets against state-of-the-art baselines.

Warning: This method may be misused for malicious purposes. Large Language Models (LLMs) are increasingly deployed in high-risk domains.