Deep Generative AI has been a long-standing essential topic in the machine learning community, which can impact a number of application areas like text generation and computer vision. The major paradigm to train a generative model is maximum likelihood estimation, which pushes the learner to capture and approximate the target data distribution by decreasing the divergence between the model distribution and the target distribution. This formulation successfully establishes the objective of generative tasks, while it is incapable of satisfying all the requirements that a user might expect from a generative model. Reinforcement learning, serving as a competitive option to inject new training signals by creating new objectives that exploit novel signals, has demonstrated its power and flexibility to incorporate human inductive bias from multiple angles, such as adversarial learning, hand-designed rules and learned reward model to build a performant model. Thereby, reinforcement learning has become a trending research field and has stretched the limits of generative AI in both model design and application. It is reasonable to summarize and conclude advances in recent years with a comprehensive review. Although there are surveys in different application areas recently, this survey aims to shed light on a high-level review that spans a range of application areas. We provide a rigorous taxonomy in this area and make sufficient coverage on various models and applications. Notably, we also surveyed the fast-developing large language model area. We conclude this survey by showing the potential directions that might tackle the limit of current models and expand the frontiers for generative AI.

This paper aims to provide differential privacy (DP) guarantees for Markov chain Monte Carlo (MCMC) algorithms. In a first part, we establish DP guarantees on samples output by MCMC algorithms as well as Monte Carlo estimators associated with these methods under assumptions on the convergence properties of the underlying Markov chain. In particular, our results highlight the critical condition of ensuring the target distribution is differentially private itself. In a second part, we specialise our analysis to the unadjusted Langevin algorithm and stochastic gradient Langevin dynamics and establish guarantees on their (R\'enyi) DP. To this end, we develop a novel methodology based on Girsanov's theorem combined with a perturbation trick to obtain bounds for an unbounded domain and in a non-convex setting. We establish: (i) uniform in $n$ privacy guarantees when the state of the chain after $n$ iterations is released, (ii) bounds on the privacy of the entire chain trajectory. These findings provide concrete guidelines for privacy-preserving MCMC.

We establish thresholds for the feasibility of random multi-graph alignment in two models. In the Gaussian model, we demonstrate an "all-or-nothing" phenomenon: above a critical threshold, exact alignment is achievable with high probability, while below it, even partial alignment is statistically impossible. In the sparse Erd\H{o}s-R\'enyi model, we rigorously identify a threshold below which no meaningful partial alignment is possible and conjecture that above this threshold, partial alignment can be achieved. To prove these results, we develop a general Bayesian estimation framework over metric spaces, which provides insight into a broader class of high-dimensional statistical problems.

Large language models (LLMs) have demonstrated remarkable in-context learning (ICL) abilities. However, existing theoretical analysis of ICL primarily exhibits two limitations: (a) Limited i.i.d. Setting. Most studies focus on supervised function learning tasks where prompts are constructed with i.i.d. input-label pairs. This i.i.d. assumption diverges significantly from real language learning scenarios where prompt tokens are interdependent. (b) Lack of Emergence Explanation. Most literature answers what ICL does from an implicit optimization perspective but falls short in elucidating how ICL emerges and the impact of pre-training phase on ICL. In our paper, to extend (a), we adopt a more practical paradigm, auto-regressive next-token prediction (AR-NTP), which closely aligns with the actual training of language models. Specifically, within AR-NTP, we emphasize prompt token-dependency, which involves predicting each subsequent token based on the preceding sequence. To address (b), we formalize a systematic pre-training and ICL framework, highlighting the layer-wise structure of sequences and topics, alongside a two-level expectation. In conclusion, we present data-dependent, topic-dependent and optimization-dependent PAC-Bayesian generalization bounds for pre-trained LLMs, investigating that ICL emerges from the generalization of sequences and topics. Our theory is supported by experiments on numerical linear dynamic systems, synthetic GINC and real-world language datasets.

Motivated by the great success of Bayesian additive regression trees (BART) on regression, we propose a nonparametric Bayesian approach for the function-on-scalar regression problem, termed as Functional BART (FBART). Utilizing spline-based function representation and tree-based domain partition model, FBART offers great flexibility in characterizing the complex and heterogeneous relationship between the response curve and scalar covariates. We devise a tailored Bayesian backfitting algorithm for estimating the parameters in the FBART model. Furthermore, we introduce an FBART model with shape constraints on the response curve, enhancing estimation and prediction performance when prior shape information of response curves is available. By incorporating a shape-constrained prior, we ensure that the posterior samples of the response curve satisfy the required shape constraints (e.g., monotonicity and/or convexity). Our proposed FBART model and its shape-constrained version are the new advances of BART models for functional data. Under certain regularity conditions, we derive the posterior convergence results for both FBART and its shape-constrained version. Finally, the superiority of the proposed methods over other competitive counterparts is validated through simulation experiments under various settings and analyses of two real datasets.

We develop an analysis of Thompson sampling for online learning under full feedback - also known as prediction with expert advice - where the learner's prior is defined over the space of an adversary's future actions, rather than the space of experts. We show regret decomposes into regret the learner expected a priori, plus a prior-robustness-type term we call excess regret. In the classical finite-expert setting, this recovers optimal rates. As an initial step towards practical online learning in settings with a potentially-uncountably-infinite number of experts, we show that Thompson sampling with a certain Gaussian process prior widely-used in the Bayesian optimization literature has a $\mathcal{O}(\beta\sqrt{T\log(1+\lambda)})$ rate against a $\beta$-bounded $\lambda$-Lipschitz adversary.

Emergency Response Time (ERT) is crucial for urban safety, measuring cities' ability to handle medical, fire, and crime emergencies. In NYC, medical ERT increased 72% from 7.89 minutes in 2014 to 14.27 minutes in 2024, with half of delays due to Emergency Vehicle (EMV) travel times. Each minute's delay in stroke response costs 2 million brain cells, while cardiac arrest survival drops 7-10% per minute. This dissertation advances EMV facilitation through three contributions. First, EMVLight, a decentralized multi-agent reinforcement learning framework, integrates EMV routing with traffic signal pre-emption. It achieved 42.6% faster EMV travel times and 23.5% improvement for other vehicles. Second, the Dynamic Queue-Jump Lane system uses Multi-Agent Proximal Policy Optimization for coordinated lane-clearing in mixed autonomous and human-driven traffic, reducing EMV travel times by 40%. Third, an equity study of NYC Emergency Medical Services revealed disparities across boroughs: Staten Island faces delays due to sparse signalized intersections, while Manhattan struggles with congestion. Solutions include optimized EMS stations and improved intersection designs. These contributions enhance EMV mobility and emergency service equity, offering insights for policymakers and urban planners to develop safer, more efficient transportation systems.

A tenet of reinforcement learning is that rewards are always observed by the agent. However, this is not true in many realistic settings, e.g., a human observer may not always be able to provide rewards, a sensor to observe rewards may be limited or broken, or rewards may be unavailable during deployment. Monitored Markov decision processes (Mon-MDPs) have recently been proposed as a model of such settings. Yet, Mon-MDP algorithms developed thus far do not fully exploit the problem structure, cannot take advantage of a known monitor, have no worst-case guarantees for ``unsolvable'' Mon-MDPs without specific initialization, and only have asymptotic proofs of convergence. This paper makes three contributions. First, we introduce a model-based algorithm for Mon-MDPs that addresses all of these shortcomings. The algorithm uses two instances of model-based interval estimation, one to guarantee that observable rewards are indeed observed, and another to learn the optimal policy. Second, empirical results demonstrate these advantages, showing faster convergence than prior algorithms in over two dozen benchmark settings, and even more dramatic improvements when the monitor process is known. Third, we present the first finite-sample bound on performance and show convergence to an optimal worst-case policy when some rewards are never observable.

We study a ranking and selection (R&S) problem when all solutions share common parametric Bayesian input models updated with the data collected from multiple independent data-generating sources. Our objective is to identify the best system by designing a sequential sampling algorithm that collects input and simulation data given a budget. We adopt the most probable best (MPB) as the estimator of the optimum and show that its posterior probability of optimality converges to one at an exponential rate as the sampling budget increases. Assuming that the input parameters belong to a finite set, we characterize the $\epsilon$-optimal static sampling ratios for input and simulation data that maximize the convergence rate. Using these ratios as guidance, we propose the optimal sampling algorithm for R&S (OSAR) that achieves the $\epsilon$-optimal ratios almost surely in the limit. We further extend OSAR by adopting the kernel ridge regression to improve the simulation output mean prediction. This not only improves OSAR's finite-sample performance, but also lets us tackle the case where the input parameters lie in a continuous space with a strong consistency guarantee for finding the optimum. We numerically demonstrate that OSAR outperforms a state-of-the-art competitor.

State-of-the-art data stream mining in supervised classification has traditionally relied on ensembles of incremental decision trees. However, the emergence of large tabular models, i.e., transformers designed for structured numerical data, marks a significant paradigm shift. These models move beyond traditional weight updates, instead employing in-context learning through prompt tuning. By using on-the-fly sketches to summarize unbounded streaming data, one can feed this information into a pre-trained model for efficient processing. This work bridges advancements from both areas, highlighting how transformers' implicit meta-learning abilities, pre-training on drifting natural data, and reliance on context optimization directly address the core challenges of adaptive learning in dynamic environments. Exploring real-time model adaptation, this research demonstrates that TabPFN, coupled with a simple sliding memory strategy, consistently outperforms ensembles of Hoeffding trees across all non-stationary benchmarks. Several promising research directions are outlined in the paper. The authors urge the community to explore these ideas, offering valuable opportunities to advance in-context stream learning.