Using a martingale representation, we introduce a novel deep-learning approach, which we call DeepMartingale, to study the duality of discrete-monitoring optimal stopping problems in continuous time. This approach provides a tight upper bound for the primal value function, even in high-dimensional settings. We prove that the upper bound derived from DeepMartingale converges under very mild assumptions. Even more importantly, we establish the expressivity of DeepMartingale: it approximates the true value function within any prescribed accuracy $\varepsilon$ under our architectural design of neural networks whose size is bounded by $\tilde{c}\,D^{\tilde{q}}\varepsilon^{-\tilde{r}}$, where the constants $\tilde{c}, \tilde{q}, \tilde{r}$ are independent of the dimension $D$ and the accuracy $\varepsilon$. This guarantees that DeepMartingale does not suffer from the curse of dimensionality. Numerical experiments demonstrate the practical effectiveness of DeepMartingale, confirming its convergence, expressivity, and stability.

We study meta-reinforcement learning in finite-horizon MDPs where related tasks share similar structures in their optimal action-value functions. Specifically, we posit a linear representation $Q^*_h(s,a)=Φ_h(s,a)\,θ^{(k)}_h$ and place a Gaussian meta-prior $ \mathcal{N}(θ^*_h,Σ^*_h)$ over the task-specific parameters $θ^{(k)}_h$. Building on randomized value functions, we propose two Thompson-style algorithms: (i) MTSRL, which learns only the prior mean and performs posterior sampling with the learned mean and known covariance; and (ii) $\text{MTSRL}^{+}$, which additionally estimates the covariance and employs prior widening to control finite-sample estimation error. Further, we develop a prior-alignment technique that couples the posterior under the learned prior with a meta-oracle that knows the true prior, yielding meta-regret guarantees: we match prior-independent Thompson sampling in the small-task regime and strictly improve with more tasks once the prior is learned. Concretely, for known covariance we obtain $\tilde{O}(H^{4}S^{3/2}\sqrt{ANK})$ meta-regret, and with learned covariance $\tilde{O}(H^{4}S^{3/2}\sqrt{AN^3K})$; both recover a better behavior than prior-independent after $K \gtrsim \tilde{O}(H^2)$ and $K \gtrsim \tilde{O}(N^2H^2)$, respectively. Simulations on a stateful recommendation environment (with feature and prior misspecification) show that after brief exploration, MTSRL/MTSRL\(^+\) track the meta-oracle and substantially outperform prior-independent RL and bandit-only meta-baselines. Our results give the first meta-regret guarantees for Thompson-style RL with learned Q-priors, and provide practical recipes (warm-start via RLSVI, OLS aggregation, covariance widening) for experiment-rich settings.

Motivated by the need to efficiently identify multiple candidates in high trial-and-error cost tasks such as drug discovery, we propose a near-optimal algorithm to identify all ε-best arms (i.e., those at most ε worse than the optimum). Specifically, we introduce LinFACT, an algorithm designed to optimize the identification of all ε-best arms in linear bandits. We establish a novel information-theoretic lower bound on the sample complexity of this problem and demonstrate that LinFACT achieves instance optimality by matching this lower bound up to a logarithmic factor. A key ingredient of our proof is to integrate the lower bound directly into the scaling process for upper bound derivation, determining the termination round and thus the sample complexity. We also extend our analysis to settings with model misspecification and generalized linear models. Numerical experiments, including synthetic and real drug discovery data, demonstrate that LinFACT identifies more promising candidates with reduced sample complexity, offering significant computational efficiency and accelerating early-stage exploratory experiments.

We study nonstationary newsvendor problems under nonparametric demand models and general distributional measures of nonstationarity, addressing the practical challenges of unknown degree of nonstationarity and demand censoring. We propose a novel distributional-detection-and-restart framework for learning in nonstationary environments, and instantiate it through two efficient algorithms for the uncensored and censored demand settings. The algorithms are fully adaptive, requiring no prior knowledge of the degree and type of nonstationarity, and offer a flexible yet powerful approach to handling both abrupt and gradual changes in nonstationary environments. We establish a comprehensive optimality theory for our algorithms by deriving matching regret upper and lower bounds under both general and refined structural conditions with nontrivial proof techniques that are of independent interest. Numerical experiments using real-world datasets, including nurse staffing data for emergency departments and COVID-19 test demand data, showcase the algorithms' superior and robust empirical performance. While motivated by the newsvendor problem, the distributional-detection-and-restart framework applies broadly to a wide class of nonstationary stochastic optimization problems. Managerially, our framework provides a practical, easy-to-deploy, and theoretically grounded solution for decision-making under nonstationarity.

Ranking and selection (R&S) aims to identify the alternative with the best mean performance among $k$ simulated alternatives. The practical value of R&S depends on accurate simulation input modeling, which often suffers from the curse of input uncertainty due to limited data. Distributionally robust ranking and selection (DRR&S) addresses this challenge by modeling input uncertainty via an ambiguity set of $m > 1$ plausible input distributions, resulting in $km$ scenarios in total. Recent DRR&S studies suggest a key structural insight: additivity in budget allocation is essential for efficiency. However, existing justifications are heuristic, and fundamental properties such as consistency and the precise allocation pattern induced by additivity remain poorly understood. In this paper, we propose a simple additive allocation (AA) procedure that aims to exclusively sample the $k + m - 1$ previously hypothesized critical scenarios. Leveraging boundary-crossing arguments, we establish a lower bound on the probability of correct selection and characterize the procedure's budget allocation behavior. We then prove that AA is consistent and, surprisingly, achieves additivity in the strongest sense: as the total budget increases, only $k + m - 1$ scenarios are sampled infinitely often. Notably, the worst-case scenarios of non-best alternatives may not be among them, challenging prior beliefs about their criticality. These results offer new and counterintuitive insights into the additive structure of DRR&S. To improve practical performance while preserving this structure, we introduce a general additive allocation (GAA) framework that flexibly incorporates sampling rules from traditional R&S procedures in a modular fashion. Numerical experiments support our theoretical findings and demonstrate the competitive performance of the proposed GAA procedures.

We study a class of multi-period online decision-making problems with sequence-based predictions, which may be generated by machine learning models but whose accuracy is not guaranteed. In each period, the decision-maker observes the realized request and must take an irrevocable action that yields a reward or incurs a cost, without knowledge of future arrivals. We introduce a bounded-influence framework, in which past decisions and requests exert only limited impact on the future optimal reward. Within this framework, we propose the AdaSwitch meta-algorithm, which exploits predictions to attain performance close to the offline benchmark when predictions are accurate, while preserving classical competitive-ratio guarantees under highly inaccurate predictions. Our framework and meta-algorithm apply to diverse settings, including lead-time quotation in processing systems, the $k$-server problem, and online allocation of reusable resources. These applications illustrate the flexibility and broad applicability of our approach to learning-augmented online decision-making.

This paper studies a bandit optimization problem where the goal is to maximize a function $f(x)$ over $T$ periods for some unknown strongly concave function $f$. We consider a new pairwise comparison oracle, where the decision-maker chooses a pair of actions $(x, x')$ for a consecutive number of periods and then obtains an estimate of $f(x)-f(x')$. We show that such a pairwise comparison oracle finds important applications to joint pricing and inventory replenishment problems and network revenue management. The challenge in this bandit optimization is twofold. First, the decision-maker not only needs to determine a pair of actions $(x, x')$ but also a stopping time $n$ (i.e., the number of queries based on $(x, x')$). Second, motivated by our inventory application, the estimate of the difference $f(x)-f(x')$ is biased, which is different from existing oracles in stochastic optimization literature. To address these challenges, we first introduce a discretization technique and local polynomial approximation to relate this problem to linear bandits. Then we developed a tournament successive elimination technique to localize the discretized cell and run an interactive batched version of LinUCB algorithm on cells. We establish regret bounds that are optimal up to poly-logarithmic factors. Furthermore, we apply our proposed algorithm and analytical framework to the two operations management problems and obtain results that improve state-of-the-art results in the existing literature.

Motivated by our collaboration with a major refugee resettlement agency in the U.S., we study a dynamic matching problem where each new arrival (a refugee case) must be matched immediately and irrevocably to one of the static resources (a location with a fixed annual quota). In addition to consuming the static resource, each case requires post-allocation service from a server, such as a translator. Given the time-consuming nature of service, a server may not be available at a given time, thus we refer to it as a dynamic resource. Upon matching, the case will wait to avail service in a first-come-first-serve manner. Bursty matching to a location may result in undesirable congestion at its corresponding server. Consequently, the central planner (the agency) faces a dynamic matching problem with an objective that combines the matching reward (captured by pair-specific employment outcomes) with the cost for congestion for dynamic resources and over-allocation for the static ones. Motivated by the observed fluctuations in the composition of refugee pools across the years, we design algorithms that do not rely on distributional knowledge constructed based on past years' data. To that end, we develop learning-based algorithms that are asymptotically optimal in certain regimes, easy to interpret, and computationally fast. Our design is based on learning the dual variables of the underlying optimization problem; however, the main challenge lies in the time-varying nature of the dual variables associated with dynamic resources. To overcome this challenge, our theoretical development brings together techniques from Lyapunov analysis, adversarial online learning, and stochastic optimization. On the application side, when tested on real data from our partner agency, our method outperforms existing ones making it a viable candidate for replacing the current practice upon experimentation.

Problem definition: Traditionally, New York City's top 8 public schools have selected candidates solely based on their scores in the Specialized High School Admissions Test (SHSAT). These scores are known to be impacted by socioeconomic status of students and test preparation received in middle schools, leading to a massive filtering effect in the education pipeline. The classical mechanisms for assigning students to schools do not naturally address problems like school segregation and class diversity, which have worsened over the years. The scientific community, including policymakers, have reacted by incorporating group-specific quotas and proportionality constraints, with mixed results. The problem of finding effective and fair methods for broadening access to top-notch education is still unsolved. Methodology/results: We take an operations approach to the problem different from most established literature, with the goal of increasing opportunities for students with high economic needs. Using data from the Department of Education (DOE) in New York City, we show that there is a shift in the distribution of scores obtained by students that the DOE classifies as "disadvantaged" (following criteria mostly based on economic factors). We model this shift as a "bias" that results from an underestimation of the true potential of disadvantaged students. We analyze the impact this bias has on an assortative matching market. We show that centrally planned interventions can significantly reduce the impact of bias through scholarships or training, when they target the segment of disadvantaged students with average performance.

Contextual bandit with linear reward functions is among one of the most extensively studied models in bandit and online learning research. Recently, there has been increasing interest in designing \emph{locally private} linear contextual bandit algorithms, where sensitive information contained in contexts and rewards is protected against leakage to the general public. While the classical linear contextual bandit algorithm admits cumulative regret upper bounds of $\tilde O(\sqrt{T})$ via multiple alternative methods, it has remained open whether such regret bounds are attainable in the presence of local privacy constraints, with the state-of-the-art result being $\tilde O(T^{3/4})$. In this paper, we show that it is indeed possible to achieve an $\tilde O(\sqrt{T})$ regret upper bound for locally private linear contextual bandit. Our solution relies on several new algorithmic and analytical ideas, such as the analysis of mean absolute deviation errors and layered principal component regression in order to achieve small mean absolute deviation errors.