In restless multi-arm bandits, a central agent is tasked with optimally distributing limited resources across several bandits (arms), with each arm being a Markov decision process. In this work, we generalize the traditional restless multi-arm bandit problem with a risk-neutral objective by incorporating risk-awareness. We establish indexability conditions for the case of a risk-aware objective and provide a solution based on Whittle index. In addition, we address the learning problem when the true transition probabilities are unknown by proposing a Thompson sampling approach and show that it achieves bounded regret that scales sublinearly with the number of episodes and quadratically with the number of arms. The efficacy of our method in reducing risk exposure in restless multi-arm bandits is illustrated through a set of numerical experiments.

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.

In this study, we introduce Modular State-based Stackelberg Games (Mod-SbSG), a novel game structure developed for distributed self-learning in modular manufacturing systems. Mod-SbSG enhances cooperative decision-making among self-learning agents within production systems by integrating State-based Potential Games (SbPG) with Stackelberg games. This hierarchical structure assigns more important modules of the manufacturing system a first-mover advantage, while less important modules respond optimally to the leaders' decisions. This decision-making process differs from typical multi-agent learning algorithms in manufacturing systems, where decisions are made simultaneously. We provide convergence guarantees for the novel game structure and design learning algorithms to account for the hierarchical game structure. We further analyse the effects of single-leader/multiple-follower and multiple-leader/multiple-follower scenarios within a Mod-SbSG. To assess its effectiveness, we implement and test Mod-SbSG in an industrial control setting using two laboratory-scale testbeds featuring sequential and serial-parallel processes. The proposed approach delivers promising results compared to the vanilla SbPG, which reduces overflow by 97.1%, and in some cases, prevents overflow entirely. Additionally, it decreases power consumption by 5-13% while satisfying the production demand, which significantly improves potential (global objective) values.

Meta learning is a promising paradigm in the era of large models and task distributional robustness has become an indispensable consideration in real-world scenarios. Recent advances have examined the effectiveness of tail task risk minimization in fast adaptation robustness improvement \citep{wang2023simple}. This work contributes to more theoretical investigations and practical enhancements in the field. Specifically, we reduce the distributionally robust strategy to a max-min optimization problem, constitute the Stackelberg equilibrium as the solution concept, and estimate the convergence rate. In the presence of tail risk, we further derive the generalization bound, establish connections with estimated quantiles, and practically improve the studied strategy. Accordingly, extensive evaluations demonstrate the significance of our proposal and its scalability to multimodal large models in boosting robustness.

Offline paired preference optimization algorithms have become a popular approach for fine-tuning on preference data, outperforming traditional supervised fine-tuning in various tasks. However, traditional implementations often involve redundant computations, especially for tasks with long shared prompts. We introduce prefix sharing for preference tuning, a novel technique that processes chosen and rejected responses as one sequence with a shared prefix. To prevent cross-response contamination, we use a custom block-sparse attention mask. Our method achieves 1.1-1.5 improvement in training throughput on popular DPO datasets, without any effect on convergence. When combined with sequence packing, we observe consistent 1.3-1.6 speedups, benefiting even datasets with smaller sequence lengths. While we focus on Direct Preference Optimization (DPO), our approach is applicable to other paired preference tuning methods. By enhancing computational efficiency, our work contributes to making preference-based fine-tuning more accessible for a wider range of applications and model sizes.

In system analysis and design optimization, multiple computational models are typically available to represent a given physical system. These models can be broadly classified as high-fidelity models, which provide highly accurate predictions but require significant computational resources, and low-fidelity models, which are computationally efficient but less accurate. Multi-fidelity methods integrate high-and low-fidelity models to balance computational cost and predictive accuracy. This perspective paper provides an in-depth overview of the emerging field of machine learning-based multi-fidelity methods, with a particular emphasis on uncertainty quantification and optimization. For uncertainty quantification, a particular focus is on multi-fidelity graph neural networks, compared with multifidelity polynomial chaos expansion. For optimization, our emphasis is on multifidelity Bayesian optimization, offering a unified perspective on multi-fidelity priors and proposing an application strategy when the objective function is an integral or a weighted sum. We highlight the current state of the art, identify critical gaps in the literature, and outline key research opportunities in this evolving field. Keywords multi-fidelity modeling uncertainty quantification Bayesian optimization 1 Introduction When studying a physical system, analysts often have access to multiple computational models. These models are typically classified as either high-fidelity or low-fidelity, depending on their predictive accuracy. High-fidelity models (HFMs) offer precise predictions of the system's behavior, meeting specific accuracy metrics, but they are computationally demanding.

We develop and analyze data subsampling techniques for Poisson regression, the standard model for count data $y\in\mathbb{N}$. In particular, we consider the Poisson generalized linear model with ID- and square root-link functions. We consider the method of coresets, which are small weighted subsets that approximate the loss function of Poisson regression up to a factor of $1\pm\varepsilon$. We show $\Omega(n)$ lower bounds against coresets for Poisson regression that continue to hold against arbitrary data reduction techniques up to logarithmic factors. By introducing a novel complexity parameter and a domain shifting approach, we show that sublinear coresets with $1\pm\varepsilon$ approximation guarantee exist when the complexity parameter is small. In particular, the dependence on the number of input points can be reduced to polylogarithmic. We show that the dependence on other input parameters can also be bounded sublinearly, though not always logarithmically. In particular, we show that the square root-link admits an $O(\log(y_{\max}))$ dependence, where $y_{\max}$ denotes the largest count presented in the data, while the ID-link requires a $\Theta(\sqrt{y_{\max}/\log(y_{\max})})$ dependence. As an auxiliary result for proving the tightness of the bound with respect to $y_{\max}$ in the case of the ID-link, we show an improved bound on the principal branch of the Lambert $W_0$ function, which may be of independent interest. We further show the limitations of our analysis when $p$th degree root-link functions for $p\geq 3$ are considered, which indicate that other analytical or computational methods would be required if such a generalization is even possible.

Hyperparameters are configuration variables controlling the behavior of machine learning algorithms. They are ubiquitous in machine learning and artificial intelligence and the choice of their values determine the effectiveness of systems based on these technologies. Manual hyperparameter search is often unsatisfactory and becomes unfeasible when the number of hyperparameters is large. Automating the search is an important step towards automating machine learning, freeing researchers and practitioners alike from the burden of finding a good set of hyperparameters by trial and error. In this survey, we present a unified treatment of hyperparameter optimization, providing the reader with examples and insights into the state-of-the-art. We cover the main families of techniques to automate hyperparameter search, often referred to as hyperparameter optimization or tuning, including random and quasi-random search, bandit-, model- and gradient- based approaches. We further discuss extensions, including online, constrained, and multi-objective formulations, touch upon connections with other fields such as meta-learning and neural architecture search, and conclude with open questions and future research directions.

Perception algorithms are ubiquitous in modern autonomy stacks, providing necessary environmental information to operate in the real world. Many of these algorithms depend on the visibility of keypoints, which must remain within the robot's line-of-sight (LoS), for reliable operation. This paper tackles the challenge of maintaining LoS on such keypoints during robot movement. We propose a novel method that addresses these issues by ensuring applicability to various sensor footprints, adaptability to arbitrary nonlinear dynamics, and constant enforcement of LoS throughout the robot's path. Through our experiments, we show that the proposed approach achieves significantly reduced LoS violation and runtime compared to existing state-of-the-art methods in several representative and challenging scenarios.

Sharpness-Aware Minimization (SAM) has been demonstrated to improve the generalization performance of overparameterized models by seeking flat minima on the loss landscape through optimizing model parameters that incur the largest loss within a neighborhood. Nevertheless, such min-max formulations are computationally challenging especially when the problem is highly non-convex. Additionally, focusing only on the worst-case local solution while ignoring potentially many other local solutions may be suboptimal when searching for flat minima. In this work, we propose Tilted SAM (TSAM), a generalization of SAM inspired by exponential tilting that effectively assigns higher priority to local solutions that are flatter and that incur larger losses. TSAM is parameterized by a tilt hyperparameter t and reduces to SAM as t approaches infinity. We prove that (1) the TSAM objective is smoother than SAM and thus easier to optimize; and (2) TSAM explicitly favors flatter minima as t increases. This is desirable as flatter minima could have better generalization properties for certain tasks. We develop algorithms motivated by the discretization of Hamiltonian dynamics to solve TSAM. Empirically, TSAM arrives at flatter local minima and results in superior test performance than the baselines of SAM and ERM across a range of image and text tasks.