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The class of direct preference optimization (DPO) algorithms has emerged as a promising approach for solving the alignment problem in foundation models. These algorithms work with very limited feedback in the form of pairwise preferences…
In this technical report, we discuss several sampling algorithms for Determinantal Point Processes (DPP). DPPs have recently gained a broad interest in the machine learning and statistics literature as random point processes with negative…
This paper develops a dynamic programming (DP) approach for decentralized stochastic optimal control problems with delayed sharing information patterns, which exhibits the fundamental Properties of classical DP of centralized partially…
Optimization methods have been broadly applied to two classes of objects viz. (i) modeling and description of data and (ii) the determination of the stationary points of functions. Here, a theoretical basis is developed that optimizes an…
The goal of this paper is to quantitatively describe some statistical properties of higher-dimensional determinantal point processes with a primary focus on the nearest-neighbor distribution functions. Toward this end, we express these…
Markov Decision Problems (MDPs) provide a foundational framework for modelling sequential decision-making across diverse domains, guided by optimality criteria such as discounted and average rewards. However, these criteria have inherent…
Consider the following estimation problem: there are $n$ entities, each with an unknown parameter $p_i \in [0,1]$, and we observe $n$ independent random variables, $X_1,\ldots,X_n$, with $X_i \sim $ Binomial$(t, p_i)$. How accurately can…
When model predictions inform downstream decision making, a natural question is under what conditions can the decision-makers simply respond to the predictions as if they were the true outcomes. Calibration suffices to guarantee that simple…
Diffusion probabilistic models (DPMs) have exhibited excellent performance for high-fidelity image generation while suffering from inefficient sampling. Recent works accelerate the sampling procedure by proposing fast ODE solvers that…
Deterministic Markov Decision Processes (DMDPs) are a mathematical framework for decision-making where the outcomes and future possible actions are deterministically determined by the current action taken. DMDPs can be viewed as a finite…
Order statistics play a fundamental role in statistical procedures such as risk estimation, outlier detection, and multiple hypothesis testing as well as in the analyses of mechanism design, queues, load balancing, and various other…
Determinantal point processes (DPPs) are well known models for diverse subset selection problems, including recommendation tasks, document summarization and image search. In this paper, we discuss a greedy deterministic adaptation of k-DPP.…
Let ${\mathbf d} =(d_j)_{j\in\mathbb{I}_m}\in \mathbb{N}^m$ be a decreasing finite sequence of positive integers, and let $\alpha=(\alpha_i)_{i\in\mathbb{I}_n}$ be a finite and non-increasing sequence of positive weights. Given a family…
Multipoint evaluation is the computational task of evaluating a polynomial given as a list of coefficients at a given set of inputs. And while \emph{nearly linear time} algorithms have been known for the univariate instance of multipoint…
Stochastic differential equations (SDEs) are increasingly used in longitudinal data analysis, compartmental models, growth modelling, and other applications in a number of disciplines. Parameter estimation, however, currently requires…
In this paper, we consider effective discretization strategies and iterative solvers for nonlinear PDE-constrained optimization models for pattern evolution within biological processes. Upon a Sequential Quadratic Programming linearization…
We consider deterministic Markov decision processes (MDPs) and apply max-plus algebra tools to approximate the value iteration algorithm by a smaller-dimensional iteration based on a representation on dictionaries of value functions. The…
We study how to construct compressed datasets that suffice to recover optimal decisions in linear programs with an unknown cost vector $c$ lying in a prior set $\mathcal{C}$. Recent work by Bennouna et al. provides an exact geometric…
This work presents DMPC (Data-and Model-Driven Predictive Control) to solve control problems in which some of the constraints or parts of the objective function are known, while others are entirely unknown to the controller. It is assumed…
An adaptation of Response Surface Methodology (RSM) when the covariate is of high or infinite dimensional is proposed, providing a tool for black-box optimization in this context. We combine dimension reduction techniques with classical…