Related papers: A Variational-Calculus Approach to Online Algorith…
Offline preference optimization is a key method for enhancing and controlling the quality of Large Language Model (LLM) outputs. Typically, preference optimization is approached as an offline supervised learning task using manually-crafted…
Robotic path planning problems are often NP-hard, and practical solutions typically rely on approximation algorithms with provable performance guarantees for general cases. While designing such algorithms is challenging, formally proving…
We propose an efficient algorithm for approximate computation of the profile maximum likelihood (PML), a variant of maximum likelihood maximizing the probability of observing a sufficient statistic rather than the empirical sample. The PML…
Compared to the wide array of advanced Monte Carlo methods supported by modern probabilistic programming languages (PPLs), PPL support for variational inference (VI) is less developed: users are typically limited to a predefined selection…
We propose a new randomized algorithm for solving convex optimization problems that have a large number of constraints (with high probability). Existing methods like interior-point or Newton-type algorithms are hard to apply to such…
Many online platforms, ranging from online retail stores to social media platforms, employ algorithms to optimize their offered assortment of items (e.g., products and contents). These algorithms often focus exclusively on achieving the…
Large language models (LLMs) have significant potential to improve operational efficiency in operations management. Deploying these models requires specifying a policy that governs response quality, shapes user experience, and influences…
$\ell_1$ optimization is a well known heuristic often employed for solving various forms of sparse linear problems. In this paper we look at its a variant that we refer to as the \emph{partial} $\ell_1$ and discuss its mathematical…
Conic programs arise broadly in physics, quantum information, machine learning, and engineering, many of which are defined over sparse graphs. Although such problems can be solved in polynomial time using classical interior-point solvers,…
Many problems in computer science and applied mathematics require rounding a vector $\mathbf{w}$ of fractional values lying in the interval $[0,1]$ to a binary vector $\mathbf{x}$ so that, for a given matrix $\mathbf{A}$,…
We study the problem of efficiency under $\alpha$ local differential privacy ($\alpha$ LDP) in both discrete and continuous settings. Building on a factorization lemma, which shows that any privacy mechanism can be decomposed into an…
We study a class of generalized linear programs (GLP) in a large-scale setting, which includes simple, possibly nonsmooth convex regularizer and simple convex set constraints. By reformulating (GLP) as an equivalent convex-concave min-max…
We consider a variational convex relaxation of a class of optimal partitioning and multiclass labeling problems, which has recently proven quite successful and can be seen as a continuous analogue of Linear Programming (LP) relaxation…
Pursuing invariant prediction from heterogeneous environments opens the door to learning causality in a purely data-driven way and has several applications in causal discovery and robust transfer learning. However, existing methods such as…
Approximate linear programs (ALPs) are well-known models based on value function approximations (VFAs) to obtain policies and lower bounds on the optimal policy cost of discounted-cost Markov decision processes (MDPs). Formulating an ALP…
Optimal Power Flow (OPF) is a valuable tool for power system operators, but it is a difficult problem to solve for large systems. Machine Learning (ML) algorithms, especially Neural Networks-based (NN) optimization proxies, have emerged as…
Optimization methods are at the core of many problems in signal/image processing, computer vision, and machine learning. For a long time, it has been recognized that looking at the dual of an optimization problem may drastically simplify…
The online randomized primal-dual method has widespread applications in online algorithm design and analysis. A key challenge is identifying an appropriate function space, $F$, in which we search for an optimal updating function $f \in F$…
We study offline reinforcement learning (RL) with linear MDPs under the infinite-horizon discounted setting which aims to learn a policy that maximizes the expected discounted cumulative reward using a pre-collected dataset. Existing…
This paper investigates the capabilities of large language models (LLMs) in formulating and solving decision-making problems using mathematical programming. We first conduct a systematic review and meta-analysis of recent literature to…