Related papers: A Lagrangean Relaxation Algorithm for the Simple P…
Self-alignment, whereby models learn to improve themselves without human annotation, is a rapidly growing research area. However, existing techniques often fail to improve complex reasoning tasks due to the difficulty of assigning correct…
Direct Preference Optimization (DPO) using an implicit reward model has proven to be an effective alternative to reinforcement learning from human feedback (RLHF) for fine-tuning preference aligned large language models (LLMs). However, the…
This paper considers facility location problems in which a firm entering a market seeks to open facilities on a subset of candidate locations so as to maximize its expected market share, assuming that customers choose the available…
Preference optimization methods typically begin training with a well-trained SFT model as a reference model. In RLHF and DPO, a regularization term is used during the preference optimization process to prevent the policy model from…
Model-free reinforcement learning algorithms have seen remarkable progress, but key challenges remain. Trust Region Policy Optimization (TRPO) is known for ensuring monotonic policy improvement through conservative updates within a trust…
Given facilities with capacities and clients with penalties and demands, the transportation problem with market choice consists in finding the minimum-cost way to partition the clients into unserved clients, paying the penalties, and into…
A hierarchy of semidefinite programming (SDP) relaxations approximates the global optimum of polynomial optimization problems of noncommuting variables. Generating the relaxation, however, is a computationally demanding task, and only…
The Standard Quadratic optimization Problem (StQP), arguably the simplest among all classes of NP-hard optimization problems, consists of extremizing a quadratic form (the simplest nonlinear polynomial) over the standard simplex (the…
In this paper, a green transportation location problem is considered with uncertain demand parameter. Increasing robustness influences the number of trucks for sending goods and products, and consequently, makes the air pollution enhance.…
The classical linear ordering problem seeks a single ranking representing a given preference matrix. While suitable for homogeneous populations, it fails when observed preferences arise from several latent groups with distinct ranking…
We study an LLM fine-tuning task for designing reward functions for sequential resource allocation problems in public health, guided by human preferences expressed in natural language. This setting presents a challenging testbed for…
Dynamical low-rank (DLR) approximation methods have previously been developed for time-dependent radiation transport problems. One crucial drawback of DLR is that it does not conserve important quantities of the calculation, which limits…
The set-union knapsack problem (SUKP) is a constrained composed optimization problem. It is more difficulty for solving because values and weights depend on items and elements respectively. In this paper, we present two self-adjusting…
In this paper, we introduce an adaptation of the facility location problem and analyze it within the framework of local differential privacy (LDP). Under this model, we ensure the privacy of client presence at specific locations. When n is…
In this paper, we propose an efficient algorithm for the network slicing problem which attempts to map multiple customized virtual network requests (also called services) to a common shared network infrastructure and allocate network…
Offline preference optimization offers a simpler and more stable alternative to RLHF for aligning language models. However, their effectiveness is critically dependent on ranking accuracy, a metric where further gains are highly impactful.…
We introduce optimal algorithms for the problems of data placement (DP) and page placement (PP) in networks with a constant number of clients each of which has limited storage availability and issues requests for data objects. The objective…
Logical reasoning is a key task for artificial intelligence due to it's role in major downstream tasks such as Question Answering, Summarization. Recent methods in improving the reasoning ability of LLMs fall short in correctly converting a…
We consider various {\em multi-vehicle versions of the minimum latency problem}. There is a fleet of $k$ vehicles located at one or more depot nodes, and we seek a collection of routes for these vehicles that visit all nodes so as to…
Lagrangian relaxation is a versatile mathematical technique employed to relax constraints in an optimization problem, enabling the generation of dual bounds to prove the optimality of feasible solutions and the design of efficient…