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Post-training of LLMs with RLHF, and subsequently preference optimization algorithms such as DPO, IPO, etc., made a big difference in improving human alignment. However, all such techniques can only work with a single (human) objective. In…

Multi-objective optimization problems (MOPs) often require a trade-off between conflicting objectives, maximizing diversity and convergence in the objective space. This study presents an approach to improve the quality of MOP solutions by…

We study stochastic nonconvex optimization under heavy-tailed noise. In this setting, the stochastic gradients only have bounded $p$-th central moment ($p$-BCM) for some $p \in (1,2]$. Building on the foundational work of Arjevani et al.…

Stochastic optimization is fundamental to modern machine learning. Recent research has extended the study of stochastic first-order methods (SFOMs) from light-tailed to heavy-tailed noise, which frequently arises in practice, with clipping…

We consider the problem of solving robust Markov decision process (MDP), which involves a set of discounted, finite state, finite action space MDPs with uncertain transition kernels. The goal of planning is to find a robust policy that…

In this paper we consider multi-objective optimization problems over a box. The problem is very relevant and several computational approaches have been proposed in the literature. They broadly fall into two main classes: evolutionary…

Suppose we have a memory storing $0$s and $1$s and we want to estimate the frequency of $1$s by sampling. We want to do this I/O-efficiently, exploiting that each read gives a block of $B$ bits at unit cost; not just one bit. If the input…

We investigate the finite-time analysis of finding ($\delta,\epsilon$)-stationary points for nonsmooth nonconvex objectives in decentralized stochastic optimization. A set of agents aim at minimizing a global function using only their local…

The q-Gaussian distribution results from maximizing certain generalizations of Shannon entropy under some constraints. The importance of q-Gaussian distributions stems from the fact that they exhibit power-law behavior, and also generalize…

The use of momentum in stochastic optimization algorithms has shown empirical success across a range of machine learning tasks. Recently, a new class of stochastic momentum algorithms has emerged within the Linear Minimization Oracle (LMO)…

Stochastic First-Order (SFO) methods have been a cornerstone in addressing a broad spectrum of modern machine learning (ML) challenges. However, their efficacy is increasingly questioned, especially in large-scale applications where…

Selecting prototypical examples from a source distribution to represent a target data distribution is a fundamental problem in machine learning. Existing subset selection methods often rely on implicit importance scores, which can be skewed…

We define very large-scale multiobjective optimization problems as optimizing multiple objectives (VLSMOPs) with more than 100,000 decision variables. These problems hold substantial significance, given the ubiquity of real-world scenarios…

Source-free domain adaptation (SFDA), where only a pre-trained source model is used to adapt to the target distribution, is a more general approach to achieving domain adaptation in the real world. However, it can be challenging to capture…

Safety alignment of large language models remains brittle under domain shift and noisy preference supervision. Most existing robust alignment methods focus on uncertainty in alignment data, while overlooking optimization-induced fragility…

This paper addresses the limitations of conventional vector quantization algorithms, particularly K-Means and its variant K-Means++, and investigates the Stochastic Quantization (SQ) algorithm as a scalable alternative for high-dimensional…

In this paper, we study the conditional stochastic optimization (CSO) problem which covers a variety of applications including portfolio selection, reinforcement learning, robust learning, causal inference, etc. The sample-averaged gradient…

Transformer-based architectures achieve state-of-the-art performance across a wide range of tasks in natural language processing, computer vision, and speech processing. However, their immense capacity often leads to overfitting, especially…

In planning problems, it is often challenging to fully model the desired specifications. In particular, in human-robot interaction, such difficulty may arise due to human's preferences that are either private or complex to model.…

Recent advances on large-scale pre-training have shown great potentials of leveraging a large set of Pre-Trained Models (PTMs) for improving Out-of-Distribution (OoD) generalization, for which the goal is to perform well on possible unseen…