Related papers: Boosting Data-Driven Mirror Descent with Randomiza…
Learning to optimize - the idea that we can learn from data algorithms that optimize a numerical criterion - has recently been at the heart of a growing number of research efforts. One of the most challenging issues within this approach is…
Evaluating preference optimization (PO) algorithms on LLM alignment is a challenging task that presents prohibitive costs, noise, and several variables like model size and hyper-parameters. In this work, we show that it is possible to gain…
We study two variants of the mirror descent-ascent (MDA) algorithm for solving min-max problems on the space of measures: simultaneous and alternating. We work under assumptions of convexity-concavity and relative smoothness of the payoff…
Recently there were proposed some innovative convex optimization concepts, namely, relative smoothness [1] and relative strong convexity [2,3]. These approaches have significantly expanded the class of applicability of gradient-type methods…
In this paper, we investigate the non-asymptotic stationary convergence behavior of Stochastic Mirror Descent (SMD) for nonconvex optimization. We focus on a general class of nonconvex nonsmooth stochastic optimization problems, in which…
Recent work by Woodworth et al. (2020) shows that the optimization dynamics of gradient descent for overparameterized problems can be viewed as low-dimensional dual dynamics induced by a mirror map, explaining the implicit regularization…
We study online convex optimization with switching costs, a practically important but also extremely challenging problem due to the lack of complete offline information. By tapping into the power of machine learning (ML) based optimizers,…
In machine learning and statistical data analysis, we often run into objective function that is a summation: the number of terms in the summation possibly is equal to the sample size, which can be enormous. In such a setting, the stochastic…
Modern policy optimization methods roughly follow the policy mirror descent (PMD) algorithmic template, for which there are by now numerous theoretical convergence results. However, most of these either target tabular environments, or can…
We revisit the classical problem of estimating an unknown distribution from its samples by fitting a mixture model that minimizes cross-entropy loss. Framing the task as a stochastic convex optimization problem over the space of $ M…
We consider risk-averse convex stochastic programs expressed in terms of extended polyhedral risk measures. We derive computable confidence intervals on the optimal value of such stochastic programs using the Robust Stochastic Approximation…
Distributed gradient descent algorithms have come to the fore in modern machine learning, especially in parallelizing the handling of large datasets that are distributed across several workers. However, scant attention has been paid to…
Training deep neural networks is a highly nontrivial task, involving carefully selecting appropriate training algorithms, scheduling step sizes and tuning other hyperparameters. Trying different combinations can be quite labor-intensive and…
In this paper, we propose a second-order extension of the continuous-time game-theoretic mirror descent (MD) dynamics, referred to as MD2, which provably converges to mere (but not necessarily strict) variationally stable states (VSS)…
We consider the problem of learning the optimal policy for infinite-horizon Markov decision processes (MDPs). For this purpose, some variant of Stochastic Mirror Descent is proposed for convex programming problems with Lipschitz-continuous…
Machine unlearning algorithms aim to remove the impact of selected training data from a model without the computational expenses of retraining from scratch. Two such algorithms are ``Descent-to-Delete" (D2D) and ``Rewind-to-Delete" (R2D),…
The $L_0$-regularized least squares problem (a.k.a. best subsets) is central to sparse statistical learning and has attracted significant attention across the wider statistics, machine learning, and optimization communities. Recent work has…
We introduce a principled learning to optimize (L2O) framework for solving fixed-point problems involving general nonexpansive mappings. Our idea is to deliberately inject summable perturbations into a standard Krasnosel'skii-Mann iteration…
Multi-objective learning (MOL) aims to learn under multiple potentially conflicting objectives and strike a proper balance. While recent preference-guided MOL methods often rely on additional optimization objectives or constraints, we…
Learning-to-optimize leverages machine learning to accelerate optimization algorithms. While empirical results show tremendous improvements compared to classical optimization algorithms, theoretical guarantees are mostly lacking, such that…