Related papers: Optimization Algorithms for Multi-Species Spherica…

This paper proposes a new algorithm for solving constrained global optimization problems where both the objective function and constraints are one-dimensional non-differentiable multiextremal Lipschitz functions. Multiextremal constraints…

Optimization of convex functions under stochastic zeroth-order feedback has been a major and challenging question in online learning. In this work, we consider the problem of optimizing second-order smooth and strongly convex functions…

We identify a special class of multi-species spin glass models: ones in which the species proportions serve to ''balance'' out the interaction strengths. For this class, we prove a free energy lower bound that does not require any convexity…

We focus on spherical spin glasses whose Parisi distribution has support of the form $[0,q]$. For such models we construct paths from the origin to the sphere which consistently remain close to the ground-state energy on the sphere of…

We propose an accelerated meta-algorithm, which allows to obtain accelerated methods for convex unconstrained minimization in different settings. As an application of the general scheme we propose nearly optimal methods for minimizing…

We analyze the landscape of general smooth Gaussian functions on the sphere in dimension $N$, when $N$ is large. We give an explicit formula for the asymptotic complexity of the mean number of critical points of finite and diverging index…

In this paper we review a recent proposal to understand the long time limit of glassy dynamics in terms of an appropriate Markov Chain. [1]. The advantages of the resulting construction are many. The first one is that it gives a quasi…

We suggest an iterative quantum protocol, allowing to solve optimization problems with a glassy energy landscape. It is based on a periodic cycling around the tricritical point of the many-body localization transition. This ensures that…

Gradient-based (a.k.a. `first order') optimization algorithms are routinely used to solve large scale non-convex problems. Yet, it is generally hard to predict their effectiveness. In order to gain insight into this question, we revisit the…

We consider the communication complexity of some fundamental convex optimization problems in the point-to-point (coordinator) and blackboard communication models. We strengthen known bounds for approximately solving linear regression,…

We present a conjecture on the exact location of the multicritical point in the phase diagram of spin glass models in finite dimensions. By generalizing our previous work, we combine duality and gauge symmetry for replicated random systems…

We show that multiple filamentation patterns in high-power laser beams, can be described by means of two statistical physics concepts, namely self-similarity of the patterns over two nested scales, and nearest-neighbor interactions of…

We introduce efficient algorithms for approximate sampling from symmetric Gibbs distributions on the sparse random (hyper)graph. The examples we consider include (but are not restricted to) important distributions on spin systems and…

We introduce a new approach to develop stochastic optimization algorithms for a class of stochastic composite and possibly nonconvex optimization problems. The main idea is to combine two stochastic estimators to create a new hybrid one. We…

This paper investigates a category of constrained fractional optimization problems that emerge in various practical applications. The objective function for this category is characterized by the ratio of a numerator and denominator, both…

In this paper we propose a general framework to characterize and solve the stochastic optimization problems with multiple objectives underlying many real world learning applications. We first propose a projection based algorithm which…

This work presents a unified framework that combines global approximations with locally built models to handle challenging nonconvex and nonsmooth composite optimization problems, including cases involving extended real-valued functions. We…

This paper focuses on investigating an inexact stochastic model-based optimization algorithm that integrates preconditioning techniques for solving stochastic composite optimization problems. The proposed framework unifies and extends the…

We establish nearly optimal upper and lower bounds for approximating decision tree splits in data streams. For regression with labels in the range $\{0,1,\ldots,M\}$, we give a one-pass algorithm using $\tilde{O}(M^2/\epsilon)$ space that…

Probabilistic smoothing is a standard tool for global optimization, but existing methods rely on Gaussian kernels and specific transforms, often resulting in strong hyperparameter sensitivity and limited robustness. We propose a general…