Problem-Parameter-Free Decentralized Nonconvex Stochastic Optimization

Existing decentralized algorithms usually require knowledge of problem parameters for updating local iterates. For example, the hyperparameters (such as learning rate) usually require the knowledge of Lipschitz constant of the global gradient or topological information of the communication networks, which are usually not accessible in practice. In this paper, we propose D-NASA, the first algorithm … Read more

Variance Reduction and Low Sample Complexity in Stochastic Optimization via Proximal Point Method

This paper proposes a stochastic proximal point method to solve a stochastic convex composite optimization problem. High probability results in stochastic optimization typically hinge on restrictive assumptions on the stochastic gradient noise, for example, sub-Gaussian distributions. Assuming only weak conditions such as bounded variance of the stochastic gradient, this paper establishes a low sample complexity … Read more

Extending the Reach of First-Order Algorithms for Nonconvex Min-Max Problems with Cohypomonotonicity

\(\) We focus on constrained, \(L\)-smooth, nonconvex-nonconcave min-max problems either satisfying \(\rho\)-cohypomonotonicity or admitting a solution to the \(\rho\)-weakly Minty Variational Inequality (MVI), where larger values of the parameter \(\rho>0\) correspond to a greater degree of nonconvexity. These problem classes include examples in two player reinforcement learning, interaction dominant min-max problems, and certain synthetic test problems … Read more

Distributionally Fair Stochastic Optimization using Wasserstein Distance

A traditional stochastic program under a finite population typically seeks to optimize efficiency by maximizing the expected profits or minimizing the expected costs, subject to a set of constraints. However, implementing such optimization-based decisions can have varying impacts on individuals, and when assessed using the individuals’ utility functions, these impacts may differ substantially across demographic … Read more

On Tractability, Complexity, and Mixed-Integer Convex Programming Representability of Distributionally Favorable Optimization

Distributionally Favorable Optimization (DFO) is an important framework for decision-making under uncertainty, with applications across fields such as reinforcement learning, online learning, robust statistics, chance-constrained programming, and two-stage stochastic optimization without relatively complete recourse. In contrast to the traditional Distributionally Robust Optimization (DRO) paradigm, DFO presents a unique challenge– the application of the inner infimum … Read more

Policy with guaranteed risk-adjusted performance for multistage stochastic linear problems

Risk-averse multi-stage problems and their applications are gaining interest in various fields of applications. Under convexity assumptions, the resolution of these problems can be done with trajectory following dynamic programming algorithms like Stochastic Dual Dynamic Programming (SDDP) to access a deterministic lower bound, and dual SDDP for deterministic upper bounds. In this paper, we leverage … Read more

Active Set-based Inexact Proximal Bundle Algorithm for Stochastic Quadratic Programming

In this paper, we examine two-stage stochastic quadratic programming problems, where the objective function of the first and second stages are quadratic functions, and the constraints are linear. The uncertainty is associated with the second-stage right-hand side and variable bounds. In large-scale settings, when the number of scenarios necessary to represent the underlying stochastic process … Read more

Noise-Tolerant Optimization Methods for the Solution of a Robust Design Problem

The development of nonlinear optimization algorithms capable of performing reliably in the presence of noise has garnered considerable attention lately. This paper advocates for strategies to create noise-tolerant nonlinear optimization algorithms by adapting classical deterministic methods. These adaptations follow certain design guidelines described here, which make use of estimates of the noise level in the … Read more

Alternate Training of Shared and Task-Specific Parameters for Multi-Task Neural Networks

This paper introduces novel alternate training procedures for hard-parameter sharing Multi-Task Neural Networks (MTNNs). Traditional MTNN training faces challenges in managing conflicting loss gradients, often yielding sub-optimal performance. The proposed alternate training method updates shared and task-specific weights alternately, exploiting the multi-head architecture of the model. This approach reduces computational costs, enhances training regularization, and … Read more

Adaptive Partitioning for Chance-Constrained Problems with Finite Support

This paper studies chance-constrained stochastic optimization problems with finite support. It presents an iterative method that solves reduced-size chance-constrained models obtained by partitioning the scenario set. Each reduced problem is constructed to yield a bound on the optimal value of the original problem. We show how to adapt the partitioning of the scenario set so … Read more