Non-Smooth Weakly-Convex Finite-sum Coupled Compositional Optimization Study

Centrala begrepp

The study explores non-smooth weakly-convex finite-sum coupled compositional optimization problems, extending beyond traditional smooth functions to address diverse challenges in machine learning and AI.

Sammanfattning

The paper investigates NSWC FCCO/TCCO, introducing novel algorithms for optimization problems with weakly-convex functions. It analyzes convergence rates and complexities, showcasing applications in deep learning for AUC maximization. The research expands on existing works by considering non-smooth scenarios and proposing efficient solutions.
Key points:

Introduction to non-smooth weakly-convex FCCO/TCCO problems.
Analysis of single-loop stochastic algorithms for convergence.
Application of algorithms in deep learning for two-way partial AUC maximization.
Comparison with prior works on smooth FCCO/TCCO.
Convergence analysis and complexity bounds for NSWC FCCO/TCCO.
The study provides insights into optimizing complex compositional functions efficiently, addressing challenges in non-smooth scenarios with provable convergence guarantees.

Statistik

For all i ∈ S, we assume that fi is ρf-weakly convex, Cf-Lipschitz continuous, and non-decreasing.
For all (i, j) ∈ S1 × S2, we assume that gi is ρg-weakly convex and Cg-Lipschitz continuous.

Citat

"Our research expands on this area by examining non-smooth weakly-convex FCCO."
"One limitation of prior works about non-convex FCCO is that their convergence analysis heavily relies on the smoothness conditions."

Viktiga insikter från

Non-Smooth Weakly-Convex Finite-sum Coupled Compositional Optimization

by Quanqi Hu,Di... på arxiv.org 03-05-2024

https://arxiv.org/pdf/2310.03234.pdf

Djupare frågor

Can the proposed algorithms be applied to other optimization problems outside of machine learning

The proposed algorithms for non-smooth weakly convex optimization, such as SONX and SONT, can be applied to a wide range of optimization problems outside of machine learning. These algorithms are versatile and can be used in various fields such as finance, engineering, operations research, and more. For example, they could be utilized in portfolio optimization in finance to handle non-smooth objectives or in supply chain management for optimizing complex systems with weakly convex functions.

What are the potential drawbacks or limitations of using non-smooth weakly convex optimization techniques

While non-smooth weakly convex optimization techniques offer advantages like handling a broader class of problems compared to traditional methods, they also have potential drawbacks and limitations. One limitation is the complexity involved in convergence analysis due to the lack of smoothness assumptions. This can make it challenging to derive theoretical guarantees or analyze the behavior of these algorithms rigorously. Additionally, dealing with non-smooth functions may lead to slower convergence rates or require more sophisticated strategies for parameter tuning.

How can the concept of Moreau envelopes be applied to different areas beyond compositional optimization

The concept of Moreau envelopes from compositional optimization can be applied beyond this specific area to various other domains. In physics, Moreau envelopes are used in modeling energy dissipation processes where they represent the total energy stored minus the dissipated energy over time. In economics, Moreau envelopes can help analyze utility functions by capturing preferences under uncertainty or risk aversion. Furthermore, in signal processing applications like image denoising or compression, Moreau envelopes play a role in preserving important features while reducing noise levels effectively.