M-HOF-Opt: Multi-Objective Hierarchical Output Feedback Optimization via Multiplier Induced Loss Landscape Scheduling

2024-03-20

arXiv.org

AI Summary

This work addresses the challenges of jointly optimizing numerous loss terms and managing high memory and computational overhead in multi-objective deep learning. Methodologically, we propose a hierarchical output-feedback control framework that eliminates explicit Lagrange multipliers by introducing time-varying multipliers, dynamically reshaping the loss landscape at the epoch level. We further introduce a novel hypervolume-based likelihood probabilistic graphical model that jointly captures the co-evolution of model parameters and multipliers, decomposing multi-objective optimization into a sequence of Pareto-adaptive constrained hierarchical optimal control subproblems. Evaluated on the PACS domain generalization benchmark—featuring a six-loss-term variational autoencoder—we demonstrate that our approach significantly outperforms existing multiplier-scheduling methods in both accuracy and robustness, while substantially reducing memory footprint and computational cost. Moreover, the framework supports modular extension for diverse multi-objective architectures.

Technology Category

• Computer Vision: Learning & Optimization for CV
• Machine Learning: Optimization
• Search and Optimization: Learning to Search

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems
• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs

Abstract

We address the online combinatorial choice of weight multipliers for multi-objective optimization of many loss terms parameterized by neural works via a probabilistic graphical model (PGM) for the joint model parameter and multiplier evolution process, with a hypervolume based likelihood promoting multi-objective descent. The corresponding parameter and multiplier estimation as a sequential decision process is then cast into an optimal control problem, where the multi-objective descent goal is dispatched hierarchically into a series of constraint optimization sub-problems. The subproblem constraint automatically adapts itself according to Pareto dominance and serves as the setpoint for the low level multiplier controller to schedule loss landscapes via output feedback of each loss term. Our method is multiplier-free and operates at the timescale of epochs, thus saves tremendous computational resources compared to full training cycle multiplier tuning. It also circumvents the excessive memory requirements and heavy computational burden of existing multi-objective deep learning methods. We applied it to domain invariant variational auto-encoding with 6 loss terms on the PACS domain generalization task, and observed robust performance across a range of controller hyperparameters, as well as different multiplier initial conditions, outperforming other multiplier scheduling methods. We offered modular implementation of our method, admitting extension to custom definition of many loss terms.

Problem

• Optimizes multi-objective model parameters using time-varying multipliers.
• Hierarchically dispatches multi-objective descent into constraint sub-problems.
• Reduces memory and computational burden in multi-objective deep learning.

Innovation

• Probabilistic model for joint parameter-multiplier evolution
• Hierarchical optimization with time-varying multipliers
• Closed-loop dynamics reducing memory and computation