Primal Dual Neural Network for Multi-Objective Optimization
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Solution Overview
Problem
Existing neural networks face challenges in performing multi-objective tasks as they require setting predefined relative weights for objectives, which is computationally difficult and may not be suitable for cases where threshold values need to be satisfied, especially when objectives have different units.
Innovation Solution
A system using a primal network and a dual network trained alternately with a Lagrangian loss function to minimize and maximize objectives respectively, allowing for multiple objectives to be incorporated without predefined weights, enabling improved automated and semi-automated responses in conversations.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If predefined relative weights are set for multiple objectives, then the neural network can optimize multiple objectives simultaneously, but the computational complexity increases and it becomes difficult to determine appropriate weight values
Solution Approach 1:
The patent transforms the multi-objective optimization problem from a weighted sum approach to a constraint satisfaction approach by changing the mathematical formulation parameters. Instead of optimizing L = w1*f1 + w2*f2 + ... + wn*fn with predefined weights, the system optimizes each objective function independently with threshold constraints, eliminating the need for weight parameter tuning while maintaining multi-objective optimization capability
Solution Approach 2:
The patent introduces Lagrange multipliers as intermediary variables that automatically adjust during training to balance multiple objectives. These multipliers act as dynamic weight adjusters that are learned from data rather than predefined, allowing the system to adaptively find the optimal trade-off between conflicting objectives without manual intervention
2Productivity
If predefined weights are used for objectives with different units, then multi-objective optimization can proceed, but the results may not satisfy threshold requirements for individual objectives
Solution Approach 1:
The patent segments the multi-objective optimization problem into multiple independent single-objective subproblems, each with its own threshold constraint. By dividing the problem into separate optimization tasks (one for each objective function), the system can guarantee threshold satisfaction for each objective independently without the need to balance conflicting units through weight assignment
3Ease of operation
If multiple objectives are incorporated without predefined weights, then weight optimization complexity is reduced, but the computational difficulty of satisfying all objectives simultaneously increases
Solution Approach 1:
The patent introduces dynamic Lagrange multipliers that automatically adapt during the training process to balance multiple objectives. These multipliers are updated iteratively based on the current state of optimization, allowing the system to dynamically adjust the emphasis on different objectives without manual weight setting, thereby simplifying operation while maintaining convergence
Data Source
AI summary
An example system includes a processor to receive a prefix of conversation and a text input. The processor is to also generate a completed response based on the prefix of conversation and the text input via a trained primal network. The primal network is trained to minimize a Lagrangian loss function representing a number of objectives and a dual network is trained to maximize the Lagrangian loss function.