A two-phase optimizer fights to find a balance, then bargains for the best trade-off.

Training artificial intelligence on several competing goals at once is tricky because improving one goal can worsen another. To solve this, researchers built a two-phase system called NB-HalpernSGDHalpernSGDAn optimization algorithm that uses anchoring to improve convergence in stochastic settings. via LM-MultiLRSGAMultiLRSGAAn optimizer for multiple objectives that uses limited memory and rotational adjustments.. First, the system treats the goals like players in a game. It uses a memory-saving method called LM-MultiLRSGA, which keeps an important rotational correction tool, to find a balanced compromise called a Nash equilibriumNash equilibriumA state in a competitive game where no player can gain by changing their strategy alone.. Second, the system uses that balance as a starting anchor to make the goals bargain with each other. It solves this bargaining step using a technique called HalpernSGD to reach a fair, shared solution. Tested on a physics-informed neural network model, this two-step approach beat established methods like PCGrad, MultiAdam, and DualConeGD.

Why it matters

In machine learning, models often have to balance multiple competing goals, like accuracy and energy use. This method provides a better way to find compromises, helping researchers build more efficient and balanced systems. It outperforms existing approaches on a test model, showing practical improvement.

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