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Statistical Gains from Looped Estimation under Parameter Budgets

arXiv · AI, language, vision and robotics · article · Sep 22, 2026 · UTC

Growing memory demands in artificial intelligence motivate learning with fewer trainable parameters. We ask whether a looped estimator, which repeatedly applies one fitted operator with parameters shared across iterations, can improve statistical accuracy under a common parameter budget. Its conventional untied counterpart uses separate parameters at each iteration. For general likelihood models, we establish an upper bound on squared Hellinger risk for looped sieve maximum likelihood and a minimax lower bound over the tuned untied family. These bounds reveal a parameter--iteration--accuracy t

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