Optimal Rates for Learning with Monotone Adversaries
Correctly labeled insertions still force an extra logarithmic learning cost once VC dimension is at least two.
Anay Mehrotra proves the gap is inherent in the monotone-adversary model, not just a weakness of known learners. The paper gives minimax expected error rates of Θ(1/n) for VC dimension 1 and Θ((d/n) log(n/d)) for d ≥ 2 under known finite insertion budgets. The same statement is shown with Littlestone dimension replacing VC dimension, ruling out the clean online-to-batch O(dL/n) rate in this setting. The lower bounds come from one explicit construction where two target hypotheses can yield the same observed shuffled sample while differing on mass that matters. ArXiv · AI/CL/LG's note
Anay Mehrotra proves the gap is inherent in the monotone-adversary model, not just a weakness of known learners. The paper gives minimax expected error rates of Θ(1/n) for VC dimension 1 and Θ((d/n) log(n/d)) for d ≥ 2 under known finite insertion budgets. The same statement is shown with Littlestone dimension replacing VC dimension, ruling out the clean online-to-batch O(dL/n) rate in this setting. The lower bounds come from one explicit construction where two target hypotheses can yield the same observed shuffled sample while differing on mass that matters. ArXiv · AI/CL/LG's note
score 5