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Life sciences · Preprint
arXiv · September 9, 2026
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This is an unpublished theoretical preprint on online inverse linear optimization that proposes Small-Gradient Skipping (SGS), a computational mechanism to reduce regret and mistakes in weight prediction tasks. The work provides mathematical proofs of regret bounds under specific conditions (M-convex action sets, integer linear programs) but is not a clinical, biological, or empirical study and has not been peer reviewed.
Preprint.
SGS applied to online Newton step and MetaGrad achieves O(d²) regret for integer linear programs, removing the log T factor previously known Number of mistakes bounded by a quantity independent of T for all three methods tested (online gradient descent, online Newton step, MetaGrad) For M-convex action sets, regret bounded efficiently without computing a center of gravity at every round
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This is a theoretical computer science preprint proposing an algorithmic mechanism (Small-Gradient Skipping) with mathematical proofs of regret bounds; it has not been peer reviewed and addresses optimization theory rather than clinical or biomedical evidence.
Quoted from the source exactly as published.
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In online inverse linear optimization, the learner predicts a weight at each round, observes the optimal action of the agent, and updates its prediction. In the general setting, the gap of $\log T$ between the regret upper bound $O(d \log T)$ and the lower bound $Ω(d)$ is unresolved (here $T$ is the total number of rounds and $d$ is the dimension). When the action set is M-convex, the regret is known to be bounded by $O(d \log d)$, but the method attaining it computes a center of gravity at every round. This paper therefore proposes Small-Gradient Skipping (SGS), a mechanism that skips the update at rounds without a mistake in the case where the correct action is uniformly separated from the other candidates, and applies it to online gradient descent, the online Newton step, and MetaGrad. The number of mistakes is then bounded, for all three, by a quantity independent of $T$; and for the online Newton step and for MetaGrad with SGS, the dimension dependence of the regret becomes $O(d^2)$ when the forward problem is an integer linear program, that is, the factor $\log T$ is removed. Moreover, when the action set is M-convex, the regret is bounded efficiently without computing a center of gravity.
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