Jiuyao Lu

Natalie Collina, Jiuyao Lu, Georgy Noarov et al.

We prove tight lower bounds for online multicalibration, establishing an information-theoretic separation from marginal calibration. In the general setting where group functions can depend on both context and the learner's predictions, we prove an $Ω(T^{2/3})$ lower bound on expected multicalibration error using just three disjoint binary groups. This matches the upper bounds of Noarov et al. (2025) up to logarithmic factors and exceeds the $O(T^{2/3-\varepsilon})$ upper bound for marginal calibration (Dagan et al., 2025), thereby separating the two problems. We then turn to lower bounds for the more difficult case of group functions that may depend on context but not on the learner's predictions. In this case, we establish an $\widetildeΩ(T^{2/3})$ lower bound for online multicalibration via a $Θ(T)$-sized group family constructed using orthogonal function systems, again matching upper bounds up to logarithmic factors.

Yahav Bechavod, Jiuyao Lu, Aaron Roth

We introduce and study the problem of online omniprediction with long-term constraints. At each round, a forecaster is tasked with generating predictions for an underlying (adaptively, adversarially chosen) state that are broadcast to a collection of downstream agents, who must each choose an action. Each of the downstream agents has both a utility function mapping actions and state to utilities, and a vector-valued constraint function mapping actions and states to vector-valued costs. The utility and constraint functions can arbitrarily differ across downstream agents. Their goal is to choose actions that guarantee themselves no regret while simultaneously guaranteeing that they do not cumulatively violate the constraints across time. We show how to make a single set of predictions so that each of the downstream agents can guarantee this by acting as a simple function of the predictions, guaranteeing each of them $\tilde{O}(\sqrt{T})$ regret and $O(1)$ cumulative constraint violation. We also show how to extend our guarantees to arbitrary intersecting contextually defined \emph{subsequences}, guaranteeing each agent both regret and constraint violation bounds not just marginally, but simultaneously on each subsequence, against a benchmark set of actions simultaneously tailored to each subsequence.

Yahav Bechavod, Jiuyao Lu, Aaron Roth

We present an algorithm guaranteeing dynamic regret bounds for online omniprediction with long term constraints. The goal in this recently introduced problem is for a learner to generate a sequence of predictions which are broadcast to a collection of downstream decision makers. Each decision maker has their own utility function, as well as a vector of constraint functions, each mapping their actions and an adversarially selected state to reward or constraint violation terms. The downstream decision makers select actions "as if" the state predictions are correct, and the goal of the learner is to produce predictions such that all downstream decision makers choose actions that give them worst-case utility guarantees while minimizing worst-case constraint violation. Within this framework, we give the first algorithm that obtains simultaneous \emph{dynamic regret} guarantees for all of the agents -- where regret for each agent is measured against a potentially changing sequence of actions across rounds of interaction, while also ensuring vanishing constraint violation for each agent. Our results do not require the agents themselves to maintain any state -- they only solve one-round constrained optimization problems defined by the prediction made at that round.