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We study nonnegative, non-monotone $k$-submodular maximization with $k\ge2$ labels under support constraints, and show how the certified approximation coefficient improves as the support region permits more uniform selection. For a compact convex down-closed support region $P\subseteq[0,1]^n$, the diagonal level $\zeta...
We study online convex optimization with one unbiased stochastic subgradient per round and an unknown finite conditional $p$th noise moment, $1<p\le2$. For every fixed interval $I$ of length $n$ and comparator path with $\Lambda_I=1+P_I/D$, one learner achieves \[ E[Regret_I(u)]\le\min(GDn, C[GD\sqrt{n(\Lambda_I+\log^2...
We study adversarial online maximization of nonnegative, non-monotone DR-submodular functions over compact convex down-closed sets. A learner commits each action before observing its objective and competes with the best fixed action in hindsight. We prove a comparator-uniform first-order inequality that gives coefficie...
We characterize the regret attainable in online convex optimization when access to the feasible set is limited to an exact linear optimization oracle. The learner is given an inscribed ball and a diameter bound and must remain feasible on every consistent instance. For convex $G$-Lipschitz losses, diameter at most $D$,...
The main result is an adversarial resilience theorem for the Spiteful Greedy Swap Poisson Process (SGS-Poisson): without modifying its Poisson intensity, single-element exchange rule, or spiteful drop step, the algorithm retains limiting approximation factors for non-monotone objectives and monotone objectives.
We study online convex optimization with stochastic gradient noise whose conditional $p$-th central moment is bounded by $\sigma^p$, for an unknown $p\in(1,2]$. For losses with Lipschitz bound $G$ on a domain of diameter $D$, we obtain expected universal dynamic regret $\widetilde O(GD\sqrt{T\Lambda}+\sigma DT^{1/p}\La...
This work determines the minimax cumulative log-loss regret of a finite-alphabet, exogenously driven source with genuinely infinite input memory, and shows memory decay cannot determine regret, and that a profile-scaled online Newton predictor attains $O_B(\Gamma_T(r)$ in polynomial time per round.
The bounds separate uncertainty about hard feasibility from learnable signed budgets, and the hard-violation construction matches arbitrarily many moments while preserving a feasible-endpoint gap and constant endpoint probabilities.
This work studies online maximization of nonnegative, non-monotone DR-submodular functions over compact convex down-closed subsets of the $d$-dimensional unit cube and shows that the best known constructive offline approximation factor is also achievable online.
This work proposes a simple reduction that converts dueling feedback into approximate gradients, enabling the use of standard first-order methods, and shows that regret guarantees transfer under this reduction.
This work proposes Decentralized Barrier Follow-the-Regularized-Leader (Dec-BFTRL), and evaluates each agent's played action against the average of all local objectives, with applications to online continuous diminishing-return (DR) submodular maximization.
The main result is an adversarial resilience theorem for the Spiteful Greedy Swap Poisson Process (SGS-Poisson): without modifying its Poisson intensity, single-element exchange rule, or spiteful drop step, the algorithm retains limiting approximation factors for non-monotone objectives and $1-1/e for monotone objectiv...
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