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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...
The regret attainable in online convex optimization when access to the feasible set is limited to an exact linear optimization oracle is characterized and a curvature-dependent lower bound is identified above which the general characterization remains sharp.
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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