We study nonnegative submodular maximization subject to a general matroid when the offline algorithm is given an arbitrary controlled value oracle. Our 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 $1/e$ for non-monotone objectives and $1-1/e$ for monotone objectives. More precisely, under every controlled oracle $\widehat f$ satisfying $|\widehat f(S)-f(S)|\le \xi$ for every set $S$, our implementation returns a feasible set with expected value at least $(1/e-\varepsilon)\OPT-O(k\xi)$ and $(1-1/e-\varepsilon)\OPT-O(k\xi)$, respectively, using $\widetilde O(nk^2\varepsilon^{-2})$ oracle calls. As a consequence, the offline-to-online reduction yields full-bandit CMAB algorithms for general matroid-constrained submodular rewards with exact limiting approximation-regret factors $1/e$ and $1-1/e$ and $\widetilde O(n^{1/5}k^{4/5}T^{4/5})$ regret.
We study online convex optimization (OCO) in non-stationary environments under heavy-tailed noise, where the stochastic gradient oracle admits only a finite $p$-th central moment for some $p \in (1, 2]$. While static regret is well-understood, achieving universal dynamic regret in a parameter-free manner remains an open challenge. We resolve this by proposing \textbf{HT-PAder}, a parameter-free algorithm combining restarted AdaGrad experts over a geometric pool of block lengths with a pathwise meta-algorithm, \textbf{AdaGrad-Hedge}, which requires no moment conditions on meta-losses. For a domain of diameter $D$, Lipschitz constant $G$, noise level $\sigma$, and comparator path length $P_T$, HT-PAder achieves an expected universal dynamic regret of \[ \widetilde O\left( GD\sqrt{T(1+P_T/D)} + \sigma D T^{1/p}(1+P_T/D)^{(p-1)/p} \right). \] The algorithm does not require prior knowledge of any of these problem parameters. Even in the special case of finite variance ($p=2$), HT-PAder provides the first parameter-free minimax universal dynamic regret guarantee. We also prove a matching lower bound, establishing the optimality of the path-length exponent.