This paper considers online convex optimization (OCO) with stochastic constraints, which generalizes Zinkevich's OCO over a known simple fixed set by introducing multiple stochastic functional constraints that are i.i.d.

Generalized Linear Bandits (GLBs), a natural extension of the stochastic linear bandits, has been popular and successful in recent years.

Elon Musk says X's new algorithm will be made open source next week That includes'all code used to determine what organic and advertising posts are recommended to users,' he wrote. X may soon provide more insight into how its algorithm works. On Saturday, Elon Musk posted on the platform to say that the company will make the new X algorithm, including all code used to determine what organic and advertising posts are recommended to users, open source in 7 days. X's recommendation algorithm has been the subject of investigations by France and the European Commission, the latter of which recently extended through 2026 a retention order that it sent to the company at the beginning of last year. And scrutiny into the platform, along with demands for accountability, have only increased after its chatbot, Grok, was caught generating CSAM at users' requests and continues to be used to digitally undress women nonconsensually.

Boosting is an extremely successful idea, allowing one to combine multiple low accuracy classifiers into a much more accurate voting classifier. In this work, we present a new and surprisingly simple Boosting algorithm that obtains a provably optimal sample complexity. Sample optimal Boosting algorithms have only recently been developed, and our new algorithm has the fastest runtime among all such algorithms and is the simplest to describe: Partition your training data into 5 disjoint pieces of equal size, run AdaBoost on each, and combine the resulting classifiers via a majority vote. In addition to this theoretical contribution, we also perform the first empirical comparison of the proposed sample optimal Boosting algorithms. Our pilot empirical study suggests that our new algorithm might outperform previous algorithms on large data sets.

We develop two new algorithms, called, FedDR and asyncFedDR, for solving a fundamental nonconvex composite optimization problem in federated learning. Our algorithms rely on a novel combination between a nonconvex Douglas-Rachford splitting method, randomized block-coordinate strategies, and asynchronous implementation. They can also handle convex regularizers. Unlike recent methods in the literature, e.g., FedSplit and FedPD, our algorithms update only a subset of users at each communication round, and possibly in an asynchronous manner, making them more practical. These new algorithms can handle statistical and system heterogeneity, which are the two main challenges in federated learning, while achieving the best known communication complexity. In fact, our new algorithms match the communication complexity lower bound up to a constant factor under standard assumptions. Our numerical experiments illustrate the advantages of our methods over existing algorithms on synthetic and real datasets.

We investigate multiarmed bandits with delayed feedback, where the delays need neither be identical nor bounded. We first prove that delayed Exp3 achieves the $O(\sqrt{(KT + D)\ln K})$ regret bound conjectured by Cesa-Bianchi et al. [2016] in the case of variable, but bounded delays. Here, $K$ is the number of actions and $D$ is the total delay over $T$ rounds. We then introduce a new algorithm that lifts the requirement of bounded delays by using a wrapper that skips rounds with excessively large delays. The new algorithm maintains the same regret bound, but similar to its predecessor requires prior knowledge of $D$ and $T$. For this algorithm we then construct a novel doubling scheme that forgoes the prior knowledge requirement under the assumption that the delays are available at action time (rather than at loss observation time). This assumption is satisfied in a broad range of applications, including interaction with servers and service providers. The resulting oracle regret bound is of order $\min_\beta (|S_\beta|+\beta \ln K + (KT + D_\beta)/\beta)$, where $|S_\beta|$ is the number of observations with delay exceeding $\beta$, and $D_\beta$ is the total delay of observations with delay below $\beta$. The bound relaxes to $O(\sqrt{(KT + D)\ln K})$, but we also provide examples where $D_\beta \ll D$ and the oracle bound has a polynomially better dependence on the problem parameters.

This paper presents new algorithms to solve the feature-sparsity constrained PCA problem (FSPCA), which performs feature selection and PCA simultaneously. Existing optimization methods for FSPCA require data distribution assumptions and are lack of global convergence guarantee. Though the general FSPCA problem is NP-hard, we show that, for a low-rank covariance, FSPCA can be solved globally (Algorithm 1). Then, we propose another strategy (Algorithm 2) to solve FSPCA for the general covariance by iteratively building a carefully designed proxy. We prove (data-dependent) approximation bound and convergence guarantees for the new algorithms. For the spectrum of covariance with exponential/Zipf's distribution, we provide exponential/posynomial approximation bound. Experimental results show the promising performance and efficiency of the new algorithms compared with the state-of-the-arts on both synthetic and real-world datasets.

In this work we consider a variant of adversarial online learning where in each round one picks $B$ out of $N$ arms and incurs cost equal to the $\textit{minimum}$ of the costs of each arm chosen. We propose an algorithm called Follow the Perturbed Multiple Leaders (FPML) for this problem, which we show (by adapting the techniques of Kalai and Vempala [2005]) achieves expected regret $\mathcal{O}(T^{\frac{1}{B+1}}\ln(N)^{\frac{B}{B+1}})$ over time horizon $T$ relative to the $\textit{single}$ best arm in hindsight. This introduces a trade-off between the budget $B$ and the single-best-arm regret, and we proceed to investigate several applications of this trade-off. First, we observe that algorithms which use standard regret minimizers as subroutines can sometimes be adapted by replacing these subroutines with FPML, and we use this to generalize existing algorithms for Online Submodular Function Maximization [Streeter and Golovin, 2008] in both the full feedback and semi-bandit feedback settings. Next, we empirically evaluate our new algorithms on an online black-box hyperparameter optimization problem. Finally, we show how FPML can lead to new algorithms for Linear Programming which require stronger oracles at the benefit of fewer oracle calls.