arXiv subjects

Milan Vojnović

Publications and source records attributed to Milan Vojnović.

6 recordsLinked to original sources

arXiv2026

Oracle-Efficient Combinatorial Semi-Bandits

We study the combinatorial semi-bandit problem where an agent selects a subset of base arms and receives individual feedback. While this generalizes the classical multi-armed bandit and has broad applicability, its scalability is limited by the high cost of combinatorial optimization, requiring oracle queries at every round. To tackle this, we propose oracle-efficient frameworks that significantly reduce oracle calls while maintaining tight regret guarantees. For the worst-case linear reward setting, our algorithms achieve $\tilde{O}(\sqrt{T})$ regret using only $O(\log\log T)$ oracle queries. We also propose covariance-adaptive algorithms that leverage noise structure for improved regret, and extend our approach to general (non-linear) rewards. Overall, our methods reduce oracle usage from linear to (doubly) logarithmic in time, with strong theoretical guarantees.

stat.ML↗

arXiv2026

GL-LowPopArt: A Nearly Instance-Wise Minimax-Optimal Estimator for Generalized Low-Rank Trace Regression

We present `GL-LowPopArt`, a novel Catoni-style estimator for generalized low-rank trace regression. Building on `LowPopArt` (Jang et al., 2024), it employs a two-stage approach: nuclear norm regularization followed by matrix Catoni estimation. We establish state-of-the-art estimation error bounds, surpassing existing guarantees (Fan et al., 2019; Kang et al., 2022), and reveal a novel experimental design objective, $\mathrm{GL}(π)$. The key technical challenge is controlling bias from the nonlinear inverse link function, which we address with our two-stage approach. We prove a *local minimax lower bound*, showing that our `GL-LowPopArt` enjoys instance-wise optimality up to the condition number of the ground-truth Hessian. Our method immediately achieves an improved Frobenius error guarantee for generalized linear matrix completion. We also introduce a new problem setting called **bilinear dueling bandits**, a contextualized version of dueling bandits with a general preference model. Using an explore-then-commit approach with `GL-LowPopArt', we show an improved Borda regret bound over naïve vectorization (Wu et al., 2024).

stat.ML↗

arXiv2026

Sketching stochastic valuation functions

We consider the problem of sketching set valuation functions, defined as the expectation of a valuation function applied to independent random item values. For valuation functions that are monotone and either subadditive or submodular, and that satisfy a weak homogeneity condition (or other structural conditions), we show that there exist discretized versions of the item value distributions -- each with support size $O(k \log k)$ -- that yield a sketch valuation function providing a constant-factor approximation to the true valuation for any subset of items of size at most $k$. These discretized distributions can be computed efficiently for each item independently, making the approach highly scalable. Our results apply broadly to valuation functions commonly encountered in practice, including team performance based on the best member (e.g., maximum functions), constant elasticity of substitution (CES) production functions with diminishing returns in economics, and others. Sketch valuation functions are especially useful in optimization problems such as best set selection and welfare maximization, where exact value computations are costly or intricate. They enable efficient approximate evaluation of value oracle queries while preserving provable approximation guarantees for the original stochastic optimization problem.

math.ST↗

arXiv2023

Doubly Adversarial Federated Bandits

We study a new non-stochastic federated multi-armed bandit problem with multiple agents collaborating via a communication network. The losses of the arms are assigned by an oblivious adversary that specifies the loss of each arm not only for each time step but also for each agent, which we call ``doubly adversarial". In this setting, different agents may choose the same arm in the same time step but observe different feedback. The goal of each agent is to find a globally best arm in hindsight that has the lowest cumulative loss averaged over all agents, which necessities the communication among agents. We provide regret lower bounds for any federated bandit algorithm under different settings, when agents have access to full-information feedback, or the bandit feedback. For the bandit feedback setting, we propose a near-optimal federated bandit algorithm called FEDEXP3. Our algorithm gives a positive answer to an open question proposed in Cesa-Bianchi et al. (2016): FEDEXP3 can guarantee a sub-linear regret without exchanging sequences of selected arm identities or loss sequences among agents. We also provide numerical evaluations of our algorithm to validate our theoretical results and demonstrate its effectiveness on synthetic and real-world datasets

stat.ML↗

arXiv2023

On Regret-optimal Cooperative Nonstochastic Multi-armed Bandits

We consider the nonstochastic multi-agent multi-armed bandit problem with agents collaborating via a communication network with delays. We show a lower bound for individual regret of all agents. We show that with suitable regularizers and communication protocols, a collaborative multi-agent \emph{follow-the-regularized-leader} (FTRL) algorithm has an individual regret upper bound that matches the lower bound up to a constant factor when the number of arms is large enough relative to degrees of agents in the communication graph. We also show that an FTRL algorithm with a suitable regularizer is regret optimal with respect to the scaling with the edge-delay parameter. We present numerical experiments validating our theoretical results and demonstrate cases when our algorithms outperform previously proposed algorithms.

stat.ML↗

arXiv2023

Combinatorial Bandits for Maximum Value Reward Function under Max Value-Index Feedback

We consider a combinatorial multi-armed bandit problem for maximum value reward function under maximum value and index feedback. This is a new feedback structure that lies in between commonly studied semi-bandit and full-bandit feedback structures. We propose an algorithm and provide a regret bound for problem instances with stochastic arm outcomes according to arbitrary distributions with finite supports. The regret analysis rests on considering an extended set of arms, associated with values and probabilities of arm outcomes, and applying a smoothness condition. Our algorithm achieves a $O((k/Δ)\log(T))$ distribution-dependent and a $\tilde{O}(\sqrt{T})$ distribution-independent regret where $k$ is the number of arms selected in each round, $Δ$ is a distribution-dependent reward gap and $T$ is the horizon time. Perhaps surprisingly, the regret bound is comparable to previously-known bound under more informative semi-bandit feedback. We demonstrate the effectiveness of our algorithm through experimental results.

cs.LG↗